2nd workshop on porous media · heat transfer in packed beds. none of the papers deals with...

UNIVERSITY OF WARMIA AND MAZURY IN OLSZTYN

FACULTY OF TECHNICAL SCIENCES

POLISH SOCIETY OF THEORETICAL AND APPLIED MECHANICS

2nd Workshop on Porous Media

BOOK OF ABSTRACTS

OLSZTYN - POLAND

28-30 JUNE 2018

2 | 2 n d W o r k s h o p o n P o r o u s M e d i a O l s z t y n 2 8 - 3 0 J u n e 2 0 1 8

SCIENTIFIC COMMITEE

Wojciech Sobieski (chair of committee)

Janusz Badur

Mariusz Kaczmarek

Adam Lipiński

Teodor Skiepko

Mieczysław Cieszko

Piotr Srokosz

Adam Szymkiewicz

Anna Trykozko

Maciej Marek

Maciej Matyka

Joanna Wiącek

ORGANIZING COMMITEE


Seweryn Lipiński

Dariusz Grygo

Tomasz Tabaka

Aneta Molenda

Book of abstracts published from materials provided by Authors

Edited by Seweryn Lipiński


CONTENTS

Dariusz Asendrych Paweł Niegodajew

Interfacial heat transfer modelling in packed beds 5

Janusz Badur Marcin Lemański Tomasz Kowalczyk Paweł Zioacutełkowski Bartosz Kraszewski

Porous media as an important element of fuel cell in high efficiency energy production 6

Włodzimierz Bielski Ryszard Wojnar

Plane flow through the porous medium with chessboard-like distribution of permeability 7

Renata Cicha-Szot Piotr Such Grzegorz Leśniak

A comparative study of nanoscale pore structures in geomaterials 8

Mieczysław Cieszko

Minkowski Metric Dirichlet Energy and Pore Tortuosity 9

Tomasz Czerwiński Mieczysław Cieszko Chaplya Yevhen

Influence of pore structure parameters on saturation of a ball

with liquid during intrusion-extrusion process

10

Waldemar Dudda Wojciech Sobieski

Experimental investigations of pressure drops in chosen granular beds 11

Marek Gawor

Experimental determination of the kinetics of sorption and the kinetics of gas filtration in coal 12

Karolina Grabowska Jarosław Krzywański Karol Sztekler Wojciech Kalawa Wojciech Nowak

Fuzzy logic approach in the analysis of heat transfer in a porous sorbent bed of the adsorption chiller 13

Paweł Guzik Krzysztof Mudryk

A concept of a two-stage process of non-pressure granulation of mineral materials 14

Daniel Janecki

Mathematical model of the course of process of catalytic wet air oxidation of phenol (CWAO) in trickle bed reactors (TBR)

15

Łukasz Jasiński Marcin Dąbrowski

Depth-averaged model for flow in a propped fracture 16

Dariusz Kardaś Sylwia Polesek-Karczewska Paweł Zioacutełkowski Janusz Badur

A unified thermodynamic approach to description of whole phenomena during a coke production 17

Marcin Kempiński Mieczysław Cieszko Marcin Burzyński Zbigniew Szczepański

Determination of pore size distribution in sintered glass bead samples

based on mercury porosimetry and microtomographic image analysis

18

Wojciech Kiński Wojciech Sobieski

Geometry extraction from GCODE files destined for 3D printing 19


The application of 3D printing technology in the investigations of porous media 20

Jarosław Krzywański

Selected artificial intelligence methods in modeling of energy devices and systems 21

Anna Kułakowska

Evaluation of plasticity criterion applicability in the porous materials research 22

Sylwia Kwiatkowska-Marks Justyna Miłek Ilona Trawczyńska

Diffusion of Cd(II) Pb(II) and Zn(II) on calcium alginate beads 23

Grzegorz Leśniak

Effect of microfracture on ultratight matrix permeability 24

Grzegorz Leśniak Renata Cicha-Szot Krzysztof Labus

Multi-scale core to pore imaging and modelling of the heterogonous rocks 25

Grzegorz Leśniak Karol Spunda Renata Cicha-Szot

Pore scale modelling of fluid transport using FIB-SEM images 26

Seweryn Lipiński Wojciech Sobieski

Reliability of the tortuosity value obtained on the basis of other parameters of the porous bed 27

Seweryn Lipiński Zenon Syroka

Relations between the various probability density functions describing the distribution of particles in a granular bed

28

Wojciech Ludwig

Effect of friction coefficient on results of particles velocity calculation using

Euler-Lagrange model in spout-fluid bed apparatus

29


Janusz Łukowski Mieczysław Cieszko

Analysis of Influence of Model Parameters on the Capillary Imbibition of Porous Materials with Liquid 30

Marcin Majkrzak

Possibilities of using glass microspheres to build models and simulation of fluid flow through geological strata

31

Ewelina Małek Danuta Miedzińska Wiesław Szymczyk Arkadiusz Popławski

Application of 3D printing technology to random porous structures study 32

Marcin Małek Wojciech Życiński Mateusz Jackowski Marcin Wachowski Waldemar Łasica

Effect of polypropylene fiber addition on mechanical properties of concrete based on portland cement 33

Maciej Marek

Numerical generation of a random packed bed of saddles 34

Kinga Michalak Janusz A Szpaczyński

Sludge dewatering by thin-film freezing in the north-east of Poland 35

Danuta Miedzińska

Numerical modeling of porous ceramics microstructure 37

Justyna Miłek Sylwia Kwiatkowska-Marks Ilona Trawczyńska

Application of silica gel in the process of trypsin immobilization 38

Agnieszka Niedźwiedzka

Numerical modeling of cavitation phenomenon in a small-sized converging-diverging nozzle 39

Anna Pajdak

The influence of comminution degree on structural properties of rocks of various porous structure 40

Norbert Skoczylas Mateusz Kudasik

A multiparameter description of the rock-gas system by the use of original methods 41

Karolina Słomka-Polonis Jakub Fitas Jakub Styks Bogusława Kordon-Łapczyńska

Measurement of porosity of comminuted Salix Viminalis L in aspects of uncertainty of measurement 42

Wojciech Sobieski

Numerical investigations of tortuosity in randomly generated pore structures 43

Wojciech Sobieski

Path Searching Algorithm 44

Aleksander Sulkowski

Application of the contour erosion function in shape analysis of a solid particle 45

Zbigniew Szczepański Mieczysław Cieszko

Influence of Microscopic Pore Geometry on the Parameter of Pore Tortuosity 46

Janusz A Szpaczyński

The use of natural soil as a porous medium for the treatment of secondary effluent in the northern climate

47

Adriana Szydłowska Jerzy Hapanowicz

The stand for testing flow of two-phase system through the metal foams 48

Piotr Szymczak Filip Dutka Florian Osselin

Dissolution of porous media studied in a simple microfluidic setup 49

Adam Szymkiewicz Witold Tisler Wioletta Gorczewska-Langner

Rafał Ossowski Danuta Leśniewska Stanisław Maciejewski

Numerical simulations of laboratory-scale dike overflowing using two phase flow model

50

Ilona Trawczyńska Justyna Miłek Sylwia Kwiatkowska-Marks

Effect of temperature concentration of alcohols and time on bakers yeast permeabilization process 51

Anna Trykozko

Pore scale simulations of flows in weakly permeable porous media 52

Grzegorz Wałowski Gabriel Filipczak

Using of the SEM image method to evaluate the porosity of materials with varied internal structure 53

Joanna Wiącek Marek Molenda Mateusz Stasiak

Numerical analysis of compression mechanics of granular packings with various number of particle size fractions

54

Eliza Wolak Elżbieta Vogt Jakub Szczurowski

Determination of the heat of wetting of selected liquids on modified activated carbons 55


Interfacial heat transfer modelling in packed beds Dariusz Asendrych Paweł Niegodajew

Institute of Thermal Machinery Częstochowa University of Technology

darekimcpczczestpl

Keywords packed bed multiphase flow trickling flow regime interfacial heat transfer

Packed bed columns are commonly used in chemical and process industries just to mention absorption distillation or

rectification processes as examples The packing material ensures large contact area between phases as well as sufficient liquid

holdup required to reach expected process efficiency Modelling of 2-phase flows in packed beds is a challenging task [1] even if

isothermal conditions are assumed However most of processes include heat transfer phenomena thus the changes in material

properties have to be taken into account

During recent years a lot of effort has been done in the field of packed beds operated in trickling flow regime mostly dedicated

to flow hydrodynamics Prediction of pressure drop liquid holdup liquid spreading or wetting efficiency has become much more

accurate and reliable Much less works however is related to heat transfer phenomena and in principle they are devoted to overall

heat transfer in packed beds None of the papers deals with interfacial (gas-liquid) heat transfer except for the experimental work

of Heidari and Hashemabadi [2] The weak point of this work is however a simplified model of a packed bed as composed of

large spheres filling the column of the same diameter Practical lack of reliable data does not allow to model nonisothermal

multiphase flows in packed beds That is why it was decided to undertake experimental studies to investigate the interfacial gas-

liquid heat transfer

The experiment was conducted with the use of a small laboratory test rig equipped with a 100mm column filled in with 6mm

glass Raschig rings Air and water were used as working media Hot water was circulated in a closed loop it was supplied to the

top of the packing section and flowed down The ambient air was sucked at the bottom of the column and it flowed countercurrently

to the liquid phase Water and air flowrates as well as water inlet temperature were controlled independently A system of

flowmeters thermocouples and humidity meters allowed to measure heat fluxes and thus to determine the interfacial gas-liquid

heat transfer coefficient and the corresponding Nusselt number More details about the experiment and the methodology can be

found in [3]

Fig1 Nusselt number dependence on gas and liquid loads and liquid inlet temperature

The results of measurements are shown in Fig 1 as the Nusselt number dependence on superficial gas and liquid velocities for

3 different inlet water temperatures As can be seen Nu is strongly influenced by the gas load which intensifies the heat transfer

Fig 1 indicates also a slight Nu dependence on liquid velocity which becomes especially evident for the lowest loads Moreover

temperature difference between gas and liquid phases influences the Nusselt number

The Nu results were then used to develop a correlation describing the interfacial heat transfer for the trickling flow regime with

the use of various group numbers to account for such influences as gravity inertia surface tension viscosity buoyancy and thermal

diffusion As a results of detailed regression analysis the following correlation was found as the best fit to the experimental data

119873119906 = 119877119890119866117 ∙ 119866119886119866

minus084 ∙ 119864119900072 (1)

where ReG and GaG are the gas Reynolds and gas Galileo numbers and Eo is the Eotvos number The value of correlation coefficient

R=0992 indicates nearly perfect fitting proving its relevance

The correlation (1) describing the interfacial gas-liquid heat transfer coefficient for the trickling flow regime is a step ahead in

modelling complex thermal phenomena in multiphase flow systems in packed beds It should be remarked that the correlation was

developed for limited gas and liquid loads and for particular type and size of packing elements Thus there is a need for further

research including wider (closer to industrial application) ranges of loads as well as different catalyst types

References [1] Niegodajew P Asendrych D Amine based CO2 capture - CFD simulation of absorber performance Appl Math Model 40

10222-10237 2016

[2] Heidari A Hashemabadi SH Numerical evaluation of the gasndashliquid interfacial heat transfer in the trickle flow regime of

packed beds at the micro and meso-scale Chem Eng Sci 104 674-689 2013

[3] Niegodajew P Asendrych D An interfacial heat transfer in a countercurrent gas-liquid flow in a Trickle Bed Reactor Int

J of Heat amp Mass Transfer 108A 703-711 2017


Porous media as an important element of fuel cell in high efficiency energy production Janusz Badur Marcin Lemański Tomasz Kowalczyk Paweł Zioacutełkowski Bartosz Kraszewski

Energy Conversion Department Institute of Fluid Flow Machinery PAS-ci Gdańsk

jbimpgdapl pziolkowskiimpgdapl

Keywords porosity SOFC poro-thermo-chemo-mechanical interactions continua with microstructure

In the future hydrogen energy and solid oxide fuel cells (SOFCs) may be a competitive technology for large power units [1]

Promising electrical efficiency and emission level respectively ca 60 and 030 kg CO2 MWh for hybrid fuel cell systems

(SOFCGT) cause large energy companies to become interested in this technology

Fuel cells are profitable modern devices being the best examples of a useful machinery where complex conversion of energy at

nanoscale with porous media takes place Especially we observe such conversion at the high temperature solid oxide fuel cell

(SOFC) that is built from ceramic nanomaterials Anode supported fuel cell consist mainly of two nanoporous electrodes (cermets

lanthanum strontium manginite) separated as was presented in Fig1a by a thin very dense solid electrolyte (yttria-stabilized

zirconia or perovskite-type material) Finding of a mathematical model of an acting SOFC at temperatures as high as 1000oC is a

serious challenge as well for nanomechanics as for nanothermo-chemistry

In our works [1-3] a further development of the authors model of thermo-chemical flow of fuel air oxygen steam water

species ionic and electron currents within nanochannels and nanostructures of novel divides is presented Integrated geometrical

characteristics of working fluids and canal materials such as porosity tortuosity and mean radii are finally involved into a

macroscopic continuum model and implemented into the standard CFD code The mean pore radii has been taken to be equal 300

nm In Fig 1b) dependence of generated voltage on current at various porosities are presented When lower porosities are assumed

the concentration polarization is higher [4]

a) b)

Fig1 a) 3D Computational domain for a SOFC tubular with electrolyte as a porous media b) Influence of porosity

nanoparameter on SOFC performance [4]

Different transport enhancement models should be taken into account ndashamong them the most important are the velocity slip

connected with complex external friction the Darcy mobility and the Reynolds transpiration Increasing gas path to the triple-

phase-boundary (TPB) enhances mass and electricity fluxes due to the concentration jump and the electron resistivity jump

References [1] J Badur M Karcz M Lemański L Nastałek Enhancement transport phenomena in the Navier-Stokes shell like slip layer

Computer Modeling In Engineering and Science 73299ndash310 2011

[2] P Zioacutełkowski J Badur A theoretical numerical and experimental verification of the Reynolds thermal transpiration law

International Journal of Numerical Methods for Heat amp Fluid Flow vol28 iss1 pp 64-80

[3] J Badur P Zioacutełkowski S Kornet T Kowalczyk K Banaś M Bryk PJ Zioacutełkowski M Stajnke Enhanced energy

conversion as a result of fluid-solid interaction in micro and nanoscale Journal of Theoretical and Applied Mechanics 56 1

pp 329-332 Warsaw 2018 DOI 1015632jtam-pl561329

[4] M Karcz S Kowalczyk and J Badur On the influence of geometric nanostructural properties of porous materials on the

modelling of a tubular fuel cell Chem Proc Eng 31489ndash503 2010


Plane flow through the porous medium with chessboard-like distribution of permeability Włodzimierz Bielski1 Ryszard Wojnar2

1 Institute of Geophysics Polish Academy of Sciences 2 Institute of Fundamental Technological Research PAS

wbielskiigfedupl rwojnaripptgovpl

Keywords geometrical mean effective permeability Darcyrsquos law Brinkmanrsquos flow Keller - Dykhne formula

Theoretical trials to determine the effective properties of heterogeneous porous media are widely performed In particular the

methods of asymptotical homogenisation are applied cf [1 2] In this contribution we study a special case of a chessboard-like

distribution of permeability coefficients in which simple algebraic arguments are applied

First Darcyrsquos flow is considered described by the equation

119959 = minus 119870

120578 nabla(119901 + 119880)

Here the vector 119959 is the flow velocity K ndash permeability 120578 - viscosity p ndash the pressure and U ndash the external potential We assume

the flow being incompressible it is nabla ∙ 119959 = 0 It is known from the papers by Keller [3] and Dykhne [4] that the symmetry of

equations describing stationary potential flows in the planar systems composed of two constituents combined with geometrical

symmetry of both constituents of the considered medium permits to find the effective conductivity of such a body This elegant

non-perturbative result is known as Keller - Dykhnes formula There are three main assumptions needed

(i) considered fields are two-dimensional

(ii) the flow is stationary and has a potential

(iii) statistical symmetry and isotropy of the composite is assumed both components are equivalent in statistical

meaning they have the areas of the same dimension and can be mutually changed without the change of the

whole composite cf Figure 1

If one constituent has the permeability K1 and the second K2 then the effective permeability is radic 1198701 1198702 in agreement with

experiments and simulations of Warren and Price [5]

Fig1 Chessboard-like distributions of the permeability Examples of different tessellations of more dense (dark) and more rare

(light) areas of a rock cross-section which are in agreement with Keller-Dykhnersquos geometrical assumption

Similar result we obtain for the problem in which the flow is described by Brinkmanrsquos equation cf [6]

119959 = 119870

120578 [minus nabla(119901 + 119880) + 120578prime ∆ 119959 ]

Here the coefficient 120578prime means Brinkmanrsquos effective viscosity This equation permits to satisfy in full the boundary conditions at

the interfaces of regions with different permeabilities what as it is known is impossible when Darcyrsquos equation is used But now

the flow 119959 is not potential any more Let us substitute 119958 = 119959 minus (119870 120578prime120578) ∆ 119959 Then Brinkmanrsquos equation has the form of Darcyrsquos

equation 119958 = minus(119870120578)nabla(119901 + 119880) Such vector 119958 is the potential and divergence-free one as the vector 119959 is divergence-free Thus

it satisfies all Keller - Dykhnes formula assumptions Hence in the case Brinkmanrsquos flow the effective permeability is radic 1198701 1198702

also

References [1] V V Jikov S M Kozlov O A Oleinik Homogenization of differential operators and integral functionals

Springer-Verlag Berlin Heidelberg 1994

[2] G Allaire One-phase newtonian flow in Homogenization and porous media Ed U Hornung Springer Verlag New York -

Berlin - Heidelberg 1997 pp 45-76

[3] J B Keller A theorem on the conductivity of a composite medium Journal of Mathematical Physics 5 (4) 548-549 1964

[4] A M Dykhne Conductivity of a two-dimensional two-phase system Soviet Physics JETP 32(1) 63-65 1971 in Russian

Zh Eksp Teor Fiz 59(1) 110-115 1970

[5] JE Warren HS Price Flow in heterogeneous porous media Society of Petroleum Engineers Journal 1 (03) 1961

[6] HC Brinkman A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles Applied

Scientific Research 1(1) 27ndash34 1949


A comparative study of nanoscale pore structures in geomaterials Renata Cicha-Szot Piotr Such Grzegorz Leśniak

Oil and Gas Institute ndash National Research Institute 31-503 Krakoacutew Lubicz 25A Str Poland

renatacichainigpl

Keywords nanoscale pores shales gas slippage

Nanoscale pore structures are common in unconventional hydrocarbon reservoirs The most diverse pore structures might be found

in shale rocks which are investigated all over the world due to its hydrocarbon potential One of the challenges of economically

exploiting shale gas reservoirs is proper estimation of gas flow rate To achieve this goal better understanding of pore structure

and flow paths in fine grained rocks is needed The nano to micrometer scales of pore systems requires more complex analysis

and application of different techniques to understand pore changes in shale systems With the exception of pore size analysis using

scanning electron microscopy in this study mercury intrusion capillary pressure (MICP) nitrogen adsorption and Klinkenberg

gas slippage analysis are taken into account for evaluating pore size Moreover the latter technique characterizes only the part of

the pore system that is responsible for fluid flow Very few studies have been published that include gas slippage measurement on

stressed shale samples [1][2] however these studies were performed on mudstones or siltstones whereas Central European shale

formations are mainly claystones which are more prone to deformation of pore space with effective stress

In this study slippage was measured on plugs oriented parallel to bedding All samples were pre-stressed at reservoir conditions

(σeff~33 MPa) Due to the high heterogeneity of the analyzed shale samples Klinkenberg permeability SEM MICP and nitrogen

adsorption analysis were performed on the same plug in order to obtain the most adequate and coherent pore size results

Theoretical calculations of average pore diameter derived from slippage data collected in this study for samples with high clay

content and low carbonate content yielded lower diameters than estimates from MICP data Pore size evaluated with MICP and

Klinkenberg gave similar results for samples with existing microfractures Although similar pore diameters might be distinguished

on SEM images detailed pore size analysis using FIB-SEM showed very different results when evaluated with gas slippage

Table 1 Comparison of slit-shaped pore size and tube-shaped pore size from SEM and Klinkenberg

Sample ID

Pore width

Klinkenberg Pore width SEM

Pore diameter

Klinkenberg Pore diameter FIBSEM (median)

[m] [m] [m] [m]

8 40510-8 1198 10-8 16110-8 10010-7

32 235 10-8 721 10-8 93910-9 25010-8

42 33110-8 758 10-8 13210-8 15310-8

In order to provide more accurate estimation of clay rich shale permeability additional pore characterization using Klinkenberg

slippage is needed on an existing well-characterized plug Pore size distribution obtained by conventional analysis performed in

unstressed conditions may lead to significant errors However as has been shown in the paper microfractures may reduce the

effect of stress in rocks with specific mineral composition and pore space structure thus dominant pore diameter might be included

in estimations of permeability Initially it seemed that SEM image analysis produced similar pore diameter measurements as

Klinkenberg slippage However more detailed analysis showed a large discrepancy between the results Moreover for production

simulation correction related to reservoir temperature needs to be taken into account (as with other reservoir conditions

temperature is naturally included in permeability Pulse Decay measurements)

The research leading to these results were performed within the project Methodology for sweet spots determination based on geochemical petrophysical and geomechanical properties based on the correlation between laboratory investigations and geophysical measurements and a 3D

generation model co-funded by the National Centre for Research and Development as part of the programme BLUE GAS ndash POLISH SHALE

GAS Contract No BG1MWSSSG13

References [1] Cui A Wust R Nassichuk B Glover K Brezovski R Twemlow C A nearly complete characterization of permeability

to hydrocarbon gas and liquid for unconventional reservoirs a challenge to conventional thinking SPE 168730

Unconventional Resources Technology Conference 12-14 August Denver USA 2013

[2] Heller R Vermylen J Zoback M Experimental investigation of matric permeability of gas shales AAPG Bulletin 98

975-995 2014


Minkowski Metric Dirichlet Energy and Pore Tortuosity Mieczysław Cieszko

Institute of Mechanics and Applied Computer Science

Kazimierz Wielki University Bydgoszcz

cieszkoukwedupl

Keywords anisotropic pore space Minkowski metric space Dirichleta energy pore tortuosity and its microscopic representation

Parameter of the pore tortuosity together with the volume porosity and permeability form a set of basic parameters characterizing

macroscopic pore space structure of permeable porous materials This parameter plays important role in all transport processes

taking place in porous materials This concerns among others the flow of fluids electrical current and also diffusion and heat

conduction The importance of general description of the pore space structure is determined by the fact that

engineering of transport processes in porous media is directly related with engineering of pore structure In spite of the

fundamental character of the tortuosity parameter and great number of publications devoted to its definition analysis of the

physical and geometrical meaning and the methods of determination (eg [1-3]) there is still no commonly accepted general

definition of this macroscopic notion and its relation with microscopic pore structure This problem becomes even more

complicated in materials with anisotropic pore space structure

The aim of the paper is to present the general solution of the problem of macroscopic description of the anisotropic pore

space structure which allows precise and consistent formulation of definitions of macroscopic parameters of pore space structure

pore tortuosity and surface porosity and also their natural introduction into macroscopic description of processes occurring in

porous materials The general character of these definitions is also a necessary condition for formulation of general representation

of these parameters by quantities characterizing microscopic pore structure

Considerations have been based on the model assumptions presented in papers [4] and [5] It was assumed that at the

macroscopic point of view interconnected pores in permeable porous materials form anisotropic space the structure of which is

determined by its metric and this space is modelled as Minkowski metric space Such approach to this problem raises a number of

consequences a) modelling of the pore space structure is a primary problem in comparison to the modelling of processes occurring

in the pore space b) parameters of the pore space structure are defined by the metric of the space c) pore structure parameters

codetermine the course of each process occurring in the pore space and are independent of them

Application of the concept of Minkowski metric space as a model of anisotropic pore space enables precise and consistent

definition of macroscopic measures of distance surface and volume in this space and as a consequence also definition of

macroscopic parameters of pore space structure pore tortuosity and surface porosity directly related to these measures It was

shown that these parameters and their tensor characteristics are directly defined by the metric tensor of the pore space This means

that character of these parameters is purely geometrical

Definitions of the pore structure parameters formulated based on the concept of Minkowski metric space are also the basis

for precise determination of their relation with quantities characterising microscopic pore structure General form of such relation

for surface porosity and pore tortuosity have been obtained requiring the full representation of macroscopic density of fluid kinetic

energy in the potential flow by microscopic velocity field The microscopic representation of tortuosity for porous media with

isotropic pore space structure has the form

1

1205752=

1

119881119901int (119847119903 ∙ 119847)2Ω119901

119889119881 (1)

where 119847 i 119847119903 are unit vectors defining directions of gradient of macroscopic potential inducing fluid flow and of microscopic

potential in the pore space respectively

It was shown that such approach is directly related with the variational problem of minimization of scalar field

inhomogeneity defined in the pore region the measure of which is the integral of square of gradient of this scalar field called

Dirichlet integral or Dirichlet energy Euler equation for this problem takes form of the Laplace equation that is the basic equation

describing various types of potential transport This equation do not contain any material characteristics and due to the pure

geometrical character of the variational problem its solutions are contingent also upon geometry of the region on which it is

defined In the case of potential flow of fluid the variational problem means minimization of kinetic energy of fluid in the

considered pore region and with regard to the microscopic representation of the pore tortuosity given by expression (1) it means

minimization of the value of integral present there

References [1] Carman P Fluid Flow through Granular Beds Trans Inst Chem Engng 15 150-166 1937

[2] Lorentz P B Tortuosity in Porous Media Nature 189 386-387 1961

[3] Clennel M Tortuosity A Guide through the Maze in Developments in Petrophysics eds Lovell MA amp Harvey PK

Geological Society London Special Publication No 122 299-344 1997

[4] Cieszko M Fluid Mechanics in Anisotropic Pore Space of Permeable Materials Application of Minkowski Metric Space (in

polish) Wyd Uniwersytetu Kazimierza Wielkiego Bydgoszcz 2001

[5] Cieszko M Description of Anisotropic Pore Space Structure of Permeable Materials Based on Minkowski Metric Space

Archives of Mechanics 61 6 (425-444) 2009



with liquid during intrusion-extrusion process Tomasz Czerwiński1 Mieczysław Cieszko2 Chaplya Yevhen3



thhomekczgmailcom1 cieszkoukwedupl2 czaplaukwedupl3

Keywords macroscopic description non-wetting liquid intrusion porous ball intrusion-extrusion hysteresis

The problem of macroscopic description of non-wetting liquid (mercury) intrusion and extrusion from a ball of a porous

material is presented in the paper and the influence of pore structure parameters on saturation of the ball with liquid is analyzed

Modeling of these processes play an important role in the interpretation of mercury intrusion curves used for determination of pore

size distribution and other pore structure parameters For interpretation of such curves the simplified capillary models of pore

structure [1] or computer network models [2] are commonly used The use of macroscopic description of mercury intrusion-

extrusion process is a new approach to this problem

The analysis is based on the new continuum model of the capillary transport of liquid and gas in unsaturated porous material

presented in the paper [3] [4] The key assumptions of this model are division of liquid in the pore space into two macroscopic

constituents called mobile liquid and capillary liquid description of menisci motion by an additional macroscopic velocity field

parametrization of saturation changes by a macroscopic pressure-like quantity that for quasi static and stationary processes is equal

to the capillary pressure This model significantly changes the image of processes of liquid and gas capillary transport in an

unsaturated porous material It shows that these processes are running in a five dimensional pressure-time-space continuum and

quasi static processes of intrusion and extrusion of non-wetting liquid are non-stationary processes running in pressure-space

continuum The intrusion-extrusion processes in a porous ball are described by equation

120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) minus 119888119898(119904119898 119901) (

120597119904119898

120597119903)2= 119888119904(119904119898 119901) (1)

where 119904119898(119903 119901) and 119904119888(119903 119901) are local parameters describing saturation of a ball with the mobile and capillary liquid respectively

while 119901 represent pressure in the mobile liquid Quantities 119888119898(119904119898 119901) and 119888119904(119904119898 119901) are coefficients characterizing gradient and

volume diffusive transport of the menisci in the pore space Equation (1) is an extension of the model proposed in the paper [4]

In the case when the process of liquid extrusion is starting from full saturation of the sample the whole process will be described

by the reduced form of equation (2)

120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) = 119888119904(119904119898 119901) (2)

Such form of equation (2) results from the fact that in the state of complete saturation it is homogeneous and during the extrusion

process there are no mechanisms inducing inhomogeneity of this distribution In addition to the change of liquid wetting coefficient

in the intrusion-extrusion processes this is the main mechanism generating hysteresis of the capillary potential curve

The problem liquid intrusion into a ball has been solved analytically using the method of characteristics The expressions

describing liquid distribution in the ball and the curves of its capillary potential were determined This made it possible to analyze

the dependence of these curves on the pore structure parameters and to determine the saturation curves with mercury during the

extrusion process

References [1] Winslow DN Advances in Experimental Techniques for Mercury Intrusion Porosimetry Surface and Colloid Science 13

259-282 1984

[2] Xiong Q Baychev TG Jivkov AP Review of pore network modelling of porous media Experimental characterisations

network constructions and applications to reactive transport J Contam Hydrol 192 101ndash117 2016

[3] Cieszko M Macroscopic Description of Capillary Transport of Liquid and Gas in Unsaturated Porous Materials Meccanica

22 1-22 2016

[4] Cieszko M Czapla E Kempiński M Continuum Description of Quasi Static Intrusion of non-Wetting Liquid into a Porous

Body Continuum Mechanics and Thermodynamics 27(1) 133-144 2015


Experimental investigations of pressure drops in chosen granular beds Waldemar Dudda Wojciech Sobieski

University of Warmia and Mazury Olsztyn Poland

waldemarduddauwmedupl

Keywords granular porous media permeability Forchheimer law

Investigations of pressure drop in porous media filled by water andor air are very important in many areas of science and

technique The nature of such flows is very complicated and dependent on many factors In particular very interesting is the

question whether the pressure drops obtained for the air flow correlate with the pressure drops received for the water flow (for the

same porous column) Such investigations were performed in the past [123] however the results are not unambiguous To

continue these investigations a new laboratory stand was designed and built (Fig 1 left) and appropriate experiments were

performed The experiment was performed for three diameters of glass marbles (4 6 and 8 [mm] see Fig 1 right) two fluids

(air and water) and over 20 various filtration velocities Every measurement was repeated 10 times Important is that in both sets

of experiments (with air and water) the spatial arrangement of glass marbles was the same

Fig 1 Schema of the used laboratory stand (left) and a sample of glass marbles used in the experiment (right)

Fig 2 Comparison of results for air (left) and water (right) flow through porous column (d = 6 [mm])

In Fig 2 exemplary results of measurements for air (left) and water (right) flow for one chosen size of glass marbles are shown

All results were compared with the Forchheimer Andreasen-Poulsen and Kozeny-Carman mathematical formulas To obtain the

Forchheimer coefficient the so-called Forchheimer Plot Method was applied [4] The data of glass marbles were taken from the

monograph [4] The presented results will serve as data for a comparative study of air and water flows through granular porous

beds

References 1 Andreasen RR Canga E Kjaergaard C et al Water Air Soil Pollut (2013) 224 1469 doi101007s11270-013-

1469-5

2 Loll P Moldrup P Schjoslashnning P Rile H Predicting saturated hydraulic conductivity from air permeability

Application in stochastic water infiltration modelling Water Resouces Research Vol 35(8) 1999 pp 2387-2400

3 Pugliese L Poulsen TG Linking Gas and Liquid Pressure Loss to Particle Size Distribution and Particle Shape in

Granular Filter Materials Water Air Soil Pollut (2014) 2251811 DOI 101007s11270-013-1811-y

4 Sobieski W Lipiński S Dudda W Trykozko A Marek M Wiacek J Matyka M Gołembiewski J Granular

porous media (in Polish) University of Warmia and Mazury in Olsztyn Olsztyn p 180 (2016)


Experimental determination of the kinetics of sorption

and the kinetics of gas filtration in coal Marek Gawor

The Strata Mechanics Research Institute of the Polish Academy of Sciences

gaworimg-pankrakowpl

Keywords sorption filtration sorption kinetics filtration kinetics

The paper presents tests rigs for experiments on sorption kinetics and gas filtration kinetics in a porous medium It was observed

that two phenomena occur in these processes transportation of gas into the porous solid and settling of gas molecules on the walls

of the solid or in its volume The adsorption kinetics is understood as the gas molecule transition rate from the free state to the

bound state This sorption process takes place when a molecule of the sorbed gas is already on the surface of the solid and there is

a reaction of sorption forces between that particle and the atoms of the solid Filtration is the gas transportation process into the

solid that takes place as a result of the gas pressure gradient Both sorption and filtration occur at a certain rate Sorption involves

heat release (adsorption) or heat transfer which is connected with the change of temperature

The paper presents the results of three experiments In the first one a thin resistance thermometer was quickly taken out of an

argon stream and placed in carbon dioxide or the other way round (Fig1) The measurement made it possible to determine the

sorption time constant It was demonstrated that the sorption rate is much higher than the filtration rate Thus filtration is the

process describing the rate at which gas molecules penetrating the porous substance are adsorbed or desorbed The sorption time

constant is not higher than 50 msec

In the second experiment the authors determined the rate at which gas is liberated from coal grains The measurement

method was based on the measurement of the pressure of desorbing gas in constant volume (Fig2) The experiment involved a

measurement of the pressure of the gas liberated from the coal grains in a closed chamber The kinetics curves obtained in this

way were used to determine the carbon dioxide filtration coefficient in coal grains During the experiment a particular focus was

put on the initial stage of gas liberation (up to 04 sec)

Gas transportation in a porous structure of coal briquettes is a slower process In the third experiment the variety of the

boundary conditions allowed for a fuller verification of the assumed theoretical model and if necessary a more precise

specification of filtration parameters The test rig that was built for that purpose (Fig3) allowed for the measurement of the pressure

and the temperature in the edge of a briquette

Fig 1 The measurement principle of the sorption time

constant

Fig 2 The scheme of the rig for experiments on gas filtration

coefficient in coal grains

Fig 3 The scheme of the measurement rig for determination of gas filtration coefficient in coal briquettes


Fuzzy logic approach in the analysis of heat transfer in a porous sorbent bed

of the adsorption chiller Karolina Grabowska1 Jarosław Krzywański1 Karol Sztekler2 Wojciech Kalawa2 Wojciech Nowak2

1Jan Dlugosz University al 1315 Armii Krajowej PL42-200 Czestochowa Poland 2AGH University of Science and Technology ul Czarnowiejska 30 PL30-059 Cracow Poland

kgrabowskaajdczestpl

Keywords adsorption chiller porous media fuzzy logic thermal conductivity coated adsorption bed

Thermal conductivity in boundary layer of heat exchange surface is the crucial parameter of adsorption processes efficiency

which are carried out in the adsorption bed In order to improve of heat transfer conditions in the adsorption chiller the novel

constructions of adsorption beds are currently investigated The porous structure of sorbent layer is low thermal conductivity of

the whole adsorption bed One of the methods is the modification of porous media bed structure with glue which is characterized

by higher thermal conductivity The optimum parameters of sorbents and glues to build the novel coated construction in terms of

improving the COP (Coefficient of Performance) of chiller were defined in [1]

The paper implemented the fuzzy logic approach to predict the thermal conductivity of modified porous media layer The

analogic approach was applied in [2] for the prediction of local heat transfer coefficient in the combustion chamber of a circulating

fluidized bed combustor The developed model present changes of sorbent layer thermal conductivity depending on the change of

input parameters defining the heat transfer layer The data from empirical research were used to build up the model by the fuzzy

logic techniques The sample geometry used in the experiment is shown in the figure 1

Fig1 Coated sorbent layer

References [1] Grabowska K Krzywański J Nowak W Wesołowska M Budowa innowacyjnej konfiguracji złoża sorbentu w

adsorpcyjnym agregacie chłodniczym ndash Kryterium doboru optymalnej pary sorbent ndash klej XXIII Zjazd Termodynamikoacutew

2017 Beskid Śląski 2017

[2] Krzywanski J Nowak W Modeling of bed-to-wall heat transfer coefficient in a large-scale CFBC by fuzzy logic approach International Journal of Heat and Mass Transfer 94 327-334 2016


A concept of a two-stage process of non-pressure granulation of mineral materials Paweł Guzik1 Krzysztof Mudryk1

1 1University of Agriculture in Krakow Faculty of Production and Power Engineering

Department of Mechanical Engineering and Agrophysics

Krakow ul Balicka 120 30-149 Krakoacutew Poland

pawelguzikurkedupl

Keywords Slow-release fertilizers non-pressurized agglomeration Compressive strength disc fertilizer granulator

Mechanism of granules formation in the disk granulation process is based on the adhesive properties of drops of the liquid used

Substance is putting with the liquid into the fluidized bed is deposited partly on the surface of the granules in the layer and forms

separate particles The growth of granules is possible when the strength of liquid drop bonds with solid particles are large In the

fluidized bed apart from the formation of new granules there is an increase in already existing granules A characteristic feature

of the fluidized bed is the classification of particles in different zones of the layer Granulation process in the apparatus with the

fluidized bed as a rule proceeds with the simultaneous separation of particles in terms of their size This phenomenon significantly

affects the nature of the granulation process and should be taken into account when calculating the granulometric composition of

the layer In order to obtain a homogeneous granulate a selective discharge of granules from the apparatus and the return of fine

particles to the sprinkling zone is used At this point there is a chance to use an additional device (surrounding drum) cooperating

with the disk granulator As the amount of mass in the granulator increases the granule bed will exceed the edge of the granulator

pouring out of the granulator Receiving pouring granules in this way and directing them to further relaxing surrounding may

allow obtaining granules with greater mechanical strength It has been proved that the surrounding time has a positive effect in

correlation with the obtained higher compressive strength in strength tests In addition to the main concept of influencing the

hardening of the obtained granules a rotating drum could fulfill the task of sifting sieve (through the applied perforation) too small

granule fraction and shredding too large Only a part of the raw material would be recycled to re-granulation In my earlier research

on the granulation process I showed the dependence of the mechanical strength of granules on the angle of the granulators disc

and the rotational speed

Fig1 Comparison of strength from the angle of inclination of the granulators plate

Graph above shows the dependence of the strength of the granules on the rotational speed the highest result is characterized by

the target fraction obtained at the highest angle of inclination of the granulators disc of 55 deg at any rotational speed It is difficult

to indicate unequivocally what effect of the parameters results in a lower compressive strength of the obtained raw material but

it is clearly visible that the average highest results are on the cattle speed of 20 rpm in all angles of inclination of the granulators

plate Visually the lowest compressive strength parameters below 4 N are characterized by samples obtained at 45 deg and 50 deg and

the lowest rotational speed of 175 RPM The obtained results are the starting point for further agglomeration tests

Results above in the necessity of further searching for parameters allowing to control the process of non-pressure granulation

From sources of literature there are indications that prolong the time of surrounding granules However leaving granules too long

in the fluidized bed causes their excessive growth which is undesirable in the case of the selected range of expected granule size

for fertilizing purposes The homogeneous particle size allows precise application of the fertilizer dose The aforementioned idea

is the concept of a two-stage granulation allowing to continue the process of hardening the granules outside the main bed at the

same time allowing testing in a continuous granulation process and not as in the intermittent form after full granulator platter has

been obtained The presented concept of a two-stage non-pressure granulation is subject to further research in my field

References [1] Pietsch W Aninterdisciplinary approach to size enlargement by agglomeration 2003

[2] Domoradzki M The kinetics of dust granulation in a disk granulator 1978

[3] P W Kłassien I G Griszajew Basics of granulation techniques 1989


Mathematical model of the course of process of catalytic wet air oxidation

of phenol (CWAO) in trickle bed reactors (TBR) Daniel Janecki

Department of Process Engineering University of Opole ul Dmowskiego 7-9 45-365 Opole Poland

zecjanuniopolepl

Keywords trickle-bed reactors multiphase flow (CFD) catalytic phenol wet oxidation active carbon as catalyst

Despite progress achieved in recent years in the use of Computational Fluid Dynamics (CFD) in modelling work of trickle bed

reactor (TBR) still predicting hydrodynamic and kinetic parameters compliant to an experiment encounters major difficulties It

is connected among other things with lack of reliable reports describing interactions between phases for multiphase systems as

well as limited number of experimental data used at verification of estimated spatial and temporal changes of the discussed

parameters

The aim of the present study is modelling of process of catalytic wet air oxidation of phenol (CWAO) in TBR This process

was chosen because phenol and its derivatives are the most frequent ingredients of pollution present in industrial waste and their

toxicity and ability of bioaccumulation forces to establish more and more effective methods of removing phenol from the polluted

water One of the possibilities is the use of catalytic process of wet air oxidation of phenol while in the experiments instead of

commonly used metal oxides (the most frequent being copper oxide) active carbon was used as a catalyst of the process (granules

of active carbon of 15 mm diameter piled in a layer 070 m high) The reactor was working at the pressure of 185 MPa (Janecki

et al (2016)) In the discussed process one could differentiate stages transport of oxygen from gas to liquid phase and directly

from gas to external surface of the catalyst transport of oxygen and phenol from the core of liquid to external surface of the

catalyst transport of oxygen and phenol inside the pores of the catalyst and reaction on the internal surface of contact Making

mass balance of reacting substances it was assumed that the reactor works in the established state in isothermal and isobaric

conditions at stable activity of the catalyst It was assumed also that external surface of the catalyst is partially moistened with

liquid which makes contact of the oxygen contained in the air with the surface of the catalyst possible while the pores of the

catalyst sprinkled intensively before each experiment are filled with liquid Speed of reaction and factors of transport of mass

from gas to liquid and solid phase were obtained from available literature data Balance equations were adjusted to the shape which

allows to use them in Fluent program Source elements which appear in the equations of this model have been introduced to this

program with the use of user function UDF To recreate the area taken by the bed and liquids flowing through it a structural net

was generated with the use of GAMBIT preprocessor As initial conditions experimental values of gas and liquid velocity average

volume share of liquid phase and mass shares of elements in gas and liquid at the inlet to the reactor were adopted

Calculations were performed in two stages In order to obtain the distribution of velocity of liquid and gas and distribution of

volume share of gas and liquid phase the Eulerian model was used which includes the balance of mass and momentum for each

phase For calculations in which the change of porosity of the bed along the radius of the apparatus is considered with the use of

Martin correlations (1978) (the ratio of the diameter of the reactor to the diameter of the catalyst was equal 133) it is best to use

Ergun constant values estimated with the use of neuron networks by Iliuta et al (1998) (Janecki et al (2014)) For the reactor and

catalyst used in the research these constants equal E1 = 155 E2 = 207 In the next stage a simulation of the field of concentration

of elements in the whole reactor at the assumption of invariability of the field of flows and volume shares of all phases was

conducted which was fully justified due to small interphase streams of mass As result of the calculations local values of

concentration of elements were obtained as well as their values at the outlet from the reactor

For comparison a single-dimensional isothermal model of catalytic process of oxidation of phenol in trickle reactor with piston

flow of both phases was worked out with the use of which a change of concentration of elements along the reactor and their values

at the outlet from the apparatus was calculated The equations of the model were solved numerically with the use of Runge-Kutta

method of the fourth order While analysing the obtained results one may state that the results of numerical simulations obtained

with the use of CFD model are closer to experimental values Average relative error of estimation of phenol concentration at the

outlet of the reactor obtained from CFD model equals 116 while average standard deviation is 52 for values obtained from

single-dimension model it is respectively 169 and 122 Taking into account the number of parameters the value of which had

to be calculated from empirical correlations (equation of reaction velocity mass-transfer coefficients) one may notice that a

satisfying compliance of measured values and those calculated from the model was achieved

References [1] Iliuta I Larachi F Grandjean BPA Pressure drop and liquid holdup in trickle flow reactors improved Ergun constants

and slip correlations for the slit model Ind Eng Chem Res 37 4542-4550 1998

[2] Janecki D Burghardt A Bartelmus G Influence of the porosity profile and sets of Ergun constants on the main hydrodynamic

parameters in the trickle-bed reactors Chem Eng J 237 176-188 2014

[3] Janecki D Szczotka A Burghardt A Bartelmus G Modelling of wet-air oxidation of phenol in a trickle-bed reactor using

active carbon as a catalyst J of Chem Techn amp Biotech 91 596-607 2016

[4] Martin H Low Peclet number particle to fluid heat and mass transfer in packed beds Chem Eng Sci 33 913-919 1978


Depth-averaged model for flow in a propped fracture Łukasz Jasiński1 Marcin Dąbrowski12

1Computational Geology Laboratory (CGL) Polish Geological Institute ndash National Research Institute Wrocław

Poland 2Physics of Geological Processes University of Oslo Norway

lukaszjasinskipgigovpl marcindabrowskipgigovpl

Keywords fracture flow Brinkman flow model numerical simulation

Propped fractures largely contribute in overall flow through low matrix permeability formations such as shales or

crystalline rocks Therefore they may play an important role during natural processes (ie hydrocarbon migration hydrothermal

circulation metamorphism) as well as in industrial applications (ie gas storage in caverns radioactive waste repositories oil

and gas extraction from reservoirs) Moreover similar geometries may also be found in manufactured system for example

microfluidic devices for microbiological filtration and separation systems high performance liquid chromatography

dielectrophoretic platforms or heat spreading and dissipation systems for microelectronic

Fig 4 A geometric model of a plane-walled fracture with cylindrical circular obstacles b denotes the fracture aperture and R

and d are the cylindrical obstacle radius and diameter respectively

In our model the fracture walls are planar and proppant grains are approximated by circular cylindrical obstacles (see

Fig 1) We study the local and the effective flow properties in a propped fracture and how they are influenced by two geometric

parameters the obstacle fraction f and the ratio between the fracture aperture b and the obstacle diameter d Due to the symmetry

of geometry along the fracture aperture the problem is reduced to two dimensions and to fulfill the no-slip boundary condition at

the rims of the obstacles the Brinkman flow model [1] is adopted to the fracture flow problem [2]

minus119887nabla119901 + 120583nabla2119921 minus119887

119870119921 + 119887119943 = 0 (1)

nabla ∙ 119921 = 0 (2)

where p is fluid pressure micro denotes fluid shear viscosity f is the body force J is the local flow rate (ie the depth-integrated in-

plane components of the velocity vector) and K is the permeability of an empty plane-walled channel of an aperture b 119870 =

1121198872 The additional Brinkman term 120583

119870119921 in equation (1) corresponds to the viscous drag due to the presence of the fracture

walls

The Brinkman flow model is carefully validated against the analytical solution for a single obstacle and compared to

fully resolved three-dimensional Stokes model for the case with many obstacles Described flow models are solved numerically

using Finite Element Method based on the modified version of MILAMIN codes [3]

Finally the results of systematic calculations are analysed in terms of the velocity fields probability distributions and

effective fracture transmissivity

References [1] Brinkman H C A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles Flow Turbulence

and Combustion 1(1) 27 1949

[2] Jasinski L Dabrowski M The Effective Transmissivity of a Plane-Walled Fracture With Circular Cylindrical Obstacles

Journal of Geophysical Research Solid Earth 123(1) 242ndash263 2018

[3] Dabrowski M Krotkiewski M Schmid D W MILAMIN MATLAB-based finite element method solver for large problems

Geochemistry Geophysics Geosystems 9(4) Q04030 2008


A unified thermodynamic approach to description of whole phenomena

during a coke production Dariusz Kardaś Sylwia Polesek-Karczewska Paweł Zioacutełkowski Janusz Badur

Institute of Fluid Flow Machinery PAS-ci Gdańsk

dkimpgdapl pziolkowskiimpgdapl

Keywords coke poro-mechanics poro-thermo-chemo-mechanical interactions

Coke industrial production still is based on a mysterious and hidden technology procedures coming from the beginning of XIX-

century These procedures speaking directly have a roofs from the renascence alchemy and have nothing common with modern

science Many parameters that play a key role in the coking process such as a rate of heating the length of thermal plateau etc

are taken from an accidental knowledge of a producer We have found that due to lack of scientific recognize a coking process is

generally at engineering level ndash therefore it is a chance for science to improve its efficiency and to reduce its cost

In our best opinion a proposed unified thermodynamic

approach should take into account the following

phenomena such as

in the wall zone

in the semi-coke

zone

in the closed

porosity zone

in the plastic

layer zone

in the coal zone

surface radiation turbulent heat

transfer depletion of flue gases

sorptiondesorption swelling cracking

thermal creep thermal and sorption

stresses radiation heat diffusion

porous flow of gases

chemical reaction porosity creation

effective stresses heat conductivity

vaporization internal pressure gas

confinement

enhancement heat transport

devolution thermoplasticity

heat and mass conductivity

watersteam adsorption swelling and

hydration behavior of coal gas

sorptiondesorption in porous media

It is evident that spatial and temporal monitoring of the progress of coke would also aid in characterizing the local variations in

pore size and tortuosity of broad relevance to all unconventionals and transport processes In this study starting from a common

thermodynamic approach and from our previous works on fluid flow in such systems dominated by various mechanisms (such

as Darcy flow slip flow desorption Knudsen diffusion Reynolds transpiration thermal creep multiscale radiation) we propose

a thermodynamically justified FSI model for modeling whole coke production process A particular data of several processes are

taken from the literature and form our own experiments ndash the process from the beginning should be treated to be nonstationary

(whole about 3 hours) Modeling has also been used to describe fluid transfer from coal matrix to fractures incorporating the

significant Navier diffusion in nanopores Graham sorption gas mechanism of thermal pyrolysis and so on The coal pores which

occur in the process could be classified into micropores (pore size d=6-10 nm) mesopores (10 nm ltd lt 1000 nm) and macropores

(dgt1000 nm) The literature studies have shown that the micropores account for over 60 of total coal pore volume in the closed

porosity zone to be zero in the plastic layer zone Therefore the sophisticated concept of porosity evolution is a key in our

modeling



based on mercury porosimetry and microtomographic image analysis Marcin Kempiński1 Mieczysław Cieszko Marcin Burzyński2 Zbigniew Szczepański


Kazimierz Wielki University Kopernika 1 85-074 Bydgoszcz Poland 1 kempinskiukwedupl 2 marcinburzynskipostpl

Keywords pore size distribution sintered glass beads MIP CT

In the paper the capillary and random chain models of pore architecture presented in the paper [1] are applied for determining

the limit pore size distributions in sintered glass bead samples based on mercury intrusion curves [2] They estimate the range of

pore sizes in the investigated material It is proved that capillary model commonly used in mercury porosimetry and the chain

model are two limit cases of net models of pore architecture for a given pore size distribution Both distributions determine the

range in which the pore diameter distribution of the investigated material occurs and defines the degree of inaccuracy of the method

based on the mercury intrusion data caused by the indeterminacy of the sample shape and its pore space structure The capillary

and chain model with constant length has been used as a basis for the procedure of determining the limit pore size distributions in

sintered glass beads samples The limit distributions are compared with distributions determined from microscopic image analysis

of samples obtained by the micro computed tomography (CT) method These distributions are considered as actual distributions

of the pore space and are determined by prescription to each point (voxel) of the pore space of porous material the diameter of

the maximal sphere that contains this point and is completely inside the pore space [3]

The models of the pore space of porous materials are analysed in which the individual pores are cylindrical links of random

length and diameter distributions Two independent factors determinate the pore space structure of such media the link size

distributions and the way of their connections The second factor is called the pore space architecture The pore architecture causes

that even for the same pore diameter distribution in the model material its pore space structure can be different Regarding the

pore architecture in the paper we will distinguish three kinds of models of the pore space structures capillary chain and network

In the capillary model the links of equal diameter are joined in series and form the long capillaries of constant diameters crossing

the whole material In the chain model the links are joined at random in series and form the capillaries of step-wise changing cross-

section In the network model a random connected links from the space network

Fife special cases of the capillary potential curves of porous layer are presented in Figure 1 Four cases concern the chain pore

architecture of the layer with the same link diameter distribution and different distributions of link length capillary model (CM)

periodic (PM) and random periodic (RPM) models with constant link length and model with random link length (RM) The fifth

case concerns the porous ball with isotropic chain pore architecture It was assumed in this case that the mean length of the capillary

chords in the ball is equal to the thickness of the layer

Figure 1 Capillary potential curves of the porous layer with capillary (CM) periodic (PM) random-periodic (RPM)

random (RM) pore space architecture and porous ball with isotropic chain pore structure (BM)

From this figure results that link length distribution in the layer and capillary chord distribution in the ball does not influence

significantly the capillary potential curves Therefore description of this curve for porous material of chain pore architecture can

be effectively represented by the model with constant link length Then the thickness of the layer can be interpreted as the mean

length of capillary chains in sample of any shape It was shown that capillary potential curves for capillary and periodic models

are limit curves for network models of the same pore size distribution This means that both models can be used for estimation of

the range of pore diameter distribution determined basing on the mercury intrusion data

Both models have been applied for determination of limit pore size distributions of sintered bead samples The obtained results

were compared with distributions determined from micro tomographic images using the methods of morphological image analysis

References [1] Cieszko M Kempiński M Determination of Limit Pore Size Distributions of Porous Materials from Mercury Intrusion

Curves Engng Trans 54 2 pp 143-158 2006

[2] Webb PA Orr C Analitical Methods in Fine Particle Technology Micrometitics Instrument Corporation Norcross GA

USA 1997

[3] Hildebrand T Ruegsegger P A new Method for the Model-Independent Assessment of Thickness in Three-Dimensional

Images Journal of Microscopy 185 1 pp 67-75 1997


Geometry extraction from GCODE files destined for 3D printing Wojciech Kiński Wojciech Sobieski


wojtekkinskiwppl

Keywords 3D printing GCODE reverse engineering

Nowadays the 3D printers are very popular and their importance grows every year They are used in many areas of engineering

technique medicine and even food industry To obtain any printed object first its geometry must be defined with taking into

account all limitations of the 3D printing technology To reach this aim any software destined to preparing 3D geometry (in the

STL file format) may be used At this stage assumptions related to the used material must be accept too Very important is that

the virtual geometry cannot be printed directly on a 3D printer The geometry must to be converted to a set of instructions which

will be sequentially read and execute by the printer In particular the movement of the print head and the material feeding speed

must be specified Here a specific programming language the so-called GCODE is used It is a standardized command language

that it uses to operate numerically controlled devices (CNC) The practical experience in 3D printing shows that sometimes the

original geometry data are no longer available That means that having only a GCODE file there is no possibility to see the

geometry prepared to printing This problem as well as the lack of appropriate software was the main motivation to performing

investigations described in the paper The aim is to develop an algorithm which convert GCODE files to a format which may be

easy visualised

Fig 1 Examples of geometry prepared in the MatterControl [2] software and saved to STL files

The applied methodology cover three steps 1) preparing exemplary geometries in the STL format 2) converting STL files to

GCODE files 3) decoding GCODE files to reconstruct the geometry It should be stressed that the fully reconstruction of STL

files is very difficult (and perhaps not possible at all) In the investigations was assumed that geometry representation in the form

of a point cloud would be sufficient

Fig 2 Examples of decoding chosen GCODE files

In Fig 1 three examples of geometry are shown thin-walled object (left) filled object (centre) and object with a thread (right)

In turn in Fig 2 the decoded geometry of the same objects in a form of point clouds are visible As it can be seen the obtained

shapes correspond well to the original geometry Such result is enough to identify the geometry saved in GCODE files It should

be stressed that the developed algorithm is destined only for files prepared for 3d printers and donrsquot have an universal character

The data converter is written in the Fortran language [1] Visualization of point clouds is made in the ParaView software [3] with

the use of VTK file format [4]

The main observations and final conclusions are as follows it is possible to reconstruct the geometry saved in a GCODE file

and the most convenient form of its visualization is a point cloud the movement of the print head must be interpolated to

reconstruct filled structures duplicates of points in a cloud should be detected and removed the decoding process is hindered by

the fact that from one geometry many differing GCODE files may be obtained (it depends on settings of the algorithm converting

the STL files to the GCODE files)The last problem causes sometimes appearing points located outside the original geometry It

is difficult to develop a universal algorithm to filter such points for all possible variants of GCODE files

References 1 GNU Fortran Home Page [on-line] URLhttpsgccgnuorgfortran (available at February 6 2018)

2 MatterControl Home Page [on-line] URL httpswwwmatterhackerscom (available at February 6 2018)

3 ParaView Home Page [on-line] URL httpswwwparavieworg (available at February 6 2018)

4 VTK - The Visualization Toolkit[on-line] URL httpswwwvtkorg (available at February 6 2018)


The application of 3D printing technology in the investigations of porous media Wojciech Kiński Wojciech Sobieski


wojtekkinskiwppl

Keywords 3D printing porous media controlled geometry

The porous media found in the nature as well as in the modern technique are very diverse [1] Usually the spatial structure of

porous media cannot be freely modified and depends on many factors including random ones However to obtain specific and

desirable features it would be good to control the porosity tortuosity specific surface and the other parameters characterizing the

geometry of the porous body The question is whether the 3D printing technology may be applicable to creating porous media

with such controlled geometry The main aim of the presented study is to recognize possibilities in this area Currently two

possibilities are taken into account 1) generation of porous media based on filling patterns 2) generation of porous media based

on full 3D geometry

In Fig 1 left the most popular filling patterns are visible They are applied to save the material and to shorting the printing

time Usually the same patterns are repeated in every layer due the fact that every next layer must be supported from below In

Fig 1 right other filling pattern is shown In this case the holes have an regular three-dimensional shape

Fig 1 Exemplary filling of models

In Fig 2 application of the second mentioned possibility is shown First a 3D model with specific porosity and tortuosity was

created which next was printed Important is that many geometrical information from a 3D model may be obtained Some of

them are assumed the other may be calculated (Tab 1) The ranges of geometrical parameters which are possible in the praxis is

the key question in such investigations It can mention here the maximum number of channels its diameter the minimum porosity

and the maximum tortuosity as well as correlations between these parameters

Fig 2 Stages of creating an porous object with specific porosity and tortuosity

Table 1 Geometrical parameters of the porous body

number of channels height [mm] volume [mm3] porosity [-] tortuosity [i]

straight channels 16 100 334 880 0898 1

curved channels 16 1068 345 800 087 1068

References 1 Thingiverse Home Page [on-line] URLhttpsthingiversecom (available at February 20 2018)


Selected artificial intelligence methods in modeling of energy devices and systems Jarosław Krzywański

Akademia im Jana Długosza w Częstochowie Wydział Matematyczno-Przyrodniczy

jkrzywanski ajdczestpl

Keywords artificial intelligence neural networks fuzzy logic energy systems modelling

The work deals with the artificial intelligence methods in modeling of energy systems Selected artificial intelligence techniques

ie artificial neural networks fuzzy logic and genetic algorithms are applied in the study A wide range of applications are

considered Heat transfer in a large-scale circulating fluidized bed boiler hydrogen production via CaO sorption enhanced

gasification of sawdust in a fluidized bed unit NOx emissions from calcium looping in fluidized bed systems and the CaSO4

decomposition during coal pyrolysis are discussed in the work [1-3]

The developed models constitute a series of easily-applicable and powerful tools allowing to describe the complex energy systems

Original models developed in the book have a high value from practical point of view and are consistent with the latest scientific

achievements in the discussed subject

References [1] Krzywanski J Nowak W Modeling of bed-to-wall heat transfer coefficient in a large-scale CFBC by fuzzy logic approach

International Journal of Heat and Mass Transfer 201694327ndash 34

[2] Krzywanski J Grabowska K Herman F Pyrka P Sosnowski M Prauzner T Nowak W Optimization of a three-bed

adsorption chiller by genetic algorithms and neural networks Energy Conversion and Management 1532017 313ndash322

[3] Krzywański J Nowak W Neurocomputing approach for the prediction of NOx emissions from CFBC in air-fired and oxygen-

enriched atmospheres Journal of Power Technologies 97 (2) 201775-84


Evaluation of plasticity criterion applicability in the porous materials research Anna Kułakowska

Institute of Technical Education amp Safety Systems Jan Długosz University in Częstochowa

Al Armii Krajowej 1315 42-218 Częstochowa

akulakowskaajdczestpl

Keywords plasticity criterion shear deformation destruction

At the moment conventional bulk materials are being increasingly replaced by sintered materials with the same chemical

composition These materials could be characterised by a high value of porosity that quite often deteriorates their properties in

comparison with bulk materials One of the possible ways to improve the properties of such materials is to deform sintered billets

what may lead to additional strengthening of surface layers In this case it is very important to determine whether these materials

are able to undergo deformation The article describes an approach for determination the yield criterion according to the

Kolmogorov model he plasticity criterion is the simplest and most reliable way for determination strain capacity of materials [1

2]

According to the Kolmogorov model the use of plasticity at any time point from the period t can be determined via

equation [1 3]

120595 = int119867119889120591

120556119901

119905

0 (1)

where H ndash shear deformation rate intensity

τ ndash shear stress

Λp - shear deformation to destruction (range plasticity) when t=0-ψ=0 at the moment of destruction tp-ψ=1 and at any

time 0lttlttp value ψlt1

At the time point t=tp the value of plasticity bdquoweaknessrdquo reaches the limit value right after this a micro-gap starts to grow in

material volume When it reaches critical sizes the stage of destruction takes place [1]

120595 = int119867119889120591

120556119901

1199051199010

= 1 (2)

The value of the limit deformation Λp until the crack occurrence can be evaluate by thermomechanical deformation conditions

[1]

120556119901 = 120556119901(119896120590 120583120590 119867 119879 119861(120591) 119883119894) (3)

where kσ=σśrτi ndash stress status indicator

τi ndash intensity of shear stress

μσ ndash Lode indicator

B(τ) ndash an index of deformation non-monotonicity

H ndash intensity of shear deformation rate

T ndash temperature

Xi ndash physicochemical and structural parameters of the deformed material

The ability to plastic deformation without cracking is limited and therefore plasticity (deformability) is one of the main features

of material that determines its sensitivity to plastic forming

References [1] Kolmogorov VL Napriazhenija Dieformacja Plastichnost Mietalurgija 1970

[2] Kolmogorov VL Plasticznost i raz ruszenie Mashynostrojenije1977

[3] Dyja H Gałkin A Knapiński M Reologia metali odkształcanych plastycznie Wyd Politechniki Częstochowskiej 2010


Diffusion of Cd(II) Pb(II) and Zn(II) on calcium alginate beads Sylwia Kwiatkowska-Marks Justyna Miłek Ilona Trawczyńska

Faculty of Chemical Technology and Engineering University of Technology and Life Sciences Bydgoszcz

sylwiakwiatkowskautpedupl

Keywords diffusion cadmium zinc lead alginate beads

Heavy metals have a proven harmful effect on many forms of life Lead and cadmium are known to be especially harmful to

man and the environment [1] Wastewater that contains zinc is harmful for both irrigational and industrial applications [2]

Biosorption on materials of natural origin seems to provide the most prospective results in addition to being highly efficient it

enables elimination of the entire content of metal ions even if they are present at very low concentrations in the liquid waste

Alginates are linear copolymers of β-D-mannuronate (M) and α-L-guluronate (G) residues in (1rarr4)-linkage arranged in a block-

wise pattern along the linear chain [3] Alginates are biopolymers with high sorption capacity for heavy metals even at low

concentrations of the metals in solutions [4]

The sorption of metal ions on alginates takes place at a very fast rate and is only limited by diffusion phenomena Therefore

according to the commonly accepted belief the rate of sorption with this type of sorbent is limited by internal diffusion In order

to use the quantitative approach to the diffusive-mass movement within the porous beads having a complicated geometrical

structure the notion of effective diffusion coefficient De has been introduced Since the rate of sorption on alginate beads is

determined by the rate of diffusion in the sorbent pores it is essential to know the effective diffusion coefficient to design the

equipment In the case of alginate gels it is convenient to use the diffusion retardation coefficient φ

aq

e

D

D

(1)

where De - effective coefficient of sorbate diffusion in sorbent pores

Daq - diffusion coefficients for a highly dilute aqueous solution (in this work were calculated using the Nernst equation) The main objectives of this research work are to determine by the conductometric method the effective diffusion coefficient for

different heavy-metal salts Cd Zn and Pb in calcium alginate beads and to determine the effect of the metal type anion from the

metal salt and the alginate content in the beads on the De value

In the conductometric method determination of the effective diffusion coefficient is based on measurements of conductivity of

the solution into which the sorbate diffuses therefore assuming that dependence of conductivity on concentration is linear the

following equation is obtained (by transforming the non-stationary diffusion equation)

2

22

1

22exp

161

R

tnD

nP

P e

n

t

(2)

where Pt ndash conductivity of the solution after the time t P - conductivity of the solution after the time

A typical dependence PtP on the process duration is shown in Fig 1

0

02

04

06

08

1

12

0 10 20 30 40 50 60

PtP

t [min] Fig1 Dependence of PtP on the process duration for diffusion of CdSO4 from alginate beads with a dry weight of 15

The experimental results clearly indicate a decrease in the values of De caused by an increase in the alginate content in the

sorbent beads This is in agreement with the mechanism of the diffusion process taking place in porous carriers Good agreement

between the experimental data and the mathematical model was obtained as shown by the high values of correlation coefficients

The value of the effective diffusion coefficient is affected by the metal salt anion therefore it should also be taken into account

in the calculations

All the values of De obtained by the conductometric method are lower than the calculated diffusion coefficients in highly dilute

aqueous solution of the given this salt Daq More often than not the condition is not satisfied in literature reports especially in

calculations by conventional methods (SCM LAM)

The conductometric method is simple and it provides good results in calculating the effective diffusion coefficients for heavy

metals in alginate sorbents

References [1] Meena AK Kadirvelu K Mishra GK Rajagopal C Nagar PN Adsorption of Pb(II) and Cd(II) metal ions from aqueous

solutions by mustard husk J Hazard Mater 150619-625 2008

[2] Lai YL Annadurai G Huang FC Lee JF Biosorption of Zn(II) on the different Ca-alginate beads from aqueous solution

Bioresource Technology 99 6480-6487 2008

[3] Davis TA Volesky B Mucci A A review of the biochemistry of heavy metal biosorption by brown algae Water Res

374311ndash 4330 2003

[4] Papageorgiou SK Katsaros FK Kouvelos EP Nolan JW Le Deit H Kanellopoulos NK Heavy metal sorption by

calcium alginate beads from Laminaria Digitata Journal Of Hazardous Materials B1371765-1772 2006


Effect of microfracture on ultratight matrix permeability Grzegorz Leśniak

Oil and Gas Institute ndash NRI Cracow

lesniakinigpl

Keywords anomalous permeability shale rocks microfracture width

Measurements of reservoir rock permeability have been executed in the oil industry for several decades Depending on the type

of permeability oil and gas reservoirs can be divided into those with pore reservoirs pore ndash fracture reservoirs and fracture

reservoirs In practice pore and fracture permeability is observed in all unconventional reservoirs with varying proportions of

either type Natural microfracture systems increasing the permeability of the rock matrix are also recorded in shale rocks In this

paper anomalous results of permeability for rock samples from shale formations have been analysed Observations with the use of

SEM and petrographic microscope allow us to distinguish microfractures generated as a result of decompression of rocks (change

of stress) and natural ones The fractures generated as a result of core decompression are usually associated with very fine

laminations with a material of different grain size composition comparing with rock matrix (smaller or larger grains) or with clay

laminations within mudstones (authors microscopic observations) It has been concluded that the microfracture systems present

in the examined rocks are the reason for anomalous values of permeability measured by the Pulse-Decay method Dependences

of overburden pressure on fracture permeability have been analysed Simulative research performed for plug-type core samples

allowed us to obtain permeability values in a function of the microfractures width Finally dependence of reservoir conditions on

fracture width as well as on porosity was examined

The problem encountered during the selection of shale samples for permeability measurements is that the sample is cut in the

form of a cylinder of 254 cm in diameter and 4 cm in length which is often unfeasible This is caused by typically shale cleavage

and the presence of microfractures Observations in the petrographic microscope allows us to divide the microfractures resulting

from the expansion of the rock after pulling to the surface (change of stress) and the system of natural microfractures The fracture

resulting from the expansion of the core are associated with very fine laminations with different granulometric material from the

rock matrix (smaller or larger grains) or clay laminates within the mudstones

The research procedure was as follows

bull preparation of plug samples

bull permeability measurement - Pulse Decay (PDP-250)

bull 3D imaging - X-ray microtomography (CT) ndash resolution 10-12 m

bull 2D X-ray imaging (RTG)

bull selection of samples in which we deal with the microfracture permeability (based on permeability measurements and 3D and

2D imaging)

bull calculation of width of microfracutures based on permeability measurements

48 samples of the Baltic basin shale cores were selected for the study The range of obtained permeability researches cover the

range from 38 mD to 04 nD (that is six orders of magnitude) Samples with permeability above 1 mD were recognized as the

samples with fractures formed during their preparation For the rest of samples the base question is are the obtained permeability

values only connected with rock matrix or also with microfratures Assuming that the value of 04 nD is the lowest permeability

of the rock matrix and taking into account permeability of the rock matrix (according to available publications) [123] can be up

to 13 D we should accept that all measurements of permeability values greater than 00013 mD (13 D) should be connected

with the existence of the microfracture system present in the samples

The obtained results of the width of microfractures range from 1035 to 15201 μm This width can be compared with the average

pore size in classic sandstone reservoirs For the four microfratures in the sample these values range from 0652 to 9576 μm In

the case of the samples with permeability of less than 600 nD for one microfracture the width is from 0291 to 0652 μm and for

4 microfractures from 0183 to 0411 μm

It should be noted that the change in the number of microfractures in a sample does not alter the calculated of width of

microfractures in the same way Also the differences of the width of microfractures ndash if we ignore the permeability values of the

rock matrix - do not change drastically The variation in the width of microfractures is approximately 40

Studies have shown that the anomalous values of permeability in shale rocks correspond to microfracture systems Therefore

it is important to put more emphasis on the correct determination of permeability of the rock matrix (without microfractures)

The impact of microfracture parameters on the permeability of shale under reservoir conditions was analyzed The width existing

microfractures was calculated The permeability value over which microfracture samples (matrix permeability) should be expected

in the specimen samples of shale rock was estimated

ACKNOWLEDGEMENTS

This article is the result of research conducted as part of the project Methodology of determining sweet spots on the basis of

geochemical petrophysical and geomechanical properties based on the correlation of the results of laboratory examinations

with the geophysical measurements and the 3D generation model co-funded by the National Centre for Research and Development

as part of the BLUE GAS ndash POLISH SHALE GAS program Contract no BG1MWSSSG13

References 1 Apaydin O 2012 New coupling considerations between matrix and multiscale natural fractures in unconventional resource

reservoirs PhD thesis Colorado School of Mines

2 Cho Y Apaydin OG Ozkan E 2013 Pressure-dependent natural fracture permeability in shale and its effect on shale-gas

well production SPE Reservoir Evaluation amp Engineering (216-228)

3 Subrata Roy Reni Raju Chuang HF Cruden BA Meyyappan M 2003 Modeling gas flow through microchannels and

nanopores Journ of Applied Physics vol 93 no8 (4870 - 4879)


Multi-scale core to pore imaging and modelling of the heterogonous rocks Grzegorz Leśniak1 Renata Cicha-Szot1 Krzysztof Labus2

Oil and Gas Institute ndash National Research Institute 31-503 Krakoacutew Lubicz 25A St Poland

Silesian University of Technology Faculty of Mining and Geology 44-100 Gliwice 2 Akademicka St Poland

renatacichainigpl

Keywords fractal approach computer analysis of images pore space net model numerical modelling

Geologic systems are heterogenous on all length scales [1] Reservoir engineering captures such heterogeneity by classifying

the formation into multiple lithological facies constructing reservoir models and sampling these for further examination using

core analysis This process however only captures heterogeneity down to the scale of the 1 ndash 15rdquo ldquocore plugrdquo which is then

upscaled back to the reservoir model

Rotliegend sandstone is one of the most perspective reservoir rock in Europe It is considered as sediments which show a wide

variety of geological characteristics from homogenous rocks dominated by more or less uniform quartz cementation to

heterogeneous samples with complex distributions of authigenic clay minerals and quartz carbonate and anhydrite cementation

[2][3] Due to sedimentary and diagenesis history[3] this kind of rocks have complicated pore structures which impedes

estimation of filtration parameters with the use of conventional analysis Experimental quantification of filtration parameters

requires regularly shaped samples These fragments (plugs) are cut from cores extracted from wells Moreover coring is expensive

in general and arguably impossible where new drilling technologies (eg coiled tubing) are employed Consequently the most

important application of this study will be for estimating permeability on cuttings and irregularly shaped sidewall core samples

Recent developments in imaging technology solved that problem and can be used to bridge the gap between pore and reservoir-

core scale descriptions

In this paper we present the results of laboratory study where we compare permeability estimates obtained from several

mercury injection capillary pressure based models Klinkenberg corrected permeability in tight sands and prepared for analyzed

samples net model of pore space obtained by complex validation of the obtained parameters of rocks [4] to calculations based on

DRP Moreover the paper will show estimation of applicability limits for classical evaluation of reservoir rocks heterogeneity

degree in comparison with microscope 3D images of pore space Benchmarking of fluid flow parameters show that corrections of

Mercury Injection Capillary Pressure (MICP) experiments are absolutely necessary particularly conformance correction at low

capillary pressures On the other hand provided in this paper Digital Rock Physics calculations and results of flow modelling shed

light on the benefits of this techniques in order to explain discrepancies due to heterogeneity and tremendous influence of

compaction and cementation which are the cause of very complex flow paths in tight gas or low permeability sandstones

Moreover this paper presents a novel methodology for classifying sampling and imaging a 1rdquo core-plug such that essential

heterogeneity is maintained throughout the workflow This is applied to a subsurface sample from the Rotleigend sandstone a

Central European reservoir showing strong lamination on the mm-cm scale First the entire core-plug sample was imaged with a

resolution of around 19microm While the pore structure was not resolvable macroscopic bedding related heterogeneity was along

with a prominent fracture This image was classified creating a label image where each voxel was either labelled as a ldquohigh

porosityrdquo ldquolow porosityrdquo or fracture Locations for high resolution (1-3microm) non-destructive interior tomographies were defined

using this macroscopic lithological map As mechanical sample extraction was not required sample sites could be much more

accurately identified and the association between litho-type and microscopic structure maintained

Permeability tensors were calculated for each interior image A second model was then constructed using the macroscopically

classified image so each voxel from the high porosity and low porosity lithologies were populated with the associated average

permeability tensor derived from the high resolution images A simulation was then performed computing stokes flow through

the macroscopically visible fracture and Darcy flow through the microscopically sampled lithologies The resulting permeability

tensor was highly anisotropic with a high permeability in directions parallel to layering and low permeabilities perpendicular to

it This result was only possible because the cm scale heterogeneity associated with primary sedimentary layering was maintained

through the macroscopic model

The research leading to these results has received funding from the Polish-Norwegian Research Programme operated by the National Centre

for Research and Development under the Norwegian Financial Mechanism 2009-2014 in the frame of Project Contract No Pol-

Nor196923492013

In addition we wish to thank the Carl Zeiss Microscopy and Math2Market who developed presented methodology with Oil and Gas Institute ndash National Research Institute

References [1] Ringrose PS Martinius W Alvestad J Multiscale geological reservoir modelling in practice Geol Soc London

Spec Publ 309 123ndash134 2008

[2] Such P Maliszewska A Leśniak G Właściwości filtracyjnego utworoacutew goacuternego czerwonego spągowca a jego

wykształcenie facjalne Prace IGNiG 104 ISSN 0209 07241999

[3] Such P Leśniak G Słota M Quantitative porosity and permeability characterization of potential Rotliegend tight gas

reservoirs Przegląd Geologiczny Vol 58 4 p 347 351 2010

[4] Leśniak G Such P Fractal approach Analysis of images and diagenesis in pore space evaluation Natural Resources

Research 14 4 p 317 324 ISNN 1520 7439 2005


Pore scale modelling of fluid transport using FIB-SEM images Grzegorz Leśniak Karol Spunda Renata Cicha-Szot


cichainigpl

Keywords pore scale network modelling FIB-SEM

Pore scale imaging and modelling using focused ion beam scanning electron microscope (FIB-SEM) images develops into the

most robust technology which allows to characterize porous rock not only from the mineralogical geochemical or petrographic

point of view but also quantify petrophysical parameters such as porosity (effective and total) and permeability

This paper presents the workflow developed for examination and estimation of basic parameters such us porosity and permeability

of one of the most complicated porous system which is heterogeneous shale gas rocks using FIB-SEM images Based on the high

resolution maps (HRI) and SEM images which were take after ion beam polishing of sample surface spots for more detailed 3D

reconstruction are chosen Using ion beam mounted on the Helios NanoLab 450HP further analysis of sample by etching 20nm

slices of rocks using Auto Slice ampView automated serial sectioning and imaging through a defined volume of a specimen was

performed The sequence of images captured by Auto Slice ampView was used as input for 3-dimensional reconstruction of the

sliced volume One of the crucial step is parametrization of obtained results which was performed in this work using Avizo 3D

software (Table 1)

Table 1 Example of results obtained from the pore space 3D reconstruction

Sample No No of pores

Median of pore

volume

[nm3]

Maximum

pore volume

[nm3]

Median of

pore surface

[m2]

Maximum pore

surface

[nm3]

A-1 715 525middot105 156middot109 464middot104 449middot107

B-1 2617 160middot104 162middot108 319middot103 742middot106

Obtained results allow us to perform evaluation based on the coupling of the Navier-Stokes and Darcy equations for modeling the

porous media flows of selected region with interconnected pore structures (w kierunkach XYZ)

Fig1 Model of fluid flow in the X-XY axis The lines on the left illustrate gas inflow in the pore space the lines on the right of

the sample gas outflow [1]

Results obtained from simulation and modelling were compared to standard porosity and permeability measurements

The paper concludes by discussing limitations and challenges including finding representative samples imaging and simulating

flow and transport in pore space over several orders of magnitude in size and interpretation obtained values to reservoir conditions

We conclude that pore scale modeling gives satisfactory results which might be applied to developed petrophysical models

however it needs to be used with caution due to sample size and different stress conditions adopt during FIB-SEM imaging

The research leading to these results were performed within the project Methodology for sweet spots determination based on geochemical

petrophysical and geomechanical properties based on the correlation between laboratory investigations and geophysical measurements and a 3D generation model co-funded by the National Centre for Research and Development as part of the programme BLUE GAS ndash POLISH SHALE


References [1] Leśniak G Such P MroczkowskandashSzerszeń M Dudek L Cicha-Szot R Spunda K Metodyka analizy przestrzeni porowej

skał łupkowych Intytut nafty i Gazu ndash Państwowy Instytut Badawczy 2017 ISSN 2353-2718


Reliability of the tortuosity value obtained

on the basis of other parameters of the porous bed Seweryn Lipiński1 Wojciech Sobieski2

1 Department of Electric and Power Engineering Electronics and Automation 2 Department of Mechanics and Basics of Machine Construction

Faculty of Technical Sciences University of Warmia and Mazury in Olsztyn

sewerynlipinskiuwmedupl

Keywords granular beds tortuosity porosity

Tortuosity τ is one of the most important parameters describing porous media It is defined as the ratio of the length of the actual

path through pore channels to the thickness of the considered medium along the chosen axis [1] Tortuosity may be understood

as a geometrical quantity or as a flow property In the first case it is referenced as geometric tortuosity while in the second case

as hydraulic or diffusive tortuosity [2] The paper considers the first understanding of the term In general geometric tortuosity

can be obtained in many different ways ie experimentally numerically or indirectly - through relationship with other

parameter(s) of the analysed porous bed [3] The last approach is the most common one as it is the simplest but there appears a

problem of reliability of the tortuosity value when obtained on the basis of other parameters of the porous bed This particular

issue is being considered in this paper

A set of virtual porous beds consisting of spherical particles was analysed The set was created with the use of Discrete Element

Method and it consists of 75 beds with common mean value of particles diameters (6072 mm) and 25 values of standard deviation

(each bed was created three times hence 75 beds) Particles diameters were normally distributed

For each virtual porous bed we calculated a set of parameters describing it including ia porosity and tortuosity (using the so-

called Path Tracking Method [4]) Then we obtained approximation functions linking these parameters with standard deviation of

the particles diameters Optimal approximation functions for tortuosity τ and porosity oslash were as follows

120591 = 1208 + 0006∙ 119890154120590 (1)

oslash = 04124 + 00005σ - 00013 1205902 (2)

Above equations were used for comparison of obtained values of tortuosity with values obtained based on relationships between

tortuosity and porosity [3] We used 8 functions linking porosity with tortuosity as well as Eq 1 The achieved results given as a

function of standard deviation are shown in Fig 1

Fig1 Tortuosity vs standard deviation of particles diameters obtained using various analytical formulas and using Eq 1

As it can be seen obtained curves differ significantly but their common feature is the increase of tortuosity value with the

increase of standard deviation This increase is the most noticeable for the Eq 1 what suggests that literature relationships between

tortuosity and porosity underestimate the influence of standard deviation on the parameters of porous beds Both these observation

lead to the conclusion that the use of literature functions linking porosity with tortuosity is not advisable approach

References [1] Latour LL Kleinberg RL Mitra PP Sotak CH Pore-size distributions and tortuosity in heterogeneous porous media

Journal of Magnetic Resonance A 112(1) 83-91 1995

[2] Clennell M B Tortuosity a guide through the maze Geological Society London Special Publications 122(1) 299-344 1997

[3] Sobieski W Lipiński S The analysis of relations between porosity and tortuosity in granular beds Technical Sciences 20(1)

75-85 2017

[4] Sobieski W The use of Path Tracking Method for determining the tortuosity field in a porous bed Granular Matter 18(3) 72

2016

09

1

11

12

13

14

15

16

17

0 01 02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18 19

Tort

uo

sity

[-]

Standard deviation of particles diameter [mm]

Eq (1) Maxwell (1981) Weissberg (1963)

Kim et al (1987) Comiti amp Renaud (1989) Iversen amp Jorgensen (1993)

Boudreau (1996) Lanfrey et al (2010) Liu ampKitanidis (2013)


Relations between the various probability density functions

describing the distribution of particles in a granular bed Seweryn Lipiński Zenon Syroka

Department of Electric and Power Engineering Electronics and Automation Faculty of Technical Sciences

University of Warmia and Mazury in Olsztyn


Keywords particle size distribution probability density functions granular beds

One of the most important topics in the field of granular beds research is the analysis of the particle size distribution (PSD) -

regardless of whether it is the bed of natural or artificial origin [1] It is very important in understanding its physical and chemical

properties as it affects inter alia the strength and load-bearing properties of rocks and soils as well as the reactivity of solids that

is why PSD needs to be strictly controlled in many industrial products [2-6]

There is many probability distribution functions which are being used for the purpose of description of particle size distribution

The most commonly used are the log-normal (Galton) distribution the Weibull distribution (also known as RosinndashRammler

distribution) the log-hyperbolic distribution and the skew log-Laplace distribution but there are many other distributions being

used for that purpose many of them was developed strictly for the purpose of granular media description Particular attention

should be paid to the following types of distributions Anderson Freacutechet Fredlund GatesndashGaudinndashSchuhmann Gompertz

Gumbel Jaky Johnson Sb LifshitzndashSlyozovndashWagner NukiyamandashTanasawa and Skaggs [7-11] Thera are also modifications of

basic distributions that are being utilized for the purpose of granular beds description [812]

Such big number of various distributions being used to describe the granular beds raises a question about the relationships

between them and that is the main subject of our research An attempt was made to find mathematical relationships between most

important probability distributions A network of dependencies between the most commonly used distribution types has been built

including inter alia distributions of Gompertz Gumbel Freacutechet and Weibull Knowledge on this subject makes it possible to

analyse and compare granular beds described with the use of different models

References [1] Lipiński S Pozyskiwanie informacji o typie rozkładu złoża granularnego oraz generacja rozkładoacutew wirtualnych Granularne

ośrodki porowate University of Warmia and Mazury in Olsztyn Publishing House 57-70 2016

[2] Grace JR Sun G Influence of particle size distribution on the performance of fluidized bed reactors The Canadian Journal

of Chemical Engineering 69(5) 1126-1134 1991

[3] Meddah MS Zitouni S Belacircabes S Effect of content and particle size distribution of coarse aggregate on the compressive

strength of concrete Construction and Building Materials 24(4) 505-512 2010

[4] Nan C W Clarke DR The influence of particle size and particle fracture on the elasticplastic deformation of metal matrix

composites Acta Materialia 44(9) 3801-3811 1996

[5] Servais C Jones R Roberts I The influence of particle size distribution on the processing of food Journal of Food

Engineering 51(3) 201-208 2002

[6] Verbeek CJR The influence of interfacial adhesion particle size and size distribution on the predicted mechanical properties

of particulate thermoplastic composites Materials Letters 57(13-14) 1919-1924 2003

[7] Gonzaacutelez-Tello P Camacho F Vicaria JM Gonzaacutelez PA A modified NukiyamandashTanasawa distribution function and a

RosinndashRammler model for the particle-size-distribution analysis Powder Technology 186(3) 278-281 2008

[8] Hwang SI Lee KP Lee DS Powers S E Models for estimating soil particle-size distributions Soil Science Society of

America Journal 66(4) 1143-1150 2002

[9] Macıas-Garcıa A Cuerda-Correa EM Dıaz-Dıez MA Application of the RosinndashRammler and GatesndashGaudinndashSchuhmann

models to the particle size distribution analysis of agglomerated cork Materials Characterization 52(2) 159-164 2004

[10] Nabizadeh E Harchegani HB Performance of Eight Mathematical Models in Describing Particle Size Distribution of Some

Soils from Charmahal-va-Bakhtiari Province Journal of Water and Soil Science 15(57) 63-75 2011

[11] Taşdemir A Taşdemir T A comparative study on PSD models for chromite ores comminuted by different devices Particle

and Particle Systems Characterization 26(1‐2) 69-79 2009

[12] Hwang SI Effect of texture on the performance of soil particle-size distribution models Geoderma 123(3) 363-371 2004



Euler-Lagrange model in spout-fluid bed apparatus Wojciech Ludwig1

1Wroclaw University of Technology Faculty of Chemistry Department of Chemical Engineering

wojciechludwigpwredupl

Keywords friction coefficient tangential restitution coefficient particles velocity

The presented paper is a continuation of research concerning gas-solid flow modelling using the Euler-Lagrange approach in a

spout-fluid bed apparatus with a circulating dilute bed [1] The greatest problem in this case was to determine the friction

coefficient for particles hitting against the walls of the apparatus On the basis of the properties of similar materials the value of

this quantity was estimated at 02 Therefore it proved useful to check the modelrsquos sensitivity to the value of this parameter The

study investigated the effect of friction coefficient in the range of 01-04 on calculated values of particles velocity in the draft

tube and the annular zone of the device for various masses of the circulating bed (from 100 to 390 g)

The flow of the dispersed phase elements (microcrystalline cellulose particles Celletsreg 1000) was modelled by solving the

motion equation individually for each particle Due to the low value of the solid volume fraction interactions between particles

were neglected and the main focus was on the description of particle collisions with the walls of the device The hard-sphere

method was applied assuming that all particle-wall interactions are binary and immediate (the contact time is infinitely small) and

contact forces are impulsive Particles have a spherical shape and their shape is preserved after collision During the point contact

between particles and the wall the particles undergo normal and tangential deformations resulting from the elastic forces The

tangential and normal components of the velocity after collision are calculated as the product of their pre-impact values multiplied

by the corresponding restitution coefficients Particle impact collisions with the wall were divided into elastic and elastoplastic

ones which were diagnosed on the basis of the yield velocity Vy depending only on the physical properties of the material

(microcrystalline cellulose) and the wall (glass and aluminium) such as Youngrsquos modulus Poissonrsquos ratio plasticizing pressure

The normal restitution coefficient en depending only on the normal component of the incident velocity Vni was based on the

Thorton model [2 3]

119890119899 =

(1 minus

073 11988111989911989435

100 )05

119881119899119894 lt 119881119910

(6radic3

5) [1 minus

1

6(119881119910

119881119899119894)2]

1

2

(119881119910

119881119899119894) [(

119881119910

119881119899119894) + 2radic12 minus 02 (

119881119910

119881119899119894)2]

minus1

1

4

119881119899119894 gt 119881119910

(1)

In order to calculate the tangential restitution coefficient a kinematic model of Wu et al [4] was used It makes the value of the

tangential coefficient of restitution et dependent on the angle of incidence normal restitution coefficient and friction coefficient

for the particle colliding with the wall [4]

119890119905 = 1 minus

2

120553[1198881 + 1198882 119905119886119899ℎ(1198883 + 1198884120553)] 120553 lt 120553119888119903119894119905

1 minus2

120553 120553 ge 120553119888119903119894119905

(2)

120553 =2

(1+119890119899)120583119905119886119899(90deg minus 120579) (3)

where c1c2c3c4 - equation constants 120553119888119903119894119905 - dimensionless critical angle of incidence 120553 - dimensionless angle of incidence 120579 - angle of incidence en - normal coefficient of restitution micro - friction coefficient

In the course of calculations a relatively small influence of friction coefficient on particles velocity was observed in the tested

zones of the apparatus Its increase by 300 from 01 to 04 caused an increase in particles velocity in the draft tube by maximum

16 (on average 14 ) while its decrease in the annular zone by maximum 25 (on average 18 ) The changes were most

visible for large masses of the bed which was connected with an increase in the number of collisions of particles with the walls

The different dependency of particle velocity on the friction coefficient in the draft tube and the annular zone results from the

properties of equation (2) According to it in the area of low test angles (below approximately 700 depending on the normal

restitution coefficient) an increase in the value of the coefficient of friction causes a decrease in the tangential restitution

coefficient For high incidence angles this relationship is reversed A relatively small number of collisions with a high incidence

angle occur in the draft tube especially in the bottom part of the apparatus where the bed is intensively circulating In the annular

zone on the other hand the collisions are more frequent and the particles collide with the walls at low angles

On the basis of the conducted tests it can be concluded that a possible error in estimating the value of the friction coefficient

for particles colliding with the walls of the apparatus has little influence on the accuracy of calculation of the dispersed phase

velocity by means of the applied model

Acknowledgments

The studies were funded by the Polish National Science Centre within the framework of the research grant UMO-

201309BST800157

References [1] Ludwig W Płuszka P Euler-Lagrange model of particles circulation in a spout-fluid bed apparatus for dry coating Powder

Technol 328 375-388 2018

[2] Wu CY Li LY Thornton C Energy dissipation during normal impact of elastic and elastic-plastic spheres Int J Impact

Eng 32 593-604 2005

[3] Thornton C Coefficient of restitution for collinear collisions of elastic-perfectly plastic spheres J Appl Mech 64 383-386

1997

[4] Wu CY Thornton C Li LY A semi-analytical model for oblique impacts of elastoplastic spheres Proc R Soc A 465

937ndash960 2009


Analysis of Influence of Model Parameters

on the Capillary Imbibition of Porous Materials with Liquid Janusz Łukowski1 Mieczysław Cieszko2



januszlukwedup1l cieszkoukwedupl2

Keywords unsaturated porous materials macroscopic process of fluid imbibition numerical analysis

Numerical analysis of influence of model parameters on the capillary imbibition of porous materials with liquid is performed A

new macroscopic description of fluid imbibition is proposed based on the continuum model of the capillary transport of liquid

and gas in unsaturated porous materials of homogeneous and isotropic pore space structure proposed in the paper [1] The key

assumptions of this model are division of liquid in the pore space into two macroscopic constituents called mobile liquid and

capillary liquid description of menisci motion by an additional macroscopic velocity field parametrization of saturation changes

by a macroscopic pressure-like quantity that for quasi static and stationary processes is equal to the capillary pressure This model

significantly changes the image of processes of liquid and gas capillary transport in an unsaturated porous material It shows that

these processes are running in a five dimensional pressure-time-space continuum and quasi static processes of intrusion and

extrusion of non-wetting liquid are non-stationary processes running in pressure-space continuum

A one dimensional system is considered composed of two half spaces (Fig1) The half space z gt 0 is occupied by

undeformable porous material filled with gas (air) whereas the half space z lt 0 is occupied by incompressible wetting fluid

(water) We analyze a nonstationary process of liquid imbibition of the porous material caused by the capillary forces and impeded

by the gravity and viscous interactions of liquid with the skeleton It is assumed that gas is inert and its pressure is constant The

inertial forces in the mobile liquid are omitted and at the beginning of the process liquid is present at the contact surface z = 0

Fig1 Scheme of the analyzed system

The system of equations describing nonstationary imbibition process is composed of balance equations for mass and for linear

momentum of the mobile liquid evolution equation for saturation constitutive equations for the stress tensor and viscous

interaction force of the mobile liquid with the skeleton for velocity of diffusive transport of menisci and for relation between

saturations with the mobile and capillary liquids For the limit case of static distribution of the mobile liquid attained at the end of

the imbibition process the system of equations takes the form

)()(1

2

psCp

sg

dz

spsC

ds

ds

p

sms

mm

mmm

m

cm

(1)

gdz

dpm (2)

where pgss mcm are saturations with the mobile and capillary liquid mass density gravity acceleration and pressure

respectively Quantities )()( psCpsC msmm have the form

119862119898(119904119898 119901) =1

119904119898(119901

119901119900)119898

119862119904(119904119898 119901) = 119904119898 (119901

119901119900)minus119899

(3)

and are coefficients characterizing menisci transport in the pore space They are directly related with the pore space structure of

the porous material Equation (1) is strongly nonlinear differential equation of the first order and is solved using the method of

characteristics Analysis of influence of model parameters on the imbibition process has been performed numerically

References [1] Cieszko M Macroscopic Description of Capillary Transport of Liquid and Gas in Unsaturated Porous Materials Meccanica

22 1-22 2016


Possibilities of using glass microspheres to build models and simulation of fluid flow

through geological strata Marcin Majkrzak

Department of Petroleum Engineering Oil and Gas Institute ndash National Research Institute Cracow

majkrzakinigpl

Keywords glass microspheres glass bed packs fluid flow simulation

This paper presents the results of evaluation potential possibilities of using glass microspheres to build glass bed packs and

simulation of fluid flow through created porous models

Although using original core samples enable initiate real petrophysical parameters of the porous media it has also some limitation

One of the most important limit is the fact that core samples are very valuable therefore it is impossible to carry out this type of

research on a large scale Moreover in many cases they can be used just one time (destructive measurements) The alternative is

models of porous media made of sands or glass microspheres with known granulation Projects that were performed by many

researches [1] [2] [3] indicate satisfactory results of using homogenous glass beds models which opens up a new perspective area

for flow simulation of multiphase systems

Fig1Measurement equipment (TEMCO CO) with model of glass bed pack

For the need of the task several models (glass microspheres with known granulation) with various structures and layers layout

were built and characterized in terms of their basic petrophysical and filtration properties ndash pore volume porosity absolute

permeability for gas and brine relative permeability for oil The final part of work was to define recovery factor (the recoverable

amount of hydrocarbon initially in place) for each of model Additional comparison of permeability results obtained from

measurements performed on glass bed pack to values for theoretical model of parallel and vertical layers were carried out

References [1] Mai A Kantzas A Heavy Oil Water Flooding Effects of Flow Rate and Oil Viscosity Journal of Canadian Petroleum

Technology 48 42-51 2009

[2] Mai A Kantzas A Improved Heavy Oil Recovery by Low Rate Waterflooding SPE International Thermal Operations and

Heavy Oil Symposium Calgary 2008

[3] Metin C O Bonnecaze R T Nguyen Q P The Viscosity of Silica Nanoparticle Dispersions in Permeable Media SPE

International Oilfield Nanotechnology Conference Noordwijk 2012


Application of 3D printing technology to random porous structures study Ewelina Małek Danuta Miedzińska Wiesław Szymczyk Arkadiusz Popławski

Military University of Technology Faculty of Mechanical Engineering Urbanowicza 2 St 00-908 Warsaw Poland

ewelinamalekwatedupl

Keywords Rapid Prototyping SLA (stereolitography) Fractal Models

In the field of numerical research there are various approaches and methods for modeling structures of porous materials

Therefore various material models are used for numerical analyzes of materials such as among others ceramics metallic foams

ceramic or metal composites In the case of modeling of natural porous structures for example rocks their complex structure

prevents the identification of properties and finding of material data As a consequence there is a problem with modeling the

structure of these materials The solution is the use of fractal models to modeling of porous structure [12]

An example of geometry of fractal model built on the basis of a spatial raster is Mengers sponge (Fig1) On each of the walls

of the sponge the Sierpinski carpet pattern is visible [3]

Fig1 Fractal models - Sierpinski carpet (2D structure) and Mengers sponge (3D structure) [3]

In the case of modeling the geometry of natural (random) materials there is a problem of compatibility of the FEM geometry

and real geometry This is a source of differences between the results of calculations and experimental results Application of 3D

printing technology will allow to receive a real structure in a controlled manner which exactly reflects the designed structure and

is consistent with the geometry of the numerical model The 3D printing technique used is the stereolithography method which

consists in selectively fixing the layer-applied resin with UV laser rays (Fig2) [4]

Fig2 Schematic of the upside-down SLA system [4]

An experimental research on the standard samples made of photopolymer resin using 3D printing technique is presented in

the paper The aim of the research was to determine the base material properties and consequently to select the constitutive model

necessary to carry out numerical analyses Variants of own geometry of models simulating the structure of porous materials based

on the basic fractal model were also presented

Acknowledgements

The paper supported by a grant No BG2DIOX4SHELL14 financed in the years 2014-2018 by The National Centre for

Research and Development Poland

References [1] Banhart J Manufacture characterization and application of cellular metals and metal foams Progress in Materials Science

46 559ndash632 2001

[2] Mills N J The high strain mechanical response of the wet Kelvin model for open-cell foams International Journal of Solids

and Structure 44 1 51-65 2007

[3] Menger K Classics on fractals Studies in Nonlinearity Westview Press 2004

[4] The Ultimate Guide to Stereolithography (SLA) 3D Printing Marzec 2017 formlabscom


Effect of polypropylene fiber addition on mechanical properties

of concrete based on portland cement Marcin Małek1 Wojciech Życiński1 Mateusz Jackowski1 Marcin Wachowski2 and Waldemar Łasica1

1Military University of Technology Faculty of Civil Engineering and Geodesy Warsaw Poland 2Military University of Technology Faculty of Mechanical Engineering Warsaw Poland

e-mailmarcinmalekwatedupl

Keywords polypropylene fiber concrete mechanical properties

Negative features of traditional concrete can be eliminated by using dispersed fibers in a concrete mixtures These fibers after

mixing process form composite materials called fibre concrete whose tensile strength and resistance to fatigue is higher than in

traditional concrete materials [1]

On the one hand in fiber concrete material concrete provides high compressive strength stiffness and provides fiber protection

against corrosion but on the other hand the fibers provide tensile strength and reduce shrinkage causes cracks in the concrete

Both elements are complement each other [2]

Due to the application and properties fibres can be divided into three groups of materials polymer fibers steel fibers and carbon

fibers [3] The smallest and lightest of the whole group are polypropylene fibers Most often they are added in an amount of about

06 kg m3 of concrete mixtures Their dispersion strengthens the structure of concrete in all directions Their main task is to

reduce the contraction of concrete especially during its first binding phase The shrinkage cracks are small irregular and appear

most often within 24 hours of laying the concrete mixtures These cracks are caused by plastic shrinkage or by the drying process

of concrete [4]

In this work results of polypropylene fibers addition into concrete mixture based on portland cement was characterized The

main purpose of this research was to identify directly influence fibers addition on concrete mechanical strength The recipe of

concrete was prepared using three types of aggregates 0125 ndash 0250 0250 ndash 0500 and 0500 ndash 1000 mm To identify structures

of researched samples and fibres SEM and LM observation were widely done Basic properties of concrete mixture were defined

by chemical composition sieve curve slump cone test and setting time Mechanical properties such as compressive strength and

bending test after 1 7 14 and 28 days were characterized Obtained results was compare with mixtures without fibers

modifications Study was proven that all chosen modifiers revealed increase effect on final mechanical properties and are very

perspective for future application in concrete technology

References [1 Shankar GRV Sundarraja MC Kim YY Prabhu GG Using carbon-fibre-reinforced polymer to strengthen concrete-

filled steel tubular columns Proceedings of the Institution of Civil Engineers-Structures and Buildings Volume 170 Issue

12 Pages 917-927 2017

[2] Wattick JA Chen A Development of a prototype fiber Reinforced Polymer - Concrete Filled wall panel Engineering

Structures Volume 147 Pages 297-308 2017

[3] Mansour R El Abidine RZ Brahim B Performance of polymer concrete incorporating waste marble and alfa fibers

Advances in Concrete Construction Volume 5 Issue 4 Pages 331-343 2017

[4] Li W Huang Z Hu G Duan W H Shah SP Early-age shrinkage development of ultra-high-performance concrete

under heat curing treatment Construction and Building Materials Volume 131 Pages 767-774 2017


Numerical generation of a random packed bed of saddles Maciej Marek

Faculty of Mechanical Engineering and Computer Science Częstochowa University of Technology

Częstochowa Poland

e-mailmarekmimcpczczestpl

Keywords random packed bed porosity saddles DEM

Random packed beds have a large variety of applications They can be used eg in chemical engineering systems as a means

for increasing the contact surface between reactants delivered as fluids either in counter- or co-current fashion Numerical

simulations of flows in such beds performed at the scale of individual particles require the details of the bed geometry to be

represented in the model The geometry can be obtained with the use of complex and expensive experimental techniques (eg

computer tomography) or in numerical simulations ndash much cheaper and promising alternative

The present work is devoted to numerical generation of a geometry of a random packed of saddles being a simplified variant of

Intalox saddles quite popular elements in packed columns The concept of the algorithm is an extension of the method presented

in [1] for cylinders and in [23] for rings packed in a cylindrical container Generation of the bed is treated as the simulation of the

filling process with simplified mechanics The particles are added to the structure in a sequential manner they move due to gravity

and reaction forces from other elements and the containerrsquos wall until they reach the state of mechanical equilibrium The reaction

force resulting from the contact between the active particle and the bed depends on the overlap between the particles In order to

facilitate the calculation of the overlap the active particle is covered with a uniform grid of markers Packing density is increased

by additional artificial force acting in the direction from the containerrsquos axis to its walls

Fig1 Subsequent steps in generation of the random packed bed

The final outcome of the work which will be shown during the presentation includes sample geometries of beds of saddles

(Fig 1) characteristics of such beds (global porosity distribution of local porosity orientation of particles) and their dependence

on the particular dimensions of individual particles

Acknowledgements

This study was performed within the framework of the contract UMO-201415BST804762 funded by National Science

Centre

References [1] Marek M Numerical generation of a fixed bed structure Chemical and Process Engineering 34(3) 347-359 2013

[2] Marek M Numerical simulation of a gas flow in a real geometry of random packed of Raschig rings Chemical Engineering

Science 161 382-393 2017

[3] Niegodajew P Marek M Analysis of orientation distribution in numerically generated random packings of Raschig rings in

a cylindrical container Powder Technology 297193-201 2016


Sludge dewatering by thin-film freezing in the north-east of Poland Kinga Michalak Janusz A Szpaczyński

Wrocław University of Science and Technology Faculty of Mechanical and Power Engineering

jaszpaczynskigmailcom

Keywords sludge dewatering freezethaw

Sludge dewatering and disposal is still one of the most pressing research needs in recent years Scientists and

technologists are constantly looking for new more effective methods of sludge dewatering In northern climate particular interest

is currently placed on the use of natural freezing The freezing process uses the fact that the crystallographic structure of the ice

makes it difficult to absorb contaminants in the form of a solid or dissolved phase The solid particles are pushed by the ice crystals

that incorporate only pure water Frozen water in the form of ice creates frozen channels in sludge After melting free spaces are

created which are used by melt water to flow out Freezethaw process can replace the use of chemical conditioners improve

efficiency of dewatering filterability [1] and can significantly reduce OampM costs In a cold climate the freezing process can be

carried out without significant energy inputs using negative ambient temperatures in the winter

In the paper several sets of samples of clay sludge were frozen and after that lyophilized to reveal the pore structure

(Fig 1 2) Tests with melting and drying of samples showed deformation of pores Only lyophilisation of samples allowed

examining the structure of sludge after freezing

Fig 1 Sludge before freezing Fig 2 Sludge after freezing and lyophilisation

Although most of application of freezethaw for sludge dewatering are reported from Canada and USA it is possible to use this

method in Poland too Based on the weather data from the last ten years obtained from the Institute of Meteorology and Water

Management for the Suwałki region a simulation of thin-layer freezing in a settling tank was carried out Sludge was loaded by 8

cm high layers To simulate the time of freezing a model developed by Martel [2] was used The results are shown in Fig 3

Fig 3 Calculated depth of frozen sludge for Suwałki region

The coldest winter was in 2009 and 2010 It was possible to freeze almost 3 m of sludge It should be noted that freezing can

be used interchangeably with mechanical dewatering On cold nights the sludge can be frozen In the case of positive

temperatures for an extended period of time the filtration press or solid bowl centrifuge can be used for sludge dewatering

References [1] Szpaczynski J Poprawa własności filtracyjnych i sedymentacyjnych zawiesin poprzez naturalny proces zamrażania Przemysł

Chemiczny 96 9 2017

[2] Martel C J Development and design of sludge freezing beds CRREL Report 88-20 1988


Numerical modeling of porous ceramics microstructure Danuta Miedzińska

Military University of Technology Urbanowicza 2 St 00-908 Warsaw

danutamiedzinskawatedupl

Keywords porous ceramics finite element method microstructure

Porous ceramics is a group of new and very interesting materials It can be used for thermal insulation filters bio-scaffolds for

tissue engineering and preforms for composite fabrication [1] One of the most interesting applications is usage of those materials

for production of proppants for hydraulic fracturing of shale rocks

Porous structure of a ceramic can be prepared through many processing techniques One technique is to simply sinter coarse

powders or partially sinter a green ceramic to hinder full densification [1] Other traditional methods of fabricating porous ceramics

can be divided into three basic processing techniques replica sacrificial template and direct foaming as seen in Fig 1 [2] The

development process influences the microstructure of the material what is presented in Fig 2

Fig1 Typical processing methods for the production of macroporous ceramics (a) replica technique (b) sacrificial template

technique and (c) direct foaming technique [2]

a) b)

Fig2 Porous ceramics microstructure a) grain structure made by sintering [3] structure made by replication [4]

In the paper the main interest is directed to the grain porous ceramics In the presented research the numerical modelling of

idealized microstructure of such structure was presented to study the influence of grains distribution on the porous ceramics

mechanical behaviour Some examples of the developed model are shown in Fig 3


Fig3 Geometry of numerical models of grain porous ceramics idealized structure

The analyses were conducted with the use of finite element method

Acknowledgements



References [1] Hammel EC Ighodaro OL-R Okoli OI Processing and properties of advanced porous ceramics An application based

review Ceramics International 40(10) 15351-15370 2014

[2] Studart AR Gonzenbach UT Tervoort E Gauckler LJ Processing routes to macroporous ceramics a review Journal of

the American Ceramic Society 89 1771-1789 2006

[3] httpwwwtech-ceramicscouk (access 25022018)

[4] Walsh D Boanini E Tanaka J Mann S Synthesis of tri-calcium phosphate sponges by interfacial deposition and thermal

transformation of self-supporting calcium phosphate films Journal of Materials Chemistry 15 1043-1048 2005


Application of silica gel in the process of trypsin immobilization Justyna Miłek Sylwia Kwiatkowska-Marks Ilona Trawczyńska

Faculty of Chemical Technology and Engineering University of Technology and Life Sciences Seminaryjna 3

85-326 Bydgoszcz Poland e-mailjmilekutpedupl

Keywords trypsin immobilization silica gel

Trypsin (EC 34214) is hydrolysis of proteins It causes certain peptide bonds to break decreasing the number of allergenic

proteins in hypoallergenic food production [1]

Enzyme immobilization on carriers may significantly contribute to cost reduction and improvement of the process due to the

reusability of the same portion [2] Process immobilization using involves several stages Firstly activation of the carrier is

conducted by attaching a reactive group then the enzyme attaches [3] Cross-linking agents can be glutaraldehyde and 3-

aminopropyltriethoxysilane [4] SHEN et al [4] presented that surface modification of silica nanoparticle by aminopropyl groups

(3-aminopropyltriethoxysilane) causes an increase in adsorption ability of bovine serum albumin (BSA) in comparison to

unmodified silica nanoparticles YANG et al [3] proved that activity of immobilized lipase on aminosilica gel activated by

glutaraldehyde is greater compared to immobilized lipase without being activated by glutaraldehyde Figure 1 illustrates the

process of trypsin immobilization on silica gel

Si

O

O

OH

Si

Si

Si

OHSi

OHSi

C2H5-Si-CH2-CH2-CH2NH2

OC2H5

OC2H5

50deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NH2

O

O

O O

25deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NO

O

H

O

Si

O

O

OH

Si

Si

O

OH

Si NO

O

NH

trypsintrypsin

(1)

(2) (3) Fig1 The process scheme of trypsin immobilization with the use of 3-APTES and glutaraldehyde

The aim of the study was to produce immobilized trypsin from bovine pancreas on modified silica gel in optimal conditions

Modification of silica gel by 3-aminopropyltriethoxysilane (3-APTES) and glutaraldehyde in immobilization process was

applied for the first time Activity of native and immobilized enzyme was measured using Kunitzrsquos method [5 6] Effects of

temperature within the range of 35-75 and pH between 3 and 9 on activity of native and immobilized trypsin on modified

silica gel were determined Reusability of the biocatalyst was also tested

Optimal conditions for production of immobilized trypsin on modified silica gel are as follows activation time of 10 3-

aminopropyltriethoxysilane solution 25 glutaraldehyde solution and trypsin solution is 120 minutes for each of the solutions

Optimal temperature and pH for immobilized trypsin is 55 and 76 respectively Immobilized trypsin on modified silica gel

stored for 14 days at 4 exhibits 75 of its activity After being reused for eight cycles immobilized trypsin on modified silica

gel exhibits 60 of its activity

References [1] Mohamad N R Marzuki N H C Buang N A Huyop F Waha R A Review Agriculture and environmental

biotechnology Biotechnology and Biotechnological Equipment 29 (2) 205-220 2015

[2] Acton Q A PhD (ed) Endopeptidases Advances in Research and Application 2011 (pp 159-160) A Scholarly Editions

eBook Atlanta Georgia USA 2012

[3] Yang G Wu J Xu G Yang L Comparative study of properties of immobilized lipase onto glutaraldehyde-activated

amino-silica gel via different methods Colloids and Surfaces B Biointerfaces 78 351ndash356 2010

[4] Shen S-C Ng WK Chia L Dong Y-C Tan RBH Sonochemical synthesis of (3-aminopropyl)triethoxysilane-modified

monodispersed silica nanoparticles for protein immobilization Materials Research Bulletin 461665ndash1669 2011

[5] Salara S Mehrnejada F Sajedib R H Arough J M Chitosan nanoparticles-trypsin interactions Bio-physicochemical

andmolecular dynamics simulation studies International Journal of Biological Macromolecules 103 902ndash909 2017

[6] Zhou C Wu X Jiang B Shen S Immobilization strategy of accessible transmission for trypsin to catalyze synthesis of

dipeptide in mesoporous suport Korean Journal of Chemical Engineering 28(12) 2300-2305 2011


Numerical modeling of cavitation phenomenon

in a small-sized converging-diverging nozzle Agnieszka Niedźwiedzka

Department of Mechanics and Basics of Machine Construction Faculty of Technical Sciences

University of Warmia and Mazury in Poland

agnieszkaniedzwiedzkauwmedupl

Keywords cavitation converging-diverging nozzle homogeneous approach

Cavitation is a phenomenon of liquid evaporation in the areas where the static fluid pressure drops below the saturated vapour

pressure at the given temperature Until today appeared many methods of numerical modeling of this phenomenon These methods

include a one-fluid method with the homogeneous approach In this approach apart from the balance equations of mass

momentum and energy an additional transport equation is solved Niedźwiedzka et al [1] summarized and compared the most

important homogeneous cavitation models

Although cavitation is an undesirable phenomenon because it causes noise and erosion there are a small number of devices

where cavitation is required These group of devices include small-sized converging-diverging nozzles The main role of

converging-diverging nozzles is the control of mass flow rate Small sized converging-diverging nozzles deliver constantly a very

small liquid flow rate and for that reason they find application in eg lab scale monopropellants or hybrid rocket motors

The main aim of numerical simulations is to predict the area of cavitation and based on these data to modify the construction

of the chosen devices to minimalize the negative consequences of this phenomenon In the case of the small-sized converging-

diverging nozzles the high-pressure cavitating flow is observed Numerical modeling of cavitating flow is very difficult because

the phenomenon is until today not enough physically explained and mathematically described The factor which additionally

makes the simulations more difficult are the high-pressure conditions

The main aim of the presented research is to show results of numerical calculations of cavitating flow in an example of small-

sized converging-diverging nozzle using the homogeneous cavitation model ndash the Schnerr and Sauer model The motivation to the

research is lack of any material about simulations of the high-speed cavitating flow in the small-sized converging-diverging

nozzles with the small throat ratio in the literature Some experimental measurements considering these devices have been already

published [2] The source terms of the Schnerr and Sauer model for the evaporation and condensation are formulated respectively

as follows

+ =120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(1)

+ = minus120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(2)

The transient simulations were performed using Fluent software The time step was 000003 s The boundary conditions are

defined as follow velocity inlet ndash 05 ms pressure outlet ndash 101325 Pa turbulence model ndash k-ε model The achieved contours of

vapour volume fraction are presented in Fig 1

Fig1 The contours of vapour volume fraction in the analysed converging-diverging nozzle

The main aim of the research was achieved In the numerical calculations using Fluent software were obtained the contours of

the vapour volume fraction It was established that the biggest intensity of the cavitation phenomenon was observed in the throat

In the downstream region appeared the cavitation cloud The area and the intensity of the cavitation cloud changes in the time

Also the periodicity of this phenomenon is visible To have a comprehensive picture of the high-pressure cavitating flow in the

analysed small-sized converging-diverging nozzle with a small throat ratio is necessary to conduct more simulations considering

other homogeneous cavitation models

References [1] Niedźwiedzka A Schnerr G H Sobieski W Review of numerical models of cavitating flows with the use of the homogeneous

approach Archives of thermodynamics 37 (2) 71-88 2016

[2] Niedźwiedzka A Sobieski W Analytical analysis of cavitating flow in Venturi tube on the basis of experimental data

Technical Sciences 19(3) 215-229 2016

[3] Schnerr G H Sauer J Physical and numerical modeling of unsteady cavitation dynamics In Proceedings of the Fourth

International Conference on Multiphase Flow (ICMFrsquo01) New Orleans USA 2001

[4] Singhal A K Athavale M M Li H Jiang Y Mathematical basis and validation of the full cavitation model Journal of

Fluids Engineering 124 617ndash624 2002

[5] Zwart P J Gerber A G Belamri T A two-phase flow model for prediction cavitation dynamics In Proceedings of the Fifth

International Conference on Multiphase Flow (ICMF 2004) Yokohama Japan 2004


The influence of comminution degree on structural properties of rocks of various porous

structure Anna Pajdak


pajdakimg-pankrakowpl

Keywords rock porosity coal structure dolomite structure

The knowledge of structural parameters of rocks such as surface area the size and the distribution of pores is important from the

point of view of the extraction enrichment and technological use of rocks

This paper presents the results of structural analyses of the two types of rocks that differ considerably in terms of their porous

structure coal and dolomite of different grain fractions Coal has a developed system of pores of which 90 are micropores and

submicropores [1] [2] [3] Submicropores are flexible in relation to sorbed particles of gas and the diffusion into them requires a

certain activation energy Their share in the deposition of sorbent particles is the biggest The porous structure of dolomite is

dominated by mesopores and macropores (according to UIPAC classification [4]) Those pores are of various sizes and shapes

They can function as transporters of gas in the rock strata or they can be spaces that have no contact with the outside [5] [6]

The author analyzed three coal samples from different mines and three samples of dolomite from OZG Polkowice-Sieroszowice

copper mine Each sample was crushed to a few grain fractions and was subjected to surface structural analysis using volumetric

low-pressure gas adsorption method For each grain fraction the author determined the sorption capacity in relation to nitrogen

(77K) and carbon dioxide (273K) in the absolute pressure range from 0 bar to 1 bar On the basis of the adsorption measurements

and using the Langmuir BET and BJH (Barrett Joyner and Halenda) models as well as classical pore distribution models the

author described the porous texture of those materials The author determined the surface area mean pore size and mean pore

volume which varied depending of the type of the sample and its grain size

The analysis revealed structural diversity of the analyzed rocks which was determined by the type of porosity and degree of

comminution On the basis of the degree of the diversity the author correlated the structural parameters and the grain size

References [1] Kreiner K Żyła M Binary character of surface of coal Goacuternictwo i Geoinżynieria 30 2 2006

[2] Pajdak A Skoczylas N Comparison of surface area and pore size distribution of coal use of sorption methods at different

temperatures Prace IMG PAN 16 3-4 2014

[3] Pajdak A Theoretical models of the surface area and the distribution of the pores as a tool of analysing the equilibrium data

of a low-pressure CO2 adsorption on carbon adsorbents Prace IMG PAN 16 3-4 2015

[4] IUPAC Physical chemistry division commission on colloid and surface chemistry subcommittee on characterization of porous

solids Recommendations for the characterization of porous solids Technical Report Pure and Applied Chemistry 66 8 1994

[5] Pajdak A Godyń K Kudasik M Murzyn T The use of selected research methods to describe the pore space of dolomite

from copper ore mine Poland Environmental Earth Sciences 76389 2017

[6] Pajdak A Kudasik M Structural and textural characteristic of selected copper-bearing rocks as one of the elements aiding

in the assessment of gasogeodynamic hazard Studia Geotechnica et Mechanica 39 2 51-59 2017


A multiparameter description of the rock-gas system by the use of original methods Norbert Skoczylas Mateusz Kudasik


skoczylasimg-pankrakowpl kudasikimg-pankrakowpl

Keywords rock-gas system exchange sorption under confining pressure

One of the main research topics that preoccupies the researches from The Strata Mechanics Research Institute of the Polish

Academy of Sciences concerns the rock-gas system We carry out basic research concerning both the presence of gas in rock and

its transport in porous structure of rock Also we determine parameters related to the presence of gas in rock for mining industry

On the basis of laboratory experiments and experiments in-situ we developed innovative and inventive research methods of the

rock-gas system analysis

Designed for the use in copper mines was a device that identifies the amount and the quality of gas in the porous structure of

dolomites and anhydrites and especially in their closed pores Scientific basis of the proposed method were presented The

fundamental measurement is based on the volumetric analysis supported by simultaneous analysis of pressure change

The paper presents the physical principles of the processes describing the rock-gas system on which the metrological concepts of

the presented methods are based as well as the way to evaluate the sorption parameters of coal We described a digital methane

emission reader ndash a metrological system that allows for the evaluation of desorbed amount of methane in coal and an effective

methane diffusion coefficient in coal under in-situ conditions

The paper also presents a unique in the world and innovative experimental rig together with the measurement methodology It was

developed for the purpose of thorough identification of the CO2CH4 exchange sorption in coal under confining pressure The

equipment allows for the analysis of the following phenomena changes of the sorption capacity of a sample resulting from the

changes of the confining pressure changes of the sorption capacity of a sample under various confining pressures for particular

points of sorption equilibrium the course of the exchange sorption process under various confining pressure and various pressure

gradient changes in the coal structure changes of the parameters describing filtration of gas through porous media under

changeable confining pressure and during the exchange sorption process The multitude of dependencies that can be observed and

evaluated in terms of quantity during the sorption experiments under confining pressure is a missing link of the broadly understood

analysis of the coal-gas system


Measurement of porosity of comminuted Salix Viminalis L in aspects of uncertainty of

measurement Karolina Słomka-Polonis1 Jakub Fitas1 Jakub Styks1 Bogusława Kordon-Łapczyńska1

1 University of Agriculture in Krakow Department of Mechanical Engineering and Agrophysics

karolinaslomka-polonisurkedupl

Keywords Porosimetry Measurement Density Salix Viminalis L

The knowledge of physical or mechanical properties of materials including biomass for energy production is of definite

importance for the identification of thermophysical properties modelling optimalisation and design of their thermal and

mechanical processing The density and porosity of biomass are among the more important properties widely used in description

and design of biomass processing Different methods of measuring these properties differ in regards to their accuracy Therefore

the aim of this paper was to analyse the influence of the method of measuring the porosity of comminuted willow Salix Viminalis

L on the value of measurement uncertainties Dried wood for dried substance was comminuted by a knife mill using three sieves

15 8 4 mm For porosity calculation in the first stage true and volumetric densities were assessed For each fraction the densities

were assessed by different devices AccuPyc II 1342 and GeoPyc 1365 pycnometers Using thus discerned density porosity was

indirectly measured for each fraction True density of willow was measured by AccuPyc II 1342 as 160439 kgm-3 Meanwhile

volumetric density was measured by the hydrostatic method where it was found equal to 61814 kgm-3 for the 15 mm fraction

63556 kgm-3 for 8 mm and 63684 kgm-3 for 4 mm (Tab 1) Basing on these measurements porosity was calculated for each

fraction as respectively 06147 06038 and 06031 In the course of research it was discovered that volumetric density

measurement by GeoPyc 1365 is not adequate therefore the resulting data were discarded

Table 1 Average physical parameters of the willow in dependence of measurement method and particle size

Parameter Unit Particle size

15mm 8 mm 4 mm

Absolute density r kgm-3 160439 160439 160439

Envelope density f ndash by the pycnometry kgm-3 61814 63556 63684

Porosity P ndash with the use of the pycnometry - 06147 06038 06031

Envelope density f ndash by the quasi-fluid pycnometry kgm-3 50338 48680 3305

Porosity P - with the use of the quasi-fluid pycnometry - 06862 06966 07940

The data analysis in respect to each employed method was conducted according to the prescriptions of GUM 1995 Relative

uncertainties calculated for the two techniques were respectively 21 for the hydrostatic method and 11 for the quasi-liquid

method For porosity the respective absolute uncertainties were 14 and 04 The results of the measurements and calculation

are presented in the Table 2

Table 2 Average uncertainty (U) and standard deviations (SD) of measurements in dependence of measurement method and

particle size

Parameter x Unit 119880119886119887119904(119909) U(x) SD

Absolute density U(r) kgm-3 02 032 8721

Envelope density U(f) ndash by the pycnometry kgm-3 21 1327 2130

Porosity U(P) - with the use of the pycnometry - 14 00083 00133

Envelope density U(f) ndash by the quasi-fluid pycnometry kgm-3 11 925 1156

Porosity U(f) - with the use of the quasi-fluid pycnometry - 04 00030 00060

Based on the results of the research the following conclusions were formulated

- the smallest uncertainty for the assessment of the porosity of comminuted common osier was observed for the quasi-liquid

method using GeoPyc 1365

- uncertainty fell as the degree of comminution increased

- with the increase in size of particles the porosity of samples grew


Numerical investigations of tortuosity in randomly generated pore structures Wojciech Sobieski

University of Warmia and Mazury Faculty of Technical Sciences Olsztyn Poland

wojciechsobieskiuwmedupl

Keywords porosity tortuosity Lattice Boltzmann Method Path Searching Algorithm

In the study the tortuosity in randomly generated 2D pore structures with various porosity and size of a structural element

forming the solid body is investigated Two different numerical methods are applied the Lattice Boltzmann Method (LBM) and

the self-developed algorithm the so-called Path Searching Algorithm (PSA) The first method serves to calculate the hydraulic

tortuosity based on the velocity field The second method is used to detect free passages in the porous medium in the chosen space

direction In the study 15000 different pore structures are investigated with 5 different resolutions of the numerical grid The main

result of the investigations is a new empirical function destined to estimate the tortuosity in cases where the porosity and the size

of the structural element forming the solid body are known Such a functions are not known in the literature

In Fig 1 all the obtained values of the LBM tortuosity for the highest grid are shown together with the results of the PSA

analysis The small filled points represent the values of the LBM tortuosity Circles mean that in the current case at least one free

path exists in the direction of the main fluid flow Squares are shown in cases in which the LBM tortuosity has a negative value

Fig2 Comparison of the data obtained in LBM calculations and PSA analysis

The proposed function has a following form

120591(120601 |119904|) =119886

120601119887∙|119904|119888+

119889

120601119890∙|119904|119891 (1)

where fit parameters a b c d e and f are equal to 11 033 -001 53e-08 68 and 286 respectively The other symbols

means 120591 ndash the tortuosity 120601 ndash the porosity |119904| ndash the normalized size of the structural element forming the solid body In Fig 2 it

can be seen that the new function matches the extreme values of the normalized size of the structural element especially well

Fig2 Comparison of LBM data for grid 150(middot4)times 150(middot4)

to the new proposed function and functions by Koponen [1] and Matyka [2]

In the investigations of the tortuosity based on a velocity field the data should be filtered and only these pore structures in which

at least one passage in the main space direction exists should be taken into account This issue is not obvious because sometimes

when porosity is relatively high the flow in a chosen direction is impossible For this reason additional methods destined to

analyse free passages in the pore space are needed The filtration process allows eliminating almost all cases in which the tortuosity

value is non-physical (less than 1) To eliminate the rest of the incorrect data it is enough to reject the extremely high values of

tortuosity (however after rejecting all pore structures without at least one passage such cases are very rare)

References [1] Koponen A Kataja M Timonen J Permeability and effective porosity of porous media Phys Rev E 56 3319 (1997)

[2] Matyka M Khalili A Koza Z Tortuosity-porosity relation in porous media flow Phys Rev E 78 026306 (2008)


Path Searching Algorithm Wojciech Sobieski



Keywords porosity tortuosity Path Searching Algorithm

Path Searching Algorithm it is a iteration algorithm destined to conduct searches of continuous pore channels in a selected space

direction in the earlier generated 2D pore structures The path lengths as well as the length of the porous body (1198710) are counted in

the grid nodes

An example of the acting of the developed algorithm is visible in Fig 1 The red colour denotes the nodes belonging to the

current path The blue nodes represent locations to which the path returned when no further movement was possible (eg due to

the existence of a cavity) All points omitted in this process are in green As it can be seen in the drawing in some places the path

is very tortuous and passes through many neighbouring nodes (red areas) Consequently the length of the path is overestimated

In this Figure the acting of the periodic boundary condition is additionally visible The symbols 120601 and 119904 mean the porosity and

the size of the structural element forming the porous body respectively

Fig 1 An example of a path obtained for grid 150times150 120601 = 04 and 119904 = 10 (repetition 1)

In the investigations the so-called path density indicator was introduced in the following form

120588119901 =119899119901

119888119898119886119909 (1)

where 119899119901 ndash the number of free paths (passages) in the pore structure 119888119898119886119909 ndash the maximum number of times the current grid

node is assigned to a free path It was noted that the values of the LBM tortuosity (calculated with the methodology described in

[1] or [2]) are high in areas in which the path density indicator tends to be zero (Fig 2)

Fig 2 Correlation between the path density indicator and the LBM tortuosity for grid 150(middot4)times150(middot4) (all repetitions)

The developed Path Searching Algorithm is particularly useful to reject these pore structures in which there are no free channels

in the main flow direction In such cases calculating the tortuosity does not make much sense This algorithm allows to calculate

a parameter similar to tortuosity (120591119875119878119860 =119899119901

119899119909 where 119899119901 is the number of ldquoeffectiverdquo nodes in the current path and 119899119909 is the number

of nodes in the X-derection) which may serve to estimate the complexity of the pore space However the obtained values are

overestimated in the relation to the classical tortuosity Therefore determining the practical usefulness of this parameter requires

further research and perhaps an improvement of the developed algorithm




Application of the contour erosion function in shape analysis of a solid particle Aleksander Sulkowski

Wrocław University of Technology Faculty of Mechanical and Power Engineering

Department of Cryogenic Aeronautic and Process Engineering

aleksandersulkowskipwredupl

Keywords solid particle projective image convex shell erosion convexity deficit

Particle shape is one of the most essential parameters affecting structure of granular material and determining its properties and

technological behaviour [1] [2] Thus proper geometrical description of solid particle shape becomes one of the most important

problems in powder technology [1]

In the paper a solid particle was defined to be some material object represented by its geometrical model C assumed to be a

subset of three dimensional real space satisfying the following conditions C is compact (closed and bounded) and connected set

being the closure of its connected interior Int(C) ( )C(IntC ) [2]

It is assumed that a geometric description of a solid particle may be based on the information provided by the analysis of

geometric features of its two-dimensional projective image C

In this work a method of description of the shape of a particle projective image has been proposed The theoretical basis of the

presented method is the concept of analysis of the deviation of the geometric structure of the particle image C from its convex

shell )C(ConvC which is the smallest convex set containing the considered image [3] as shown in Fig1

Considerations concern the so called convexity deficit zone CQ of particle projective image C which is defined as the

difference between the convex shell C and the image being considered ( CCQC ) as shown in Fig1 The convexity deficit

of particle image itself marked with the symbol )C( is defined by the formula

)C()C()C( (1)

where )C( is the Lebesgue measure [4] (surface area) of the set C in two dimensional real space 2R For the purpose of the

description of convexity deficit distribution within the CQ zone the so-called contour erosion function )t(C was proposed It

required introducing the concept of the erosion layer )(LC with the depth which was defined as the common part of the

convex shell C and the set of all spheres with the radius whose centres are the boundary points of the convex shell C as

shown in Fig1 For further considerations two specific depth values of the erosion layer )(LC are important ndash critical depth

X and threshold depth T Critical depth X is the smallest value of parameter for which the erosion layer )(LC absorbs

the convex shell C The threshold depth T is the smallest value of the parameter for which the difference between the

projective image of the particle C and the erosion layer )(LC becomes a convex set

The aforementioned contour erosion function )(C is given by the formula

))t(LC(())t(LC(()t( XCXCC (2)

It can be shown that the contour erosion function )t(C has the following properties 1) ]10[]10[C 2) )t(C is a

continuous non decreasing function 3) )C()0(C 4) 1)t(C for )(t XT

Thus the contour erosion function may be applied for description of the geometric structure of a solid particle In particular it

can be used to describe the distribution of the convexity deficit in the erosion layer of the particle projective image In Fig2 an

exemplary projective image of a real particle with its convex shell and erosion layer with a threshold depth has been presented

A graph of the contour erosion function corresponding to the image of the real particle considered is shown in Fig3

Fig1 Convex shell and erosion layer Fig2 Convex shell and kernel Fig3 Contour erosion function

of a particle projective image C of a real particle image of a real particle image

In addition contour erosion itself is some morphological operation [5] which can be used for the purpose of modelling the

process of evolution of the solid particle shape in case it is subject to destructive external factors such as abrasion or grinding

References [1] Wanibe Y Itoh T New Quantitative Approach to Powder Technology John Wiley amp Sons Ltd NY 1998

[2] Ohser J Mucklich F Statistical Analysis of Microstructures in Materials Science John Wiley amp Sons New York 2000

[3] Rudin W Functional Analysis Mc Graw-Hill Book Company NY 1973

[4] Fremlin DH Measure theory vol 12 Torres Fremlin Colchester 2000

[5] Serra J Image Analysis and Mathematical Morphology Academic Press London 1982

Conv(C)

C

CL


Influence of Microscopic Pore Geometry on the Parameter of Pore Tortuosity Zbigniew Szczepański Mieczysław Cieszko



e-mail zszczepukwedupl cieszkoukwedupl

Keywords pore tortuosity microscopic representation influence of pore geometry

The aim of the paper is to analyse the influence of microscopic pore geometry on the parameter of pore tortuosity of porous

materials with isotropic pore space structure Considerations are based on the general relation of this macroscopic parameter with

quantities characterising microscopic pore structure The general form of this relation have been obtained in the paper [1] requiring

the full representation of macroscopic density of kinetic energy of fluid in the potential flow by microscopic velocity field The

microscopic representation of tortuosity has the form

1

1198792=

1

119881119901int (119847119903 ∙ 119847)2

Ω119901119889119881 (1)


potential in the pore space respectively and quantity 119881119901 denotes the volume of the representative region of poresΩ119901in porous

material

Considerations presented in the paper [1] have been based on the model assumptions presented in papers [2] and [3] It was

assumed that at the macroscopic point of view interconnected pores in permeable porous materials form anisotropic space the

structure of which is determined by its metric and this space is modelled as Minkowski metric space Such approach enabled

precise and consistent definition of macroscopic parameters of pore space structure pore tortuosity and surface porosity directly

determined by the metric tensor of the pore space

Analysis of the influence of microscopic pore geometry on the parameter of pore tortuosity has been performed both

analytically and numerically for two types of pore geometry models capillary and two dimensional network In the first case the

influence of distribution of pore diameter length and cross-section were analysed It was shown among others that tortuosity of

porous layer with capillary pores of two different length is equal to the geometric mean of the arithmetic and harmonic means of

tortuosities produced by both length

Fig1 Tetragonal system of pores

Two examples of the two dimensional network models analysed in the paper have been presented in Fig1 and the obtained

values of tortuosity were presented in Fig2 It was shown that both types of pore structure are isotopic independently of the values

of their volume porosities

Fig2 Dependence of pore tortuosity of tetragonal pore space structure on the volume porosity

References [1] Cieszko M Minkowski Metric Dirichlet Energy and Pore Tortuosity INT J ENG SCI (in preparation for publication)



[3] Cieszko M Description of Anisotropic Pore Space Structure of Permeable MaterialsBased on Minkowski Metric Space



The use of natural soil as a porous medium for the treatment

of secondary effluent in the northern climate




Keywords freeze crystallization land application wastewater treatment spray irrigation

In northern climate cold temperature can significantly impact the efficiency of the biological wastewater treatment process

Systems with lagoons and spray irrigation are particularly vulnerable Unfortunately such systems are often located on the northern

rural areas because they are well suited for small communities where land is usually available and where it is important to keep

costs as low as possible In addition in cold climate during winter months discharge of an effluent to local lakes or tributaries is

usually prohibited Long term storage is required over winter months Therefore the development of each village or municipality

must be preceded by an increase in the capacity of the lagoons The idea of converting lagoon effluent to man-made snow during

winter months can help to solve the problem [1] The concept has a number of advantages that have already been described in the

professional literature [2] In the spring melting water soaks into the soil as it does during summer irrigation The system uses soil

properties as a porous medium for physical and biochemical filtration Moreover the process of phytoremediation takes place

Movement of an effluent of melt water in the pores of the soil produces its purification The soil matrix in this system acts as a

deep-bed bioreactor and has a tremendous potential to treat a secondary effluent In the upper soil layer essentially all suspended

solids and biodegradable materials can be restrained and decomposed

In the paper the results of the studies of the groundwater quality from two different sites of full scale snow storage and

treatment are presented Process factors such as the concentration of nitrogen conductivity and phosphorus have been adopted as

parameters of concern and are used to assess the effectiveness of the atomizing freeze crystallization process and its effect on the

quality of groundwater at the snow deposit site Significant reduction of phosphorus was achieved by its sorption to the fine soil

particles and precipitation The rest of dissolved phosphorus as well as other nutrients are up taken by plants Usually It happens

before they reach the ground water table (Fig 1 2)

Fig 1Total phosphorus in the soil at different depths Fig 2 Sodium bicarbonate extractable phosphorus at different depths

The analyses of soil showed that there was an evident adsorption of phosphorus in the soil profile Sodium bicarbonate

extractable phosphorus was detected only at the location of the main snowpack where the highest load of effluent took place

However it decreases significantly with the depth of the soil profile This fact suggests the conclusion that extractable P was up

taken by vegetation immobilized by soil microorganisms and fixed

Nitrate is broken down through a process of denitrification in anaerobic conditions present in the soil Vegetation at the snow

deposit site and buffer zone removes most of the nitrogen as nitrates compounds and other nutrients

Monitoring ground water quality confirms that atomizing freeze crystallization process and the treatment of secondary effluent in

the soil profile have effectively removed most of contaminants It was found that nitrates at the property boundary of the snow

deposit site are not detectable or are below drinking water standards This system is a well performing option for final polishing

of wastewater effluent

References

[1] Huber D Palmateer G Snowfluent - A join experimental project between the Ministry of the Environment and Delta

Engineering in the storage and renovation of sewage effluent by conversion to snow MOE Report Ontario Canada

[2] White JA Lefebvre P 1997 Snowfluentreg - the use of atomizing freeze crystallization on municipal agricultural

and hog manure wastes Conference World-Wisersquo97 Selkirk Manitoba

[3] Szpaczynski JA White JA 2000a Experimental studies on the application of natural process of snow

metamorphism for concentration and purification of liquid wastes WEF amp Purdue University Industrial Wastes

Technical Conference May 21 2000 St Louis Missouri USA


The stand for testing flow of two-phase system through the metal foams Adriana Szydłowska Jerzy Hapanowicz

Department of Process Engineering Faculty of Mechanical Engineering Opole University of Technology

aszydlowskadoktorantpoedupl

Keywords metal foam two-phase flow gas-liquid system hydrodynamic

Flow of multiphase systems occurs in a number of industrial technologies mainly in the chemical and petrochemical sectors

but also in the pharmaceutical food and energy sectors Processing of such substances almost always involves momentum heat

and mas transfer processes what spells necessity of having an unequivocal description of accompanying their flow phenomena

Heat transfer processes are a in an area of interest of a number of researchers which mostly aspire to improvement in the heat

exchange effectiveness Metal foam with open cells may be one of the suggested solutions in this range The metal foam as a

packing of flow pipe constitutes a specific ldquofinrdquo exchanging the heat with flow substance

The metal foams which are produced for flow apparatuses packing are manufactured of materials which are good heat

conductors eg aluminium (Fig 1) or copper alloys They are distinguished by continuity of frame a well-developed specific

surface area (a few thousands m2m3) and high porosity usually exceeding 90 Such properties of this group of materials make

them an interesting substitute for granular beds or wire-net packings

Fig 1 Metal foam

Within several last years a number of research on flow single-phase and two-phase gas-Newtonian liquid systems through the

metal foam hydrodynamic have been shown up [1] Knowledge of description of phenomena accompanying that flow is necessary

for a successful design and operation of apparatuses and technological systems There are few references concerning two-phase

systems gas-liquid and liquid-liquid flow through the metal foams Here it is noteworthy that a correct description of the heat

transfer in a given substance often requires taking into consideration the phenomena resulting from the flow hydrodynamic of this

substance particularly when it is a two-phase system Therefore there is a justified need to conduct some research in this regard

however it demands a properly constructed and equipped measuring position The subject of this paper is to present conception of

the stand its component parts measuring possibilities established methodology of carrying out the research and assessment of

results of the test studies

The stand enables measurement resistances of flow of two-phase mixtures through sections of horizontal packed as well as

unpacked with the foam pipe and also assessment of influence of presence of this foam on the flow pattern of the two-phase system

and its rheological behaviour A diameter of the flow pipe is equal to 10 mm and it constitutes a replaceable part of the stand which

can be packed with the foam with different parameters The length of the measuring pipe is divided into five segments The length

of each of them corresponds to relation Ld=15 Three middle segments are packed with the metal foam permanently while the

first and the last one function as pipe rheometers The set of supply the systems with operating fluids enables to select such fluids

fluxes that formation of the flow patterns typical of the given two-phase system flow will be possible In order to form researched

mixtures air water oil and non-Newtonian liquid may be used The measurement of these components fluxes and resistances of

two-phase mixtures flow through successive measuring sections is carried out with using analog-to-digital signal converters

working with a computer which has proper software Photographic recording of observed flow patterns in transparent fragments

of flow pipes placed at the beginning and at the end of the system supports visual identification of these patterns

As a result of the research it was found that the constructed measuring position gives opportunity of reliable assessment of

resistances of two-phase systems flow through pipe packed with the metal foam with definite parameters However the impact of

the metal foam on a possible change of flow pattern or rheological properties of the two-phase mixture will be feasible after

carrying out experiments in significantly larger scale

References [1] Dyga R Wymiana ciepła i hydrodynamika przepływu przez piany metalowe Oficyna Wydawnicza Politechniki Opolskiej

2015


Dissolution of porous media studied in a simple microfluidic setup Piotr Szymczak1 Filip Dutka1 Florian Osselin2

1University of Warsaw 2University of Calgary

PiotrSzymczakfuwedupl

Keywords reactive transport dissolution porous media

Dissolution of fractured and porous media introduces a positive feedback between fluid transport and chemical reactions at

mineral surfaces which can lead to self-focusing of the flow in pronounced wormhole-like channels [12]

We study the flow-induced dissolution in a simple microfluidic setup with a gypsum block inserted in between two

polycarbonate plates which is the simplest model of a fracture [3] This gives us a unique opportunity to observe the evolution of

the dissolution patterns in-situ and in real-time By changing the flow rate and the aperture of the fracture we can scan a relatively

wide range of Peacuteclet and Damkoumlhler numbers characterizing the relative magnitude of advection diffusion and reaction in the

system Additionally as the aperture is increased a transition is observed between the fractal and regular dissolution patterns For

small gaps the patterns are ramified fractals For larger gaps the dissolution fingers are found to have regular forms of two

different kinds either linear (for high flow rates) or parabolic (for lower flow rates) The experiments are supplemented with

numerical simulations and analytical modeling which allow for a better understanding of evolving flow patterns In particular we

find the shapes and propagation velocities of dominant fingers for different widths of the system flow rates and reaction rates

Finally we comment on the link between the experimentally observed patterns and the natural karst systems - both cave conduits

and epikarst solution pipes

Fig1 Microfluidic setup (left panel) and the examples of dissolution patterns formed spontaneously in this system

References [1] Hoefner M L and Fogler H S Pore evolution and channel formation during flow and reaction in porous media AIChE J

34 45ndash54 1988

[2] P Szymczak A J C Ladd Wormhole formation in dissolving fractures J Geophys Res 114 B06203 2009

[3] F Osselin P Kondratiuk A Budek O Cybulski P Garstecki P Szymczak Microfluidic observation of the onset of reactive

infiltration instability in an analog fracture Geophys Res Lett 43 6907-6915 2016


Numerical simulations of laboratory-scale dike overflowing using two phase flow model Adam Szymkiewicz1 Witold Tisler1 Wioletta Gorczewska-Langner1 Rafał Ossowski1 Danuta Leśniewska2

Stanisław Maciejewski2 1Gdańsk University of Technology Faculty of Civil and Environmental Engineering

2Koszalin University of Technology Faculty of Civil Engineering Environmental and Geodetic Sciences

adamspgedupl

Keywords flood dikes unsaturated flow two phase flow infiltration air trapping

Water flow in the shallow subsurface natural and artificial slopes and earth structures occurs in partially saturated conditions

ie part of the pore space is occupied by water and the other part by air In typical engineering analyses it is commonly assumed

that the air in pores is connected to the atmosphere and much more mobile than water As a consequence the air pressure can be

considered constant and only the water flow is considered In such a case the water flow can be described by the Richards equation

However the assumptions underlying the Richards equation are not always valid especially in the case of heterogeneous soils or

in the presence of barriers impermeable to air flow Air can be trapped in the soil pores when large areas of land are ponded with

surface water or when water flows over the crest of a flood dike earth dam or similar structure [1]

This contribution presents the results of laboratory experiments carried out on a model dike made of fine sand [2] During the

overflowing experiment a significant amount of air was trapped in the core of the dike Increase of the air pressure led to expulsion

of air in form of bursts leading to damages of the soil structure and creation of cracks The observations are compared to the

results of numerical simulations based on two phase flow model which accounts for both water and air phases Simulations were

carried out using finite volume discretization method implemented in an in-house code developed by the first author While the

numerical model does not include deformation the results for the early stage of infiltration process (before cracks appear) are in

a good agreement with the visual observations of the water saturation field and with air pressure measurements (Fig 1) [2]

Fig1 Calculated and observed distribution of water saturation in the model dike [2]

References [1] Bogacz P Kaczmarek J Leśniewska D (2008) Influence of air entrapment on flood embankment failure mechanics - model

tests Technol Sci 11 188-201

[2] Tisler W Gorczewska-Langner W Leśniewska D Maciejewski S Ossowski R Szymkiewicz A Simulations of air and

water flow in a model dike during overflow experiments submitted to Computational Geosciences 2018


Effect of temperature concentration of alcohols and time

on bakers yeast permeabilization process Ilona Trawczyńska Justyna Miłek Sylwia Kwiatkowska-Marks

Department of Chemical and Biochemical Engineering Jan and Jędrzej Śniadecki University of Technology

and Life Sciences in Bydgoszcz

Seminaryjna 3 85-326 Bydgoszcz Poland

ilonatrawczynskautpedupl

Keywords permeabilization bakerrsquos yeast biocatalyst response surface methodology

Many scientists have proven that the use of biocatalysts in the form of whole cells of microorganisms is often more effective

than the use of purified enzymes [1 2] However low permeability of cell wall and membrane contributes to the slow rate of

reactions catalyzed by whole cells enzymes Such difficulties can be overcome by the application of permeabilization technique

which is to improve the permeability of cell wall and membrane of microorganisms for facilitating the diffusion of reaction

reagents while also maintaining the cellrsquos properties including enzymatic activity and structure [3 4]

In this paper the influence of physical and chemical parameters on the effectiveness of permeabilization of bakers yeast cells

using alcohols was analysed For this purpose the response surface methodology (RSM) has been applied in the study The

effectiveness of the process has been represented by measuring intracellular catalase activity

The research program was designed in such manner that it was possible to obtain the necessary information performing the

fewest number of analysis possible Therefore the research was conducted according to the points of the compositional design

plan which in the form of coded variables is given in table 1 The number of necessary experiments to conduct was 20 for each of

the permeabilization processes ie with the use of ethanol 1-propanol 2-propanol

Table 1 Central composite design matrix

nr temperature concentration time enzyme activity [U∙g-1]

ethanol 1-propanol 2-propanol

1 ndash 1 ndash 1 ndash 1 190 140 230

2 ndash 1 1 ndash 1 2540 3410 4840

3 ndash 1 ndash 1 1 260 235 1990

4 ndash 1 1 1 3085 2560 5050

5 1 ndash 1 ndash 1 620 340 2690

6 1 1 ndash 1 2040 2580 4990

7 1 ndash 1 1 2120 1620 3620

8 1 1 1 1780 1935 3600

9 1682 0 0 140 1370 2570

10 ndash 1682 0 0 210 1135 360

11 0 1682 0 1005 2210 4980

12 0 ndash 1682 0 300 140 120

13 0 0 1682 4340 3590 4760

14 0 0 ndash 1682 1690 2570 3090

15 0 0 0 4390 4100 5900

16 0 0 0 5070 4220 5750

17 0 0 0 5150 4070 5880

18 0 0 0 5050 3970 5780

19 0 0 0 4760 4170 5800

20 0 0 0 5190 4145 5765

Response surface plots were created based upon experiments conducted in the points of compositional plans Plots present an

effect of two process variables on activity of catalase assuming that the value of the third variable is constant

Based upon the research conclusion can be drawn that alcohol of lower concentration provides better results along with the

increase of temperature in permeabilization process of bakerrsquos yeast cells Applying solvents of too high concentrations contribute

to the decrease of permeabilization effectiveness At high temperatures of approx 30 better results can be achieved by applying

lower concentrations of alcohol along with the increased duration of cells shaking Treatment time of the process proved to be a

parameter bearing little influence on the effectiveness of the process

References [1] Sekhar S Bhat N Bhat SG Preparation of detergent permeabilized Bakersrsquo yeast whole cell catalase Process Biochemistry

34(4) 349-354 1999

[2] Xu P Zheng G-W Du P-X Zong M-H Lou W-Y Whole-Cell Biocatalytic Processes with Ionic Liquids ACS

Sustainable Chemistry amp Engineering 4 (2) 371-386 2016

[3] Kumari S Panesar PS Bera MB Singh B Permeabilization of yeast cells for betandashgalactosidase activity using mixture

of organic solvents A response surface methodology approach Asian Journal of Biotechnology 3(4) 406-414 2011

[4] Panesar PS Panesar R Singh RS Bera MB Permeabilization of yeast yells with organic solvents for βndashgalactosidase

activity Research Journal of Microbiology 2(1) 34-41 2007


Pore scale simulations of flows in weakly permeable porous media Anna Trykozko

ICM - Interdisciplinary Centre for Mathematical and Computational Modelling University of Warsaw

ul Pawińskiego 5a 02-106 Warszawa

atrykozkoicmedupl

Keywords pore scale micro-CT imaging resolution simulations of flow

1 Computational modelling of flows through porous media performed at pore scale has become a standard procedure in the last

couple of years It is based on solving Navier-Stokes equations defined in a domain available for flow (pores) In a standard

approach only pores are taken into account in computations and a percolation through a sample is required in order to simulate

flow Moreover all pore spaces across a sample should be connected and therefore dead-end pores are removed from a domain of

flow Simulation results obtained at pore scale which are pressure and velocity fields can be lsquotranslatedrsquo by upscaling to larger

scales which are more relevant in practical engineering applications The main steps of the computational procedure we use are

described in [1] and [2] Complex shapes of flow domains result in large sizes of computational problems what remains a challenge

in spite of rapidly growing available computer resources

2 X-ray computed tomography (micro-CT) has become the more and more accessible source of realistic data describing pore

structures As a result of a segmentation of a micro-CT image a map of voids and impervious lsquosolidrsquo voxels can be obtained to

serve as data for defining flow domain in simulations A voxel size depends on a resolution of a microimage

Our study was performed based on micro-CT images of a set of samples of soils The samples were manufactured as mixtures

of sand and clay containing from 100 to 20 of sand There was no percolation detected at a micro-CT resolution in many

samples and therefore the standard computational procedure was not applicable

3 On the other hand there were significant differences in porosities evaluated at micro-CT resolution as compared to the values

obtained in laboratory measurements In order to take into account this subscale porosity we proposed an extended procedure in

which voxels classified as solids during segmentation were modelled as porous media characterized by a small permeability This

permeability was determined based on data provided by a Scanning Electron Microscopy which is another high-resolution

microimaging technique

4 Details of the extended computational procedure and results of simulations performed over various weakly permeable samples

will be presented

Acknowledgements Samples used in this study were manufactured and imaged for the needs of the project nr Pol-

Nor209820142013 supported by the Polish-Norwegian Programme operated by the National Centre for Research and

Development under the Norwegian Financial Mechanism 2009-2014

References [1] Peszynska M Trykozko A Pore-to-core simulations of flow with large velocities using continuum models and imaging data

Computational Geosciences 4(17) 623-645 2013

[2] Trykozko A Peszynska M Dohnalik M Modeling non-Darcy flows in realistic pore-scale proppant geometries Computers

and Geotechnics (71) 352-360 2016


Using of the SEM image method to evaluate the porosity of materials

with varied internal structure Grzegorz Wałowski1 Gabriel Filipczak2

1Institute of Technology and Life Sciences Renewable Energy Department - Poznan Branch 2Opole University of Technology Faculty of Mechanical Engineering Department of Process Engineering

gwalowskiitpedupl (or) walowskiggmailcom

Keywords porous material SEM image anisotropy

An important feature of porous materials resulting directly from their structure is porosity In quantitative terms this parameter

results directly from the pores volume [1] [2] as the free volume space for fluid flow When the porous material comprises a rigid

skeletal structure (Fig 1) a part of the pores and channels volume can be closed or blinded and the flow of fluid through such

material is limited only to the pores space (or channels) connected to each otherrsquos with a free space less than this as results from

the real scale of the porosity of material This greatly impedes assessment of the hydrodynamics of fluid flow through skeletal

porous media especially the linking of the permeability of these materials with their properties The problem becomes even more

complicated in case of anisotropic structure when there is a diverse spatial structure (Fig 1)

In own investigation to porosity evaluation the image analysis method based on scanning surface topography (SEM) was used

ndash Fig 2 Due to the anisotropic structure of tested materials this porosity was determined in three selected directions (X Y Z)

and next the average porosity value as resulting from the configuration of surface pores was determining

- X direction - Y direction - Z direction

Fig1 Image of the surface of a porous material (coal char) with a differentiated spatial structure


Fig2 SEM images of porous material (coke) with varied elementary structure

In the technical analysis a specialized computer program for graphic image analysis was used for the quantitative evaluation of

porous structure ndash Fig 3a This program (IRIS) makes it possible to calculate geometrical parameters of structures including

linear dimensions pores and channels surfaces with the possibility of eliminating closed structures as it exemplified in Fig 3b

The results obtained during the laboratory tests showed that based on SEM images method the assessment of porosity can be

successfully used in description of hydrodynamics of gas flow through porous materials with skeletal structure [3]

a) b)

Fig3 Calculation proceedings for determination of porosity a) program procedure b) detail of SEM scanning area

References [1] Aksielrud GA Altszuler MA Ruch masy w ciałach porowatych WNT Warszawa 1987

[2] Strzelecki T Kostecki S Żak S Modelowanie przepływoacutew przez ośrodki porowate Dolnośląskie Wydawnictwo

Edukacyjne Wrocław 2008

[3] Wałowski G Hydrodynamika przepływu gazu przez złoże porowate Praca doktorska Politechnika Opolska 2008


Numerical analysis of compression mechanics of granular packings

with various number of particle size fractions Joanna Wiącek Marek Molenda Mateusz Stasiak

Institute of Agrophysics Polish Academy of Sciences

Doswiadczalna 4 20-290 Lublin 27 Poland

e-mailjwiacekipanlublinpl

Keywords polydisperse granular packings granulometric fractions structure mechanical properties

Polydisperse granular materials exhibit complex and undefined behaviors posing considerable challenges in the design and

operation of processing plants Granular packings may be composed of one two three or more components different from one

another in size shape material properties et al Size polydispersity is an inevitable feature of granular materials which determines

structural and mechanical properties of particulate systems [1-3] Although a number of studies has been so far conducted for

polydisperse granular packings no study on effect of number of granulometric fractions on structure and mechanical

characteristics of grain assemblies with uniform particle size distribution has been so far undertaken Thus the objective of the

presented project was to analyze the effect of number of particle size fractions on structural and mechanical properties of granular

mixtures composed of spheres with size distribution uniform by number of grains A study was conducted for mixtures with

various ratios between diameter of the largest and the smallest particle to verify whether value of particle size ratio has an influence

on relationship between number of fractions and structure and micromechanics of granular packings In this study simple granular

packings composed of three five and seven granulometric fractions were examined which are the simplest polydisperse particulate

systems after binary ones Spherical particles with random initial coordinates were generated inside the rectangular box and settled

down onto the bottom of the test chamber under gravity (see Fig 1) The rigid and frictional walls did not deform under the applied

load Next spheres were compressed through the top cover of the chamber that moved vertically downwards at a constant velocity

of until a maximum vertical pressure on the uppermost particles reached 100 kPa

Fig1 Initial configuration of mixture

The effect of number of granulometric fractions on structural and micromechanical properties of frictional packings of spheres

with various particle size dispersity has been investigated by means of the discrete element simulations of confined uniaxial

compression Three-dimensional simulations were conducted using the EDEM software [4] based on the Discrete Element

Method [5] The study has shown an influence of both number of particle size fractions and degree of particle size heterogeneity

on packing density of assembly Results have shown a presence of the certain value of ratio between diameter of the largest and

the smallest particle in multicomponent granular system below which packing density decreases significantly with increasing

number of granulometric fractions however estimation of that value requires further investigations The largest average

coordination numbers were obtained in ternary samples with the smallest ratio between diameter of the largest and the smallest

particle Coordination number decreased with increasing number of granulometric fractions In more heterogeneous and disordered

packings with higher particle size dispersity small spheres filled the pores between larger particles only partially resulting in

smaller number of interparticle contacts It was found that corrected coordination number including particles with more than three

contacts was larger in samples with higher ratio of the diameter between the largest and the smallest particle which was related

to larger number of contacts between mechanically stable large spheres and surrounding them small particles Significant influence

of the particle size ratio and number of particle size fractions on distribution of contact forces in granular packings was observed

which determined global stress and energy dissipation in assemblies The dissipation of energy was found to increase with

increasing vertical pressure and increasing grain size heterogeneity

Results presented in this paper indicate that structural and micromechanical properties of granular packings with uniform

discrete particle size distribution are determined by both degree of particle size dispersity and number of grain size fractions in

mixture Knowledge of these geometric and statistical factors describing composition of granular mixtures thus plays a crucial

role in predicting and interpreting effects observed in particulate systems

References [1] McGeary RK Mechanical Packing of Spherical Particles J Am Ceram Soc 44 513-523 1961

[2] Wiącek J Molenda M Effect of particle size distribution on micro- and macromechanical response of granular packings

under compression Int J Solids Struct 51 4189-4195 2014

[3] Wiącek J Stasiak M Parafiniuk P Effective elastic properties and pressure distribution in bidisperse granular packings

DEM simulations and experiment Arch Civ Mech Eng 17 271-280 2017

[4] EDEM Software 2016 Retrieved from wwwdem-solutionscomsoftwareedem-software

[5] Cundall PA Strack OD A discrete element model for granular assemblies Geacuteotechnique 29 47-65 1979


Determination of the heat of wetting of selected liquids on modified activated carbons Eliza Wolak Elżbieta Vogt Jakub Szczurowski

AGH University of Science and Technology Faculty of Energy and Fuels Cracow Poland

eklimowsaghdupl

Keywords activated carbon hydrophobization heat of wetting

Active carbons are intensively used materials in both basic research and industrial processes mainly in the processes of

purification separation and catalysis They are one of the most popular adsorbents that are used for gas cleaning and separation

solvent recovery gas storage water treatment and many other applications Thanks to their numerous advantages microporous

carbon adsorbents are also used in unconventional mass and energy storage processes eg in adsorption cooling or air conditioning

systems [1] [2]

Their effectiveness in these kind of processes primarily depends on structural properties and chemical properties of the surface

The most widely used treatment-enhancing properties of carbon sorbents are appropriate modifications which result in the

changing of their structural and surface parameters [3] [4] The change of the hydrophobic properties of the carbon materials

which is applied during production filters for removing oil and organic pollutants [5] or in the purification processes used frying

oils is also possible [6] Techniques to modify and characterize the surface chemical properties of activated carbons constituted

the subject of interest for many scientists [7]

In this paper commercially available activated WD-extra carbon (Gryfskand) which is applied for water treatment was used

Activted carbon was modified by the following chemical agents H2O2 HNO3 and HCl The textural characteristics of the samples

were determined by the analysis of physical adsorption isotherms of nitrogen vapor at 77 K The Boehm titration general procedure

was used to determine the distribution of the surface functional groups Chemical modifications significantly affect the chemical

structural and surface properties of activated carbons Hydrophobization with ethereal stearic acid was performed on the raw

material and samples after chemical modification Hydrophobic properties of the samples were specified The relationship of the

chemical modification agents with hydrophobization degree was indicated The heat effect of adsorption was measured in

accordance with Polish Standard PN-90C-97554 and using a home-designed apparatus Gryfskand WG-12 active carbon was

used as a reference material The enthalpy of wetting by wetting liquids was calculated

The author gratefully acknowledgements the financial support of this work by the Polish Ministry of Science and Information

Society Technologies under AGH statutory project No 1111210374

References [1] Anyanwu EE Energy Conversion and Management 45(7-8) 1279-1295 2004

[2] Wolak E Buczek B Inżynieria i Aparatura Chemiczna 6(1) 11-1 2005

[3] Repelewicz M Jedynak K Choma J Ochrona środowska 31(3) 45-50 2009

[4] Buczek B Wolak E Adsorption 14(2-3) 283-287 2008`

[5] Lee CH Johnson N Drelich J Yap YK Carbon 49(2) 669-676 2011

[6] Buczek B Chwiałkowski W Żywność Nauka Technologia Jakość 4(45) 85-99 2005

[7] Menendez JA Phillips J Xia B Radovic LR Langmuir 12(18) 4404-4410 1996


NOTES


SCIENTIFIC COMMITEE


Janusz Badur

Mariusz Kaczmarek

Adam Lipiński

Teodor Skiepko

Mieczysław Cieszko

Piotr Srokosz

Adam Szymkiewicz

Anna Trykozko

Maciej Marek

Maciej Matyka

Joanna Wiącek

ORGANIZING COMMITEE


Seweryn Lipiński

Dariusz Grygo

Tomasz Tabaka

Aneta Molenda

Book of abstracts published from materials provided by Authors

Edited by Seweryn Lipiński


CONTENTS









Mieczysław Cieszko





10



Marek Gawor






Daniel Janecki


15








18







Anna Kułakowska




Grzegorz Leśniak










28

Wojciech Ludwig



29




Marcin Majkrzak


31





Maciej Marek




Danuta Miedzińska






Anna Pajdak






Wojciech Sobieski


Wojciech Sobieski








47








50



Anna Trykozko






54






darekimcpczczestpl





















found in [3]









119873119906 = 119877119890119866117 ∙ 119866119886119866

minus084 ∙ 119864119900072 (1)








10222-10237 2016

























a) b)
























119959 = minus 119870

120578 nabla(119901 + 119880)
















119959 = 119870







also







Zh Eksp Teor Fiz 59(1) 110-115 1970







renatacichainigpl




















Sample ID

Pore width


Pore diameter


[m] [m] [m] [m]

8 40510-8 1198 10-8 16110-8 10010-7

32 235 10-8 721 10-8 93910-9 25010-8

42 33110-8 758 10-8 13210-8 15310-8
















975-995 2014





cieszkoukwedupl
































1

1205752=

1

119881119901int (119847119903 ∙ 119847)2Ω119901

119889119881 (1)








































120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) minus 119888119898(119904119898 119901) (

120597119904119898

120597119903)2= 119888119904(119904119898 119901) (1)






120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) = 119888119904(119904119898 119901) (2)







extrusion process


259-282 1984




22 1-22 2016






















beds


1469-5



































constant































pawelguzikurkedupl








































zecjanuniopolepl






parameters
































































119870119921 + 119887119943 = 0 (1)

nabla ∙ 119921 = 0 (2)





walls

























phenomena such as

in the wall zone

in the semi-coke

zone

in the closed

porosity zone

in the plastic

layer zone

in the coal zone










confinement


















modeling












































USA 1997






wojtekkinskiwppl













easy visualised


























wojtekkinskiwppl








on full 3D geometry














curved channels 16 1068 345 800 087 1068

































2]


equation [1 3]

120595 = int119867119889120591

120556119901

119905

0 (1)







120595 = int119867119889120591

120556119901

1199051199010

= 1 (2)


[1]

120556119901 = 120556119901(119896120590 120583120590 119867 119879 119861(120591) 119883119894) (3)






T ndash temperature

























aq

e

D

D

(1)








2

22

1

22exp

161

R

tnD

nP

P e

n

t

(2)



0

02

04

06

08

1

12

0 10 20 30 40 50 60

PtP






in the calculations











374311ndash 4330 2003






lesniakinigpl



























2D imaging)





















ACKNOWLEDGEMENTS















renatacichainigpl










































Nor196923492013









Research 14 4 p 317 324 ISNN 1520 7439 2005




cichainigpl












software (Table 1)



Median of pore

volume

[nm3]

Maximum

pore volume

[nm3]

Median of

pore surface

[m2]

Maximum pore

surface

[nm3]






































120591 = 1208 + 0006∙ 119890154120590 (1)

oslash = 04124 + 00005σ - 00013 1205902 (2)













75-85 2017


2016

09

1

11

12

13

14

15

16

17

0 01 02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18 19

Tort

uo

sity

[-]





































Engineering 51(3) 201-208 2002






America Journal 66(4) 1143-1150 2002































Thorton model [2 3]

119890119899 =

(1 minus

073 11988111989911989435

100 )05

119881119899119894 lt 119881119910

(6radic3

5) [1 minus

1

6(119881119910

119881119899119894)2]

1

2

(119881119910

119881119899119894) [(

119881119910

119881119899119894) + 2radic12 minus 02 (

119881119910

119881119899119894)2]

minus1

1

4

119881119899119894 gt 119881119910

(1)




119890119905 = 1 minus

2

120553[1198881 + 1198882 119905119886119899ℎ(1198883 + 1198884120553)] 120553 lt 120553119888119903119894119905

1 minus2

120553 120553 ge 120553119888119903119894119905

(2)

120553 =2

(1+119890119899)120583119905119886119899(90deg minus 120579) (3)















Acknowledgments


201309BST800157


Technol 328 375-388 2018


Eng 32 593-604 2005


1997


937ndash960 2009




























)()(1

2

psCp

sg

dz

spsC

ds

ds

p

sms

mm

mmm

m

cm

(1)

gdz

dpm (2)



119862119898(119904119898 119901) =1

119904119898(119901

119901119900)119898

119862119904(119904119898 119901) = 119904119898 (119901

119901119900)minus119899

(3)





22 1-22 2016





majkrzakinigpl













































Acknowledgements




46 559ndash632 2001






















of concrete [4]











12 Pages 917-927 2017










Częstochowa Poland




















Acknowledgements


Centre



Science 161 382-393 2017





























Chemiczny 96 9 2017
















a) b)








Acknowledgements

























Si

O

O

OH

Si

Si

Si

OHSi

OHSi


OC2H5

OC2H5

50deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NH2

O

O

O O

25deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NO

O

H

O

Si

O

O

OH

Si

Si

O

OH

Si NO

O

NH

trypsintrypsin

(1)


















































as follows

+ =120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(1)

+ = minus120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(2)






































































































15mm 8 mm 4 mm











particle size





























120591(120601 |119904|) =119886

120601119887∙|119904|119888+

119889

120601119890∙|119904|119891 (1)





















the grid nodes









120588119901 =119899119901

119888119898119886119909 (1)


































)C()C()C( (1)


























Conv(C)

C

CL












1

1198792=

1

119881119901int (119847119903 ∙ 119847)2

Ω119901119889119881 (1)



material

























































References























Fig 1 Metal foam


























2015





















34 45ndash54 1988








adamspgedupl













































2 ndash 1 1 ndash 1 2540 3410 4840

3 ndash 1 ndash 1 1 260 235 1990

4 ndash 1 1 1 3085 2560 5050

5 1 ndash 1 ndash 1 620 340 2690

6 1 1 ndash 1 2040 2580 4990

7 1 ndash 1 1 2120 1620 3620

8 1 1 1 1780 1935 3600

9 1682 0 0 140 1370 2570

10 ndash 1682 0 0 210 1135 360

11 0 1682 0 1005 2210 4980

12 0 ndash 1682 0 300 140 120

13 0 0 1682 4340 3590 4760

14 0 0 ndash 1682 1690 2570 3090

15 0 0 0 4390 4100 5900

16 0 0 0 5070 4220 5750

17 0 0 0 5150 4070 5880

18 0 0 0 5050 3970 5780

19 0 0 0 4760 4170 5800

20 0 0 0 5190 4145 5765









34(4) 349-354 1999











atrykozkoicmedupl






















will be presented

































a) b)



























































eklimowsaghdupl






systems [1] [2]


























NOTES


CONTENTS









Mieczysław Cieszko





10



Marek Gawor






Daniel Janecki


15








18







Anna Kułakowska




Grzegorz Leśniak










28

Wojciech Ludwig



29




Marcin Majkrzak


31





Maciej Marek




Danuta Miedzińska






Anna Pajdak






Wojciech Sobieski


Wojciech Sobieski








47








50



Anna Trykozko






54






darekimcpczczestpl





















found in [3]









119873119906 = 119877119890119866117 ∙ 119866119886119866

minus084 ∙ 119864119900072 (1)








10222-10237 2016

























a) b)
























119959 = minus 119870

120578 nabla(119901 + 119880)
















119959 = 119870







also







Zh Eksp Teor Fiz 59(1) 110-115 1970







renatacichainigpl




















Sample ID

Pore width


Pore diameter


[m] [m] [m] [m]

8 40510-8 1198 10-8 16110-8 10010-7

32 235 10-8 721 10-8 93910-9 25010-8

42 33110-8 758 10-8 13210-8 15310-8
















975-995 2014





cieszkoukwedupl
































1

1205752=

1

119881119901int (119847119903 ∙ 119847)2Ω119901

119889119881 (1)








































120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) minus 119888119898(119904119898 119901) (

120597119904119898

120597119903)2= 119888119904(119904119898 119901) (1)






120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) = 119888119904(119904119898 119901) (2)







extrusion process


259-282 1984




22 1-22 2016






















beds


1469-5



































constant































pawelguzikurkedupl








































zecjanuniopolepl






parameters
































































119870119921 + 119887119943 = 0 (1)

nabla ∙ 119921 = 0 (2)





walls

























phenomena such as

in the wall zone

in the semi-coke

zone

in the closed

porosity zone

in the plastic

layer zone

in the coal zone










confinement


















modeling












































USA 1997






wojtekkinskiwppl













easy visualised


























wojtekkinskiwppl








on full 3D geometry














curved channels 16 1068 345 800 087 1068

































2]


equation [1 3]

120595 = int119867119889120591

120556119901

119905

0 (1)







120595 = int119867119889120591

120556119901

1199051199010

= 1 (2)


[1]

120556119901 = 120556119901(119896120590 120583120590 119867 119879 119861(120591) 119883119894) (3)






T ndash temperature

























aq

e

D

D

(1)








2

22

1

22exp

161

R

tnD

nP

P e

n

t

(2)



0

02

04

06

08

1

12

0 10 20 30 40 50 60

PtP






in the calculations











374311ndash 4330 2003






lesniakinigpl



























2D imaging)





















ACKNOWLEDGEMENTS















renatacichainigpl










































Nor196923492013









Research 14 4 p 317 324 ISNN 1520 7439 2005




cichainigpl












software (Table 1)



Median of pore

volume

[nm3]

Maximum

pore volume

[nm3]

Median of

pore surface

[m2]

Maximum pore

surface

[nm3]






































120591 = 1208 + 0006∙ 119890154120590 (1)

oslash = 04124 + 00005σ - 00013 1205902 (2)













75-85 2017


2016

09

1

11

12

13

14

15

16

17

0 01 02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18 19

Tort

uo

sity

[-]





































Engineering 51(3) 201-208 2002






America Journal 66(4) 1143-1150 2002































Thorton model [2 3]

119890119899 =

(1 minus

073 11988111989911989435

100 )05

119881119899119894 lt 119881119910

(6radic3

5) [1 minus

1

6(119881119910

119881119899119894)2]

1

2

(119881119910

119881119899119894) [(

119881119910

119881119899119894) + 2radic12 minus 02 (

119881119910

119881119899119894)2]

minus1

1

4

119881119899119894 gt 119881119910

(1)




119890119905 = 1 minus

2

120553[1198881 + 1198882 119905119886119899ℎ(1198883 + 1198884120553)] 120553 lt 120553119888119903119894119905

1 minus2

120553 120553 ge 120553119888119903119894119905

(2)

120553 =2

(1+119890119899)120583119905119886119899(90deg minus 120579) (3)















Acknowledgments


201309BST800157


Technol 328 375-388 2018


Eng 32 593-604 2005


1997


937ndash960 2009




























)()(1

2

psCp

sg

dz

spsC

ds

ds

p

sms

mm

mmm

m

cm

(1)

gdz

dpm (2)



119862119898(119904119898 119901) =1

119904119898(119901

119901119900)119898

119862119904(119904119898 119901) = 119904119898 (119901

119901119900)minus119899

(3)





22 1-22 2016





majkrzakinigpl













































Acknowledgements




46 559ndash632 2001






















of concrete [4]











12 Pages 917-927 2017










Częstochowa Poland




















Acknowledgements


Centre



Science 161 382-393 2017





























Chemiczny 96 9 2017
















a) b)








Acknowledgements

























Si

O

O

OH

Si

Si

Si

OHSi

OHSi


OC2H5

OC2H5

50deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NH2

O

O

O O

25deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NO

O

H

O

Si

O

O

OH

Si

Si

O

OH

Si NO

O

NH

trypsintrypsin

(1)


















































as follows

+ =120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(1)

+ = minus120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(2)






































































































15mm 8 mm 4 mm











particle size





























120591(120601 |119904|) =119886

120601119887∙|119904|119888+

119889

120601119890∙|119904|119891 (1)





















the grid nodes









120588119901 =119899119901

119888119898119886119909 (1)


































)C()C()C( (1)


























Conv(C)

C

CL












1

1198792=

1

119881119901int (119847119903 ∙ 119847)2

Ω119901119889119881 (1)



material

























































References























Fig 1 Metal foam


























2015





















34 45ndash54 1988








adamspgedupl













































2 ndash 1 1 ndash 1 2540 3410 4840

3 ndash 1 ndash 1 1 260 235 1990

4 ndash 1 1 1 3085 2560 5050

5 1 ndash 1 ndash 1 620 340 2690

6 1 1 ndash 1 2040 2580 4990

7 1 ndash 1 1 2120 1620 3620

8 1 1 1 1780 1935 3600

9 1682 0 0 140 1370 2570

10 ndash 1682 0 0 210 1135 360

11 0 1682 0 1005 2210 4980

12 0 ndash 1682 0 300 140 120

13 0 0 1682 4340 3590 4760

14 0 0 ndash 1682 1690 2570 3090

15 0 0 0 4390 4100 5900

16 0 0 0 5070 4220 5750

17 0 0 0 5150 4070 5880

18 0 0 0 5050 3970 5780

19 0 0 0 4760 4170 5800

20 0 0 0 5190 4145 5765









34(4) 349-354 1999











atrykozkoicmedupl






















will be presented

































a) b)



























































eklimowsaghdupl






systems [1] [2]


























NOTES




Marcin Majkrzak


31





Maciej Marek




Danuta Miedzińska






Anna Pajdak






Wojciech Sobieski


Wojciech Sobieski








47








50



Anna Trykozko






54






darekimcpczczestpl





















found in [3]









119873119906 = 119877119890119866117 ∙ 119866119886119866

minus084 ∙ 119864119900072 (1)








10222-10237 2016

























a) b)
























119959 = minus 119870

120578 nabla(119901 + 119880)
















119959 = 119870







also







Zh Eksp Teor Fiz 59(1) 110-115 1970







renatacichainigpl




















Sample ID

Pore width


Pore diameter


[m] [m] [m] [m]

8 40510-8 1198 10-8 16110-8 10010-7

32 235 10-8 721 10-8 93910-9 25010-8

42 33110-8 758 10-8 13210-8 15310-8
















975-995 2014





cieszkoukwedupl
































1

1205752=

1

119881119901int (119847119903 ∙ 119847)2Ω119901

119889119881 (1)








































120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) minus 119888119898(119904119898 119901) (

120597119904119898

120597119903)2= 119888119904(119904119898 119901) (1)






120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) = 119888119904(119904119898 119901) (2)







extrusion process


259-282 1984




22 1-22 2016






















beds


1469-5



































constant































pawelguzikurkedupl








































zecjanuniopolepl






parameters
































































119870119921 + 119887119943 = 0 (1)

nabla ∙ 119921 = 0 (2)





walls

























phenomena such as

in the wall zone

in the semi-coke

zone

in the closed

porosity zone

in the plastic

layer zone

in the coal zone










confinement


















modeling












































USA 1997






wojtekkinskiwppl













easy visualised


























wojtekkinskiwppl








on full 3D geometry














curved channels 16 1068 345 800 087 1068

































2]


equation [1 3]

120595 = int119867119889120591

120556119901

119905

0 (1)







120595 = int119867119889120591

120556119901

1199051199010

= 1 (2)


[1]

120556119901 = 120556119901(119896120590 120583120590 119867 119879 119861(120591) 119883119894) (3)






T ndash temperature

























aq

e

D

D

(1)








2

22

1

22exp

161

R

tnD

nP

P e

n

t

(2)



0

02

04

06

08

1

12

0 10 20 30 40 50 60

PtP






in the calculations











374311ndash 4330 2003






lesniakinigpl



























2D imaging)





















ACKNOWLEDGEMENTS















renatacichainigpl










































Nor196923492013









Research 14 4 p 317 324 ISNN 1520 7439 2005




cichainigpl












software (Table 1)



Median of pore

volume

[nm3]

Maximum

pore volume

[nm3]

Median of

pore surface

[m2]

Maximum pore

surface

[nm3]






































120591 = 1208 + 0006∙ 119890154120590 (1)

oslash = 04124 + 00005σ - 00013 1205902 (2)













75-85 2017


2016

09

1

11

12

13

14

15

16

17

0 01 02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18 19

Tort

uo

sity

[-]





































Engineering 51(3) 201-208 2002






America Journal 66(4) 1143-1150 2002































Thorton model [2 3]

119890119899 =

(1 minus

073 11988111989911989435

100 )05

119881119899119894 lt 119881119910

(6radic3

5) [1 minus

1

6(119881119910

119881119899119894)2]

1

2

(119881119910

119881119899119894) [(

119881119910

119881119899119894) + 2radic12 minus 02 (

119881119910

119881119899119894)2]

minus1

1

4

119881119899119894 gt 119881119910

(1)




119890119905 = 1 minus

2

120553[1198881 + 1198882 119905119886119899ℎ(1198883 + 1198884120553)] 120553 lt 120553119888119903119894119905

1 minus2

120553 120553 ge 120553119888119903119894119905

(2)

120553 =2

(1+119890119899)120583119905119886119899(90deg minus 120579) (3)















Acknowledgments


201309BST800157


Technol 328 375-388 2018


Eng 32 593-604 2005


1997


937ndash960 2009




























)()(1

2

psCp

sg

dz

spsC

ds

ds

p

sms

mm

mmm

m

cm

(1)

gdz

dpm (2)



119862119898(119904119898 119901) =1

119904119898(119901

119901119900)119898

119862119904(119904119898 119901) = 119904119898 (119901

119901119900)minus119899

(3)





22 1-22 2016





majkrzakinigpl













































Acknowledgements




46 559ndash632 2001






















of concrete [4]











12 Pages 917-927 2017










Częstochowa Poland




















Acknowledgements


Centre



Science 161 382-393 2017





























Chemiczny 96 9 2017
















a) b)








Acknowledgements

























Si

O

O

OH

Si

Si

Si

OHSi

OHSi


OC2H5

OC2H5

50deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NH2

O

O

O O

25deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NO

O

H

O

Si

O

O

OH

Si

Si

O

OH

Si NO

O

NH

trypsintrypsin

(1)


















































as follows

+ =120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(1)

+ = minus120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(2)






































































































15mm 8 mm 4 mm











particle size





























120591(120601 |119904|) =119886

120601119887∙|119904|119888+

119889

120601119890∙|119904|119891 (1)





















the grid nodes









120588119901 =119899119901

119888119898119886119909 (1)


































)C()C()C( (1)


























Conv(C)

C

CL












1

1198792=

1

119881119901int (119847119903 ∙ 119847)2

Ω119901119889119881 (1)



material

























































References























Fig 1 Metal foam


























2015





















34 45ndash54 1988








adamspgedupl













































2 ndash 1 1 ndash 1 2540 3410 4840

3 ndash 1 ndash 1 1 260 235 1990

4 ndash 1 1 1 3085 2560 5050

5 1 ndash 1 ndash 1 620 340 2690

6 1 1 ndash 1 2040 2580 4990

7 1 ndash 1 1 2120 1620 3620

8 1 1 1 1780 1935 3600

9 1682 0 0 140 1370 2570

10 ndash 1682 0 0 210 1135 360

11 0 1682 0 1005 2210 4980

12 0 ndash 1682 0 300 140 120

13 0 0 1682 4340 3590 4760

14 0 0 ndash 1682 1690 2570 3090

15 0 0 0 4390 4100 5900

16 0 0 0 5070 4220 5750

17 0 0 0 5150 4070 5880

18 0 0 0 5050 3970 5780

19 0 0 0 4760 4170 5800

20 0 0 0 5190 4145 5765









34(4) 349-354 1999











atrykozkoicmedupl






















will be presented

































a) b)



























































eklimowsaghdupl






systems [1] [2]


























NOTES




darekimcpczczestpl





















found in [3]









119873119906 = 119877119890119866117 ∙ 119866119886119866

minus084 ∙ 119864119900072 (1)








10222-10237 2016

























a) b)
























119959 = minus 119870

120578 nabla(119901 + 119880)
















119959 = 119870







also







Zh Eksp Teor Fiz 59(1) 110-115 1970







renatacichainigpl




















Sample ID

Pore width


Pore diameter


[m] [m] [m] [m]

8 40510-8 1198 10-8 16110-8 10010-7

32 235 10-8 721 10-8 93910-9 25010-8

42 33110-8 758 10-8 13210-8 15310-8
















975-995 2014





cieszkoukwedupl
































1

1205752=

1

119881119901int (119847119903 ∙ 119847)2Ω119901

119889119881 (1)








































120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) minus 119888119898(119904119898 119901) (

120597119904119898

120597119903)2= 119888119904(119904119898 119901) (1)






120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) = 119888119904(119904119898 119901) (2)







extrusion process


259-282 1984




22 1-22 2016






















beds


1469-5



































constant































pawelguzikurkedupl








































zecjanuniopolepl






parameters
































































119870119921 + 119887119943 = 0 (1)

nabla ∙ 119921 = 0 (2)





walls

























phenomena such as

in the wall zone

in the semi-coke

zone

in the closed

porosity zone

in the plastic

layer zone

in the coal zone










confinement


















modeling












































USA 1997






wojtekkinskiwppl













easy visualised


























wojtekkinskiwppl








on full 3D geometry














curved channels 16 1068 345 800 087 1068

































2]


equation [1 3]

120595 = int119867119889120591

120556119901

119905

0 (1)







120595 = int119867119889120591

120556119901

1199051199010

= 1 (2)


[1]

120556119901 = 120556119901(119896120590 120583120590 119867 119879 119861(120591) 119883119894) (3)






T ndash temperature

























aq

e

D

D

(1)








2

22

1

22exp

161

R

tnD

nP

P e

n

t

(2)



0

02

04

06

08

1

12

0 10 20 30 40 50 60

PtP






in the calculations











374311ndash 4330 2003






lesniakinigpl



























2D imaging)





















ACKNOWLEDGEMENTS















renatacichainigpl










































Nor196923492013









Research 14 4 p 317 324 ISNN 1520 7439 2005




cichainigpl












software (Table 1)



Median of pore

volume

[nm3]

Maximum

pore volume

[nm3]

Median of

pore surface

[m2]

Maximum pore

surface

[nm3]






































120591 = 1208 + 0006∙ 119890154120590 (1)

oslash = 04124 + 00005σ - 00013 1205902 (2)













75-85 2017


2016

09

1

11

12

13

14

15

16

17

0 01 02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18 19

Tort

uo

sity

[-]





































Engineering 51(3) 201-208 2002






America Journal 66(4) 1143-1150 2002































Thorton model [2 3]

119890119899 =

(1 minus

073 11988111989911989435

100 )05

119881119899119894 lt 119881119910

(6radic3

5) [1 minus

1

6(119881119910

119881119899119894)2]

1

2

(119881119910

119881119899119894) [(

119881119910

119881119899119894) + 2radic12 minus 02 (

119881119910

119881119899119894)2]

minus1

1

4

119881119899119894 gt 119881119910

(1)




119890119905 = 1 minus

2

120553[1198881 + 1198882 119905119886119899ℎ(1198883 + 1198884120553)] 120553 lt 120553119888119903119894119905

1 minus2

120553 120553 ge 120553119888119903119894119905

(2)

120553 =2

(1+119890119899)120583119905119886119899(90deg minus 120579) (3)















Acknowledgments


201309BST800157


Technol 328 375-388 2018


Eng 32 593-604 2005


1997


937ndash960 2009




























)()(1

2

psCp

sg

dz

spsC

ds

ds

p

sms

mm

mmm

m

cm

(1)

gdz

dpm (2)



119862119898(119904119898 119901) =1

119904119898(119901

119901119900)119898

119862119904(119904119898 119901) = 119904119898 (119901

119901119900)minus119899

(3)





22 1-22 2016





majkrzakinigpl













































Acknowledgements




46 559ndash632 2001






















of concrete [4]











12 Pages 917-927 2017










Częstochowa Poland




















Acknowledgements


Centre



Science 161 382-393 2017





























Chemiczny 96 9 2017
















a) b)








Acknowledgements

























Si

O

O

OH

Si

Si

Si

OHSi

OHSi


OC2H5

OC2H5

50deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NH2

O

O

O O

25deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NO

O

H

O

Si

O

O

OH

Si

Si

O

OH

Si NO

O

NH

trypsintrypsin

(1)


















































as follows

+ =120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(1)

+ = minus120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(2)






































































































15mm 8 mm 4 mm











particle size





























120591(120601 |119904|) =119886

120601119887∙|119904|119888+

119889

120601119890∙|119904|119891 (1)





















the grid nodes









120588119901 =119899119901

119888119898119886119909 (1)


































)C()C()C( (1)


























Conv(C)

C

CL












1

1198792=

1

119881119901int (119847119903 ∙ 119847)2

Ω119901119889119881 (1)



material

























































References























Fig 1 Metal foam


























2015





















34 45ndash54 1988








adamspgedupl













































2 ndash 1 1 ndash 1 2540 3410 4840

3 ndash 1 ndash 1 1 260 235 1990

4 ndash 1 1 1 3085 2560 5050

5 1 ndash 1 ndash 1 620 340 2690

6 1 1 ndash 1 2040 2580 4990

7 1 ndash 1 1 2120 1620 3620

8 1 1 1 1780 1935 3600

9 1682 0 0 140 1370 2570

10 ndash 1682 0 0 210 1135 360

11 0 1682 0 1005 2210 4980

12 0 ndash 1682 0 300 140 120

13 0 0 1682 4340 3590 4760

14 0 0 ndash 1682 1690 2570 3090

15 0 0 0 4390 4100 5900

16 0 0 0 5070 4220 5750

17 0 0 0 5150 4070 5880

18 0 0 0 5050 3970 5780

19 0 0 0 4760 4170 5800

20 0 0 0 5190 4145 5765









34(4) 349-354 1999











atrykozkoicmedupl






















will be presented

































a) b)



























































eklimowsaghdupl






systems [1] [2]


























NOTES





















a) b)
























119959 = minus 119870

120578 nabla(119901 + 119880)
















119959 = 119870







also







Zh Eksp Teor Fiz 59(1) 110-115 1970







renatacichainigpl




















Sample ID

Pore width


Pore diameter


[m] [m] [m] [m]

8 40510-8 1198 10-8 16110-8 10010-7

32 235 10-8 721 10-8 93910-9 25010-8

42 33110-8 758 10-8 13210-8 15310-8
















975-995 2014





cieszkoukwedupl
































1

1205752=

1

119881119901int (119847119903 ∙ 119847)2Ω119901

119889119881 (1)








































120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) minus 119888119898(119904119898 119901) (

120597119904119898

120597119903)2= 119888119904(119904119898 119901) (1)






120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) = 119888119904(119904119898 119901) (2)







extrusion process


259-282 1984




22 1-22 2016






















beds


1469-5



































constant































pawelguzikurkedupl








































zecjanuniopolepl






parameters
































































119870119921 + 119887119943 = 0 (1)

nabla ∙ 119921 = 0 (2)





walls

























phenomena such as

in the wall zone

in the semi-coke

zone

in the closed

porosity zone

in the plastic

layer zone

in the coal zone










confinement


















modeling












































USA 1997






wojtekkinskiwppl













easy visualised


























wojtekkinskiwppl








on full 3D geometry














curved channels 16 1068 345 800 087 1068

































2]


equation [1 3]

120595 = int119867119889120591

120556119901

119905

0 (1)







120595 = int119867119889120591

120556119901

1199051199010

= 1 (2)


[1]

120556119901 = 120556119901(119896120590 120583120590 119867 119879 119861(120591) 119883119894) (3)






T ndash temperature

























aq

e

D

D

(1)








2

22

1

22exp

161

R

tnD

nP

P e

n

t

(2)



0

02

04

06

08

1

12

0 10 20 30 40 50 60

PtP






in the calculations











374311ndash 4330 2003






lesniakinigpl



























2D imaging)





















ACKNOWLEDGEMENTS















renatacichainigpl










































Nor196923492013









Research 14 4 p 317 324 ISNN 1520 7439 2005




cichainigpl












software (Table 1)



Median of pore

volume

[nm3]

Maximum

pore volume

[nm3]

Median of

pore surface

[m2]

Maximum pore

surface

[nm3]






































120591 = 1208 + 0006∙ 119890154120590 (1)

oslash = 04124 + 00005σ - 00013 1205902 (2)













75-85 2017


2016

09

1

11

12

13

14

15

16

17

0 01 02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18 19

Tort

uo

sity

[-]





































Engineering 51(3) 201-208 2002






America Journal 66(4) 1143-1150 2002































Thorton model [2 3]

119890119899 =

(1 minus

073 11988111989911989435

100 )05

119881119899119894 lt 119881119910

(6radic3

5) [1 minus

1

6(119881119910

119881119899119894)2]

1

2

(119881119910

119881119899119894) [(

119881119910

119881119899119894) + 2radic12 minus 02 (

119881119910

119881119899119894)2]

minus1

1

4

119881119899119894 gt 119881119910

(1)




119890119905 = 1 minus

2

120553[1198881 + 1198882 119905119886119899ℎ(1198883 + 1198884120553)] 120553 lt 120553119888119903119894119905

1 minus2

120553 120553 ge 120553119888119903119894119905

(2)

120553 =2

(1+119890119899)120583119905119886119899(90deg minus 120579) (3)















Acknowledgments


201309BST800157


Technol 328 375-388 2018


Eng 32 593-604 2005


1997


937ndash960 2009




























)()(1

2

psCp

sg

dz

spsC

ds

ds

p

sms

mm

mmm

m

cm

(1)

gdz

dpm (2)



119862119898(119904119898 119901) =1

119904119898(119901

119901119900)119898

119862119904(119904119898 119901) = 119904119898 (119901

119901119900)minus119899

(3)





22 1-22 2016





majkrzakinigpl













































Acknowledgements




46 559ndash632 2001






















of concrete [4]











12 Pages 917-927 2017










Częstochowa Poland




















Acknowledgements


Centre



Science 161 382-393 2017





























Chemiczny 96 9 2017
















a) b)








Acknowledgements

























Si

O

O

OH

Si

Si

Si

OHSi

OHSi


OC2H5

OC2H5

50deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NH2

O

O

O O

25deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NO

O

H

O

Si

O

O

OH

Si

Si

O

OH

Si NO

O

NH

trypsintrypsin

(1)


















































as follows

+ =120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(1)

+ = minus120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(2)






































































































15mm 8 mm 4 mm











particle size





























120591(120601 |119904|) =119886

120601119887∙|119904|119888+

119889

120601119890∙|119904|119891 (1)





















the grid nodes









120588119901 =119899119901

119888119898119886119909 (1)


































)C()C()C( (1)


























Conv(C)

C

CL












1

1198792=

1

119881119901int (119847119903 ∙ 119847)2

Ω119901119889119881 (1)



material

























































References























Fig 1 Metal foam


























2015





















34 45ndash54 1988








adamspgedupl













































2 ndash 1 1 ndash 1 2540 3410 4840

3 ndash 1 ndash 1 1 260 235 1990

4 ndash 1 1 1 3085 2560 5050

5 1 ndash 1 ndash 1 620 340 2690

6 1 1 ndash 1 2040 2580 4990

7 1 ndash 1 1 2120 1620 3620

8 1 1 1 1780 1935 3600

9 1682 0 0 140 1370 2570

10 ndash 1682 0 0 210 1135 360

11 0 1682 0 1005 2210 4980

12 0 ndash 1682 0 300 140 120

13 0 0 1682 4340 3590 4760

14 0 0 ndash 1682 1690 2570 3090

15 0 0 0 4390 4100 5900

16 0 0 0 5070 4220 5750

17 0 0 0 5150 4070 5880

18 0 0 0 5050 3970 5780

19 0 0 0 4760 4170 5800

20 0 0 0 5190 4145 5765









34(4) 349-354 1999











atrykozkoicmedupl






















will be presented

































a) b)



























































eklimowsaghdupl






systems [1] [2]


























NOTES










119959 = minus 119870

120578 nabla(119901 + 119880)
















119959 = 119870







also







Zh Eksp Teor Fiz 59(1) 110-115 1970







renatacichainigpl




















Sample ID

Pore width


Pore diameter


[m] [m] [m] [m]

8 40510-8 1198 10-8 16110-8 10010-7

32 235 10-8 721 10-8 93910-9 25010-8

42 33110-8 758 10-8 13210-8 15310-8
















975-995 2014





cieszkoukwedupl
































1

1205752=

1

119881119901int (119847119903 ∙ 119847)2Ω119901

119889119881 (1)








































120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) minus 119888119898(119904119898 119901) (

120597119904119898

120597119903)2= 119888119904(119904119898 119901) (1)






120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) = 119888119904(119904119898 119901) (2)







extrusion process


259-282 1984




22 1-22 2016






















beds


1469-5



































constant































pawelguzikurkedupl








































zecjanuniopolepl






parameters
































































119870119921 + 119887119943 = 0 (1)

nabla ∙ 119921 = 0 (2)





walls

























phenomena such as

in the wall zone

in the semi-coke

zone

in the closed

porosity zone

in the plastic

layer zone

in the coal zone










confinement


















modeling












































USA 1997






wojtekkinskiwppl













easy visualised


























wojtekkinskiwppl








on full 3D geometry














curved channels 16 1068 345 800 087 1068

































2]


equation [1 3]

120595 = int119867119889120591

120556119901

119905

0 (1)







120595 = int119867119889120591

120556119901

1199051199010

= 1 (2)


[1]

120556119901 = 120556119901(119896120590 120583120590 119867 119879 119861(120591) 119883119894) (3)






T ndash temperature

























aq

e

D

D

(1)








2

22

1

22exp

161

R

tnD

nP

P e

n

t

(2)



0

02

04

06

08

1

12

0 10 20 30 40 50 60

PtP






in the calculations











374311ndash 4330 2003






lesniakinigpl



























2D imaging)





















ACKNOWLEDGEMENTS















renatacichainigpl










































Nor196923492013









Research 14 4 p 317 324 ISNN 1520 7439 2005




cichainigpl












software (Table 1)



Median of pore

volume

[nm3]

Maximum

pore volume

[nm3]

Median of

pore surface

[m2]

Maximum pore

surface

[nm3]






































120591 = 1208 + 0006∙ 119890154120590 (1)

oslash = 04124 + 00005σ - 00013 1205902 (2)













75-85 2017


2016

09

1

11

12

13

14

15

16

17

0 01 02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18 19

Tort

uo

sity

[-]





































Engineering 51(3) 201-208 2002






America Journal 66(4) 1143-1150 2002































Thorton model [2 3]

119890119899 =

(1 minus

073 11988111989911989435

100 )05

119881119899119894 lt 119881119910

(6radic3

5) [1 minus

1

6(119881119910

119881119899119894)2]

1

2

(119881119910

119881119899119894) [(

119881119910

119881119899119894) + 2radic12 minus 02 (

119881119910

119881119899119894)2]

minus1

1

4

119881119899119894 gt 119881119910

(1)




119890119905 = 1 minus

2

120553[1198881 + 1198882 119905119886119899ℎ(1198883 + 1198884120553)] 120553 lt 120553119888119903119894119905

1 minus2

120553 120553 ge 120553119888119903119894119905

(2)

120553 =2

(1+119890119899)120583119905119886119899(90deg minus 120579) (3)















Acknowledgments


201309BST800157


Technol 328 375-388 2018


Eng 32 593-604 2005


1997


937ndash960 2009




























)()(1

2

psCp

sg

dz

spsC

ds

ds

p

sms

mm

mmm

m

cm

(1)

gdz

dpm (2)



119862119898(119904119898 119901) =1

119904119898(119901

119901119900)119898

119862119904(119904119898 119901) = 119904119898 (119901

119901119900)minus119899

(3)





22 1-22 2016





majkrzakinigpl













































Acknowledgements




46 559ndash632 2001






















of concrete [4]











12 Pages 917-927 2017










Częstochowa Poland




















Acknowledgements


Centre



Science 161 382-393 2017





























Chemiczny 96 9 2017
















a) b)








Acknowledgements

























Si

O

O

OH

Si

Si

Si

OHSi

OHSi


OC2H5

OC2H5

50deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NH2

O

O

O O

25deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NO

O

H

O

Si

O

O

OH

Si

Si

O

OH

Si NO

O

NH

trypsintrypsin

(1)


















































as follows

+ =120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(1)

+ = minus120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(2)






































































































15mm 8 mm 4 mm











particle size





























120591(120601 |119904|) =119886

120601119887∙|119904|119888+

119889

120601119890∙|119904|119891 (1)





















the grid nodes









120588119901 =119899119901

119888119898119886119909 (1)


































)C()C()C( (1)


























Conv(C)

C

CL












1

1198792=

1

119881119901int (119847119903 ∙ 119847)2

Ω119901119889119881 (1)



material

























































References























Fig 1 Metal foam


























2015





















34 45ndash54 1988








adamspgedupl













































2 ndash 1 1 ndash 1 2540 3410 4840

3 ndash 1 ndash 1 1 260 235 1990

4 ndash 1 1 1 3085 2560 5050

5 1 ndash 1 ndash 1 620 340 2690

6 1 1 ndash 1 2040 2580 4990

7 1 ndash 1 1 2120 1620 3620

8 1 1 1 1780 1935 3600

9 1682 0 0 140 1370 2570

10 ndash 1682 0 0 210 1135 360

11 0 1682 0 1005 2210 4980

12 0 ndash 1682 0 300 140 120

13 0 0 1682 4340 3590 4760

14 0 0 ndash 1682 1690 2570 3090

15 0 0 0 4390 4100 5900

16 0 0 0 5070 4220 5750

17 0 0 0 5150 4070 5880

18 0 0 0 5050 3970 5780

19 0 0 0 4760 4170 5800

20 0 0 0 5190 4145 5765









34(4) 349-354 1999











atrykozkoicmedupl






















will be presented

































a) b)



























































eklimowsaghdupl






systems [1] [2]


























NOTES




renatacichainigpl




















Sample ID

Pore width


Pore diameter


[m] [m] [m] [m]

8 40510-8 1198 10-8 16110-8 10010-7

32 235 10-8 721 10-8 93910-9 25010-8

42 33110-8 758 10-8 13210-8 15310-8
















975-995 2014





cieszkoukwedupl
































1

1205752=

1

119881119901int (119847119903 ∙ 119847)2Ω119901

119889119881 (1)








































120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) minus 119888119898(119904119898 119901) (

120597119904119898

120597119903)2= 119888119904(119904119898 119901) (1)






120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) = 119888119904(119904119898 119901) (2)







extrusion process


259-282 1984




22 1-22 2016






















beds


1469-5



































constant































pawelguzikurkedupl








































zecjanuniopolepl






parameters
































































119870119921 + 119887119943 = 0 (1)

nabla ∙ 119921 = 0 (2)





walls

























phenomena such as

in the wall zone

in the semi-coke

zone

in the closed

porosity zone

in the plastic

layer zone

in the coal zone










confinement


















modeling












































USA 1997






wojtekkinskiwppl













easy visualised


























wojtekkinskiwppl








on full 3D geometry














curved channels 16 1068 345 800 087 1068

































2]


equation [1 3]

120595 = int119867119889120591

120556119901

119905

0 (1)







120595 = int119867119889120591

120556119901

1199051199010

= 1 (2)


[1]

120556119901 = 120556119901(119896120590 120583120590 119867 119879 119861(120591) 119883119894) (3)






T ndash temperature

























aq

e

D

D

(1)








2

22

1

22exp

161

R

tnD

nP

P e

n

t

(2)



0

02

04

06

08

1

12

0 10 20 30 40 50 60

PtP






in the calculations











374311ndash 4330 2003






lesniakinigpl



























2D imaging)





















ACKNOWLEDGEMENTS















renatacichainigpl










































Nor196923492013









Research 14 4 p 317 324 ISNN 1520 7439 2005




cichainigpl












software (Table 1)



Median of pore

volume

[nm3]

Maximum

pore volume

[nm3]

Median of

pore surface

[m2]

Maximum pore

surface

[nm3]






































120591 = 1208 + 0006∙ 119890154120590 (1)

oslash = 04124 + 00005σ - 00013 1205902 (2)













75-85 2017


2016

09

1

11

12

13

14

15

16

17

0 01 02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18 19

Tort

uo

sity

[-]





































Engineering 51(3) 201-208 2002






America Journal 66(4) 1143-1150 2002































Thorton model [2 3]

119890119899 =

(1 minus

073 11988111989911989435

100 )05

119881119899119894 lt 119881119910

(6radic3

5) [1 minus

1

6(119881119910

119881119899119894)2]

1

2

(119881119910

119881119899119894) [(

119881119910

119881119899119894) + 2radic12 minus 02 (

119881119910

119881119899119894)2]

minus1

1

4

119881119899119894 gt 119881119910

(1)




119890119905 = 1 minus

2

120553[1198881 + 1198882 119905119886119899ℎ(1198883 + 1198884120553)] 120553 lt 120553119888119903119894119905

1 minus2

120553 120553 ge 120553119888119903119894119905

(2)

120553 =2

(1+119890119899)120583119905119886119899(90deg minus 120579) (3)















Acknowledgments


201309BST800157


Technol 328 375-388 2018


Eng 32 593-604 2005


1997


937ndash960 2009




























)()(1

2

psCp

sg

dz

spsC

ds

ds

p

sms

mm

mmm

m

cm

(1)

gdz

dpm (2)



119862119898(119904119898 119901) =1

119904119898(119901

119901119900)119898

119862119904(119904119898 119901) = 119904119898 (119901

119901119900)minus119899

(3)





22 1-22 2016





majkrzakinigpl













































Acknowledgements




46 559ndash632 2001






















of concrete [4]











12 Pages 917-927 2017










Częstochowa Poland




















Acknowledgements


Centre



Science 161 382-393 2017





























Chemiczny 96 9 2017
















a) b)








Acknowledgements

























Si

O

O

OH

Si

Si

Si

OHSi

OHSi


OC2H5

OC2H5

50deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NH2

O

O

O O

25deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NO

O

H

O

Si

O

O

OH

Si

Si

O

OH

Si NO

O

NH

trypsintrypsin

(1)


















































as follows

+ =120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(1)

+ = minus120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(2)






































































































15mm 8 mm 4 mm











particle size





























120591(120601 |119904|) =119886

120601119887∙|119904|119888+

119889

120601119890∙|119904|119891 (1)





















the grid nodes









120588119901 =119899119901

119888119898119886119909 (1)


































)C()C()C( (1)


























Conv(C)

C

CL












1

1198792=

1

119881119901int (119847119903 ∙ 119847)2

Ω119901119889119881 (1)



material

























































References























Fig 1 Metal foam


























2015





















34 45ndash54 1988








adamspgedupl













































2 ndash 1 1 ndash 1 2540 3410 4840

3 ndash 1 ndash 1 1 260 235 1990

4 ndash 1 1 1 3085 2560 5050

5 1 ndash 1 ndash 1 620 340 2690

6 1 1 ndash 1 2040 2580 4990

7 1 ndash 1 1 2120 1620 3620

8 1 1 1 1780 1935 3600

9 1682 0 0 140 1370 2570

10 ndash 1682 0 0 210 1135 360

11 0 1682 0 1005 2210 4980

12 0 ndash 1682 0 300 140 120

13 0 0 1682 4340 3590 4760

14 0 0 ndash 1682 1690 2570 3090

15 0 0 0 4390 4100 5900

16 0 0 0 5070 4220 5750

17 0 0 0 5150 4070 5880

18 0 0 0 5050 3970 5780

19 0 0 0 4760 4170 5800

20 0 0 0 5190 4145 5765









34(4) 349-354 1999











atrykozkoicmedupl






















will be presented

































a) b)



























































eklimowsaghdupl






systems [1] [2]


























NOTES





cieszkoukwedupl
































1

1205752=

1

119881119901int (119847119903 ∙ 119847)2Ω119901

119889119881 (1)








































120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) minus 119888119898(119904119898 119901) (

120597119904119898

120597119903)2= 119888119904(119904119898 119901) (1)






120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) = 119888119904(119904119898 119901) (2)







extrusion process


259-282 1984




22 1-22 2016






















beds


1469-5



































constant































pawelguzikurkedupl








































zecjanuniopolepl






parameters
































































119870119921 + 119887119943 = 0 (1)

nabla ∙ 119921 = 0 (2)





walls

























phenomena such as

in the wall zone

in the semi-coke

zone

in the closed

porosity zone

in the plastic

layer zone

in the coal zone










confinement


















modeling












































USA 1997






wojtekkinskiwppl













easy visualised


























wojtekkinskiwppl








on full 3D geometry














curved channels 16 1068 345 800 087 1068

































2]


equation [1 3]

120595 = int119867119889120591

120556119901

119905

0 (1)







120595 = int119867119889120591

120556119901

1199051199010

= 1 (2)


[1]

120556119901 = 120556119901(119896120590 120583120590 119867 119879 119861(120591) 119883119894) (3)






T ndash temperature

























aq

e

D

D

(1)








2

22

1

22exp

161

R

tnD

nP

P e

n

t

(2)



0

02

04

06

08

1

12

0 10 20 30 40 50 60

PtP






in the calculations











374311ndash 4330 2003






lesniakinigpl



























2D imaging)





















ACKNOWLEDGEMENTS















renatacichainigpl










































Nor196923492013









Research 14 4 p 317 324 ISNN 1520 7439 2005




cichainigpl












software (Table 1)



Median of pore

volume

[nm3]

Maximum

pore volume

[nm3]

Median of

pore surface

[m2]

Maximum pore

surface

[nm3]






































120591 = 1208 + 0006∙ 119890154120590 (1)

oslash = 04124 + 00005σ - 00013 1205902 (2)













75-85 2017


2016

09

1

11

12

13

14

15

16

17

0 01 02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18 19

Tort

uo

sity

[-]





































Engineering 51(3) 201-208 2002






America Journal 66(4) 1143-1150 2002































Thorton model [2 3]

119890119899 =

(1 minus

073 11988111989911989435

100 )05

119881119899119894 lt 119881119910

(6radic3

5) [1 minus

1

6(119881119910

119881119899119894)2]

1

2

(119881119910

119881119899119894) [(

119881119910

119881119899119894) + 2radic12 minus 02 (

119881119910

119881119899119894)2]

minus1

1

4

119881119899119894 gt 119881119910

(1)




119890119905 = 1 minus

2

120553[1198881 + 1198882 119905119886119899ℎ(1198883 + 1198884120553)] 120553 lt 120553119888119903119894119905

1 minus2

120553 120553 ge 120553119888119903119894119905

(2)

120553 =2

(1+119890119899)120583119905119886119899(90deg minus 120579) (3)















Acknowledgments


201309BST800157


Technol 328 375-388 2018


Eng 32 593-604 2005


1997


937ndash960 2009




























)()(1

2

psCp

sg

dz

spsC

ds

ds

p

sms

mm

mmm

m

cm

(1)

gdz

dpm (2)



119862119898(119904119898 119901) =1

119904119898(119901

119901119900)119898

119862119904(119904119898 119901) = 119904119898 (119901

119901119900)minus119899

(3)





22 1-22 2016





majkrzakinigpl













































Acknowledgements




46 559ndash632 2001






















of concrete [4]











12 Pages 917-927 2017










Częstochowa Poland




















Acknowledgements


Centre



Science 161 382-393 2017





























Chemiczny 96 9 2017
















a) b)








Acknowledgements

























Si

O

O

OH

Si

Si

Si

OHSi

OHSi


OC2H5

OC2H5

50deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NH2

O

O

O O

25deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NO

O

H

O

Si

O

O

OH

Si

Si

O

OH

Si NO

O

NH

trypsintrypsin

(1)


















































as follows

+ =120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(1)

+ = minus120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(2)






































































































15mm 8 mm 4 mm











particle size





























120591(120601 |119904|) =119886

120601119887∙|119904|119888+

119889

120601119890∙|119904|119891 (1)





















the grid nodes









120588119901 =119899119901

119888119898119886119909 (1)


































)C()C()C( (1)


























Conv(C)

C

CL












1

1198792=

1

119881119901int (119847119903 ∙ 119847)2

Ω119901119889119881 (1)



material

























































References























Fig 1 Metal foam


























2015





















34 45ndash54 1988








adamspgedupl













































2 ndash 1 1 ndash 1 2540 3410 4840

3 ndash 1 ndash 1 1 260 235 1990

4 ndash 1 1 1 3085 2560 5050

5 1 ndash 1 ndash 1 620 340 2690

6 1 1 ndash 1 2040 2580 4990

7 1 ndash 1 1 2120 1620 3620

8 1 1 1 1780 1935 3600

9 1682 0 0 140 1370 2570

10 ndash 1682 0 0 210 1135 360

11 0 1682 0 1005 2210 4980

12 0 ndash 1682 0 300 140 120

13 0 0 1682 4340 3590 4760

14 0 0 ndash 1682 1690 2570 3090

15 0 0 0 4390 4100 5900

16 0 0 0 5070 4220 5750

17 0 0 0 5150 4070 5880

18 0 0 0 5050 3970 5780

19 0 0 0 4760 4170 5800

20 0 0 0 5190 4145 5765









34(4) 349-354 1999











atrykozkoicmedupl






















will be presented

































a) b)



























































eklimowsaghdupl






systems [1] [2]


























NOTES






















120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) minus 119888119898(119904119898 119901) (

120597119904119898

120597119903)2= 119888119904(119904119898 119901) (1)






120597119904119898

120597119901(1 +

119889119904119888

119889119904119898) = 119888119904(119904119898 119901) (2)







extrusion process


259-282 1984




22 1-22 2016






















beds


1469-5



































constant































pawelguzikurkedupl








































zecjanuniopolepl






parameters
































































119870119921 + 119887119943 = 0 (1)

nabla ∙ 119921 = 0 (2)





walls

























phenomena such as

in the wall zone

in the semi-coke

zone

in the closed

porosity zone

in the plastic

layer zone

in the coal zone










confinement


















modeling












































USA 1997






wojtekkinskiwppl













easy visualised


























wojtekkinskiwppl








on full 3D geometry














curved channels 16 1068 345 800 087 1068

































2]


equation [1 3]

120595 = int119867119889120591

120556119901

119905

0 (1)







120595 = int119867119889120591

120556119901

1199051199010

= 1 (2)


[1]

120556119901 = 120556119901(119896120590 120583120590 119867 119879 119861(120591) 119883119894) (3)






T ndash temperature

























aq

e

D

D

(1)








2

22

1

22exp

161

R

tnD

nP

P e

n

t

(2)



0

02

04

06

08

1

12

0 10 20 30 40 50 60

PtP






in the calculations











374311ndash 4330 2003






lesniakinigpl



























2D imaging)





















ACKNOWLEDGEMENTS















renatacichainigpl










































Nor196923492013









Research 14 4 p 317 324 ISNN 1520 7439 2005




cichainigpl












software (Table 1)



Median of pore

volume

[nm3]

Maximum

pore volume

[nm3]

Median of

pore surface

[m2]

Maximum pore

surface

[nm3]






































120591 = 1208 + 0006∙ 119890154120590 (1)

oslash = 04124 + 00005σ - 00013 1205902 (2)













75-85 2017


2016

09

1

11

12

13

14

15

16

17

0 01 02 03 04 05 06 07 08 09 1 11 12 13 14 15 16 17 18 19

Tort

uo

sity

[-]





































Engineering 51(3) 201-208 2002






America Journal 66(4) 1143-1150 2002































Thorton model [2 3]

119890119899 =

(1 minus

073 11988111989911989435

100 )05

119881119899119894 lt 119881119910

(6radic3

5) [1 minus

1

6(119881119910

119881119899119894)2]

1

2

(119881119910

119881119899119894) [(

119881119910

119881119899119894) + 2radic12 minus 02 (

119881119910

119881119899119894)2]

minus1

1

4

119881119899119894 gt 119881119910

(1)




119890119905 = 1 minus

2

120553[1198881 + 1198882 119905119886119899ℎ(1198883 + 1198884120553)] 120553 lt 120553119888119903119894119905

1 minus2

120553 120553 ge 120553119888119903119894119905

(2)

120553 =2

(1+119890119899)120583119905119886119899(90deg minus 120579) (3)















Acknowledgments


201309BST800157


Technol 328 375-388 2018


Eng 32 593-604 2005


1997


937ndash960 2009




























)()(1

2

psCp

sg

dz

spsC

ds

ds

p

sms

mm

mmm

m

cm

(1)

gdz

dpm (2)



119862119898(119904119898 119901) =1

119904119898(119901

119901119900)119898

119862119904(119904119898 119901) = 119904119898 (119901

119901119900)minus119899

(3)





22 1-22 2016





majkrzakinigpl













































Acknowledgements




46 559ndash632 2001






















of concrete [4]











12 Pages 917-927 2017










Częstochowa Poland




















Acknowledgements


Centre



Science 161 382-393 2017





























Chemiczny 96 9 2017
















a) b)








Acknowledgements

























Si

O

O

OH

Si

Si

Si

OHSi

OHSi


OC2H5

OC2H5

50deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NH2

O

O

O O

25deg C (15-120 min)

Si

O

O

OH

Si

Si

O

OH

Si NO

O

H

O

Si

O

O

OH

Si

Si

O

OH

Si NO

O

NH

trypsintrypsin

(1)


















































as follows

+ =120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(1)

+ = minus120588119907120588119897120588119898

120572119907(1 minus 120572119907)3

119877radic2

3

(119901 minus 119901119904119886119905)

120588119897

(2)






































































































15mm 8 mm 4 mm











particle size





























120591(120601 |119904|) =119886

120601119887∙|119904|119888+

119889

120601119890∙|119904|119891 (1)





















the grid nodes









120588119901 =119899119901

119888119898119886119909 (1)


































)C()C()C( (1)


























Conv(C)

C

CL












1

1198792=

1

119881119901int (119847119903 ∙ 119847)2

Ω119901119889119881 (1)



material

























































References























Fig 1 Metal foam


























2015





















34 45ndash54 1988








adamspgedupl













































2 ndash 1 1 ndash 1 2540 3410 4840

3 ndash 1 ndash 1 1 260 235 1990

4 ndash 1 1 1 3085 2560 5050

5 1 ndash 1 ndash 1 620 340 2690

6 1 1 ndash 1 2040 2580 4990

7 1 ndash 1 1 2120 1620 3620

8 1 1 1 1780 1935 3600

9 1682 0 0 140 1370 2570

10 ndash 1682 0 0 210 1135 360

11 0 1682 0 1005 2210 4980

12 0 ndash 1682 0 300 140 120

13 0 0 1682 4340 3590 4760

14 0 0 ndash 1682 1690 2570 3090

15 0 0 0 4390 4100 5900

16 0 0 0 5070 4220 5750

17 0 0 0 5150 4070 5880

18 0 0 0 5050 3970 5780

19 0 0 0 4760 4170 5800

20 0 0 0 5190 4145 5765









34(4) 349-354 1999











atrykozkoicmedupl






















will be presented

































a) b)



























































eklimowsaghdupl






systems [1] [2]


























NOTES

2nd workshop on porous media · heat transfer in packed beds. none of the papers deals with...

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