formation damage and fines migration in …...formation damage mechanism in order to diagnose and...
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PROCEEDINGS, Thirty-Ninth Workshop on Geothermal Reservoir Engineering
Stanford University, Stanford, California, February 24-26, 2014
SGP-TR-202
1
Formation damage and fines migration in geothermal reservoirs
(modelling and field case study)
Zhenjiang You1, Pavel Bedrikovetsky
1, Alexander Badalyan
1,
Martin Hand2, Chris Matthews
2
1Australian School of Petroleum, The University of Adelaide, Adelaide, South Australia, 5005, Australia
2Institute of Minerals and Energy Resources, The University of Adelaide, Adelaide, South Australia, 5005, Australia
Keywords: fines migration, geothermal well, formation damage, mathematical model
ABSTRACT
Substantial formation damage and productivity reduction have been observed in numerous geothermal fields. However,
comprehensive analysis of formation damage and prediction of productivity specifically for geothermal reservoirs are not available
in the literature. On the basis of laboratory study and mathematical modelling, the current work is focused on the analysis of
formation damage mechanism in order to diagnose and predict the productivity decline.
Case study of a typical Australian geothermal reservoir A is performed. In this case, fines migration is recognised as the most likely
candidate of all formation damage mechanisms. The attaching electrostatic forces are weak at high temperatures if compared with
drag and lifting forces, which detach the particles from rock surfaces. Mobilisation of lifted fines results in particle straining in
smaller pore throats preferentially near the well, causing severe permeability and well productivity decline. A new model based on
laboratory study is developed; and field production data are successfully treated by the model.
The potential for fines migration and induced formation damage in geothermal wells is significantly higher than that for
conventional oil and gas wells due to weakening of attaching electrostatic forces under high temperatures. The evaluated well index
from field data is in good agreement with mathematical modelling prediction.
The proposed model allows for long-term productivity prediction from short production period, which allows recommending
methods of skin prevention, mitigation and removal.
1. INTRODUCTION
Permeability decline and formation damage induced by fines migration in conventional oil and gas reservoirs has been widely
observed since 1960s, and is still a hot topic of research nowadays (Muecke, 1979; Lever and Dawe, 1984; Sharma and Yortsos,
1987; Sarkar and Sharma, 1990; Khilar and Fogler, 1998; Tiab and Donaldson, 2004; Civan, 2007; Geng et al., 2010;
Bedrikovetsky et al., 2011). Recently, formation damage caused by migration of natural reservoir fines has been reported in
numerous geothermal projects as well (Ungemach, 2003; Milsch et al., 2009; Stacey et al., 2011; Tomaszewska and Pajak, 2012;
Rosenbrand et al., 2012). The mechanism of formation damage due to fines migration is explained by fine particle mobilisation,
where the mechanical equilibrium of attaching electrostatic force and detaching drag and lifting forces is disturbed at high velocity
or reduced salinity; the detached particles are subsequently retained in thin pores causing the permeability decline. Reduced values
of electrostatic forces which attach particles to grain surfaces at high temperature indicate that the pore plugging near to geothermal
wells is severer than that in oil and gas reservoirs. Hence, geothermal reservoirs are more vulnerable to fines migration and
formation damage than conventional oil and gas reservoirs. However, the comprehensive analysis of productivity impairment due
to fines migration specific for geothermal reservoirs has not been performed so far.
Mobilisation, migration, retention of fine particles in rocks and the variation of permeability are important for geothermal and
petroleum industries due to their effects on well productivity and injectivity. The mathematical modelling of deep bed filtration
accounting for particle detachment, capture and pore plugging is an essential part of the planning and design of the processes
mentioned above. In the classical model, it is assumed that the rate of particle detachment is proportional to the difference between
the maximum and the current values of parameters, such as velocity, salinity, pH, temperature, etc. The critical values of
parameters correspond to the beginning of detachment procedure (Khilar and Fogler, 1983, 1998; Bradford et al., 2009; Gitis et al.,
2010). However, the asymptotic stabilisation after abrupt change of parameters described in this model deviates from the laboratory
tests, which show an instant response to the steep parameter change (Ochi and Vernoux, 1998; Bedrikovetsky et al., 2012). The
modified particle detachment model by Bedrikovetsky et al. (2011, 2012) applied the maximum concentration of attached particles
as a function of velocity, salinity, pH, temperature, etc., instead of the kinetic expression for the detachment rate in the classical
model. This modified model overcomes the shortcomings of the classical model mentioned previously. Therefore, in the current
work the maximum retention function is used to describe fines detachment during the exploitation of geothermal wells.
Detailed analysis of this phenomenon yields methods and measures to prevent, mitigate and remove formation damage and improve
well index. For example, determination of well rates that prevent fines mobilisation is important for optimal exploitation of
geothermal producers. Planning and design of the above methods and measures are based on results of mathematical modelling.
However, to the best of our knowledge, the sophisticated mathematical model for fines migration during exploitation of geothermal
wells is not available in the literature.
You et al.
2
In the current work, we develop the governing equation system for flow of water with fines accounting for particle detachment,
migration and straining resulting in permeability decline. A new fundamental function of porous media with fines – maximum
retention function – is applied to the calculation of attached particle concentration (Bedrikovetsky et al., 2011). The effect of fluid
velocity on fines mobilisation in rock core and fragments from two wells from the same formation has been studied in the
laboratory work. The developed theoretical model for well inflow performance is applied to the field case, where the discharge
causes significant well impedance growth. Good agreement between the model prediction and field data validates the mathematical
model.
2. PHYSICS OF FINES MOBILISATION ON ROCK SURFACE: MAXIMUM RETENTION FUNCTION
Forces exerted on fine particles at the rock surface in the reservoir include: drag force Fd, lifting force Fl, electrostatic force Fe and
gravitational force Fg (Figure 1). The hydrodynamic drag and lifting forces contribute to detachment of the particles from the rock
surface; while the electrostatic and gravitational forces tend to attach them. The criterion of fines mobilisation on the grain surface
is the same as the condition of mechanical equilibrium of the detaching and attaching torques acting on the particle, assuming that
the mobilised particle will rotate around the contacted particles in the neighbourhood or a spike of the rough surface (Freitas and
Sharma, 2001; Bedrikovetsky et al., 2011).
Figure 1: Cross section of a pore throat and forces acting on the attached particles.
The hydrodynamic drag and lifting forces are monotonically increasing functions of flow velocity U. Therefore, the amount of fines
released from the rock surface gradually increases with the velocity rise, which has been observed during coreflooding with
piecewise constant velocity increase (Khilar and Fogler, 1998; Tiab and Donaldson, 2004). On the other side, the attaching
electrostatic force is monotonically increasing function of water salinity. Therefore, coreflooding with piecewise constant salinity
decrease also leads to additional fines release. To conclude, the attached particle concentration σa is a function of flow velocity and
water salinity. More generally, other factors such as cation exchange, ion valance and Brownian force also affect the attached
concentration in certain cases.
In general, the concentration of the attached particles is a function of the ratio between the detaching and attaching torques ε
(Bedrikovetsky et al., 2011)
a c r (1)
where ε is called the erosion ratio. It is defined as
d d l n
e g n
F U l F U l
F F l
(2)
in which ld and ln are the levers for drag force and normal force, respectively.
The relationship (1) is called the maximum retention function. Equations (1,2) also describe the dependency of the maximum
attached concentration versus pH, temperature and the concentrations of different ions. The formulae for the electrostatic, drag and
lifting forces can be found in the literature (Khilar and Fogler, 1998). Applying these expressions in the torque balance equilibrium
conditions yields different forms of the velocity-, salinity-, pH- and temperature dependencies of the maximum retention function.
Especially, the velocity dependency of the maximum attached concentration of mono-sized fines for cylindrical capillary tube is
2
01
a c r
m
UU
U
(3)
Fe Fg
Fl
Fd Water flux
Grain
Grain Grain
ld
ln
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3
where σ0 is the maximum attached concentration at no-flow condition (U=0); Um corresponds to the highest velocity at which
particles can remain attached at the rock surface. All particles will be detached by the drag force if the velocity U> Um.
More general form of the maximum retention function can be derived from (3) by integration in terms of particle and pore sizes
accounting for pore and particle size distributions, on the basis of different types of micro scale models such as random walks
(Shapiro and Bedrikovetsky, 2010; Edery et al., 2011; Yuan et al., 2012), population balance (Sharma and Yortsos, 1987;
Bedrikovetsky, 2008; Chalk et al., 2012; You et al., 2013) and Boltzmann models (Chen et al., 2008). Eq. (3) indicates particle
release due to velocity increase. This equation substitutes the detachment rate expression in the classical model for particle
detachment during colloidal suspension transport in porous media.
Figure 2 shows the detachment of particles from the pore wall by drag and lifting forces, their migration in the carrying water flux
and straining in thinner pore throats. The detachment yields insignificant increase of permeability while straining at pore throats
cause significant reduction in permeability. The permeability damage due to fines mobilisation, migration and straining occurs due
to the transformation of the particles from the attached to the strained state (Khilar and Fogler, 1998; Tiab and Donaldson, 2004).
Figure 2: Fine particle attachment, detachment and straining in porous media.
3. LABORATORY STUDY ON FINES MOBILISATION IN ROCK CORE AND FRAGMENTS
The effect of fluid velocity on fines mobilisation in rock core and fragments from two wells of the same formation was studied.
High-velocity flow contributed to detachment of particles and resulted in formation damage for a rock core sample. Different
behaviour was observed for mobilized fines from rock fragments: more particles were released at lower fluid velocities due to
higher surface-to-volume ratio for fragments. Low-salinity reservoir water contributes to the reduction of the attractive electrostatic
force between particles and matrix, and, thus, leading to additional (to velocity) fines mobilisation. The lifted fines were identified
as kaolinite and chlorite.
3.1 Materials
One core and fragments from Well B from depth 2553.25 m (later in the text LBrGr-1/core and LBrGr-1/fragm) and fragments
from Well A from depth 2903-2906 m (later in the text Sal-1/fragm) were investigated for fines mobilisation in the present study.
Application of 0.6 M NaCl solution prevents lifting fines in rock samples during saturation (lifting of fines cause rock damage,
which we try to avoid during sample preparation). This salinity creates conditions favourable for fines to be attached to a porous
matrix via electrostatic attraction force.
3.2 Experimental setup
An experimental apparatus described in details in (Badalyan, Carageorgos et al., 2012) was used for the following tests: liquid
permeability measurements of rock core and composite samples made of 30-50 µm glass beads and rock fragments, and study of
velocity-induced fines migration leading to formation damage.
3.3 Velocity-induced fines migration
Velocity-induced fines migration was performed using the above experimental setup at fluid (0.6 M NaCl in MilliQ water)
velocities varied from 1.3810-5 to 1.3810-3 m/s. In this fluid velocity range, relationship between the pressure drop across the
sandstone core and the velocity is linear, thus fulfilling the requirements of Darcy’s law. Additionally, in the field case, fluid
velocity varies from 9.5410-4 to 1.3810-5 m/s at the distance in radial direction from the centre of the well varying from 0.01 to
0.70 m. Thus, the choice of studied fluid velocities covers fluid velocities in real field. Effluent samples were collected for each
value of velocity, and their concentrations and zeta-potentials were measured.
Concentration and size distribution of released fines were measured by a portable particle counter PAMAS S4031 GO (PAMAS
GmbH, Salzuflen, Germany). This unit delivered results for particles number in the 0.641-to-9.584 µm particle size range.
3.4 SEM-EDAX analyses of released fines
Effluent suspensions after concentration measurements were filtered through a 0.45 µm filter and dried. Phillips XL30 and XL40
Scanning Electron Microscopes coupled with the thin film Energy Dispersed Analysis of X-rays detector (EDAX) were used,
respectively, for imaging of sample surfaces and X-ray analyses for the identification of minerals presented in fines released due to
velocity alterations.
U
σa C σs
You et al.
4
3.5 Results and discussions of laboratory study
As follows from Figure 3, LBrGr-1/core sample showed significant permeability decline from 28.34 to 13.42 mD. This may be
caused by the mobilisation of fines not attached to the rock surface, but “loosely” located in the pore space. Formation damage
results from the mobilised larger particles blocking smaller pore throats, and/or bridging of multiple smaller particles at larger pore
throats.
Figure 3: Permeability variation for LBrGr-1/core sample with fluid velocity.
Results for velocity-induced fines migration for cores and fragments are given in Figure 4: here, σ is the ratio of incremental
volume of fines collected at each velocity to the volume of a sample (core or fragments). The amount of particles mobilized from
LBrGr-1/core show increasing trend with solution velocities. Relatively high amount of fines released by fragments at initial very
low velocity of solution is caused by the fact that “surface-to-volume ratio” for fragments is higher than that for cores, thus a
greater surface area is exposed to flowing solution, causing more particles to be released. These so-called “loose” particles are
located in pores but not attached to rock porous matrix by electrostatic forces. Hydrodynamic force of a flowing solution mobilizes
such particles located in the close vicinity to fragment surface. The particles are not trapped by the throats of deeply located pores
of rock and are carried away by a stream of a solution flowing through a porous matrix formed by glass beads (mean pore throat
radius rpore = 3.78±0.54 mm) towards the outlet of the sample holder. The fact that these particles are mobilized at high salinity of
suspension (0.6 M NaCl) indicates that DLVO forces do not play role in this process, and supports their “loose” nature. Such
velocity assisted fines mobilisation was responsible for permeability reduction of undamaged LBrGr-1/core. Sal-1/fragm sample
also show increase for normalised effluent particle concentration with increased fluid velocity, which is a sign of formation damage
in Sal-1 well at high fluid velocities in the vicinity of wellbore.
Figure 4: Normalised incremental particle volume in effluents during velocity alterations.
Effluent suspensions after concentration measurements were filtered through a 0.45 µm filter and dried. Philips XL30 and XL40
Scanning Electron Microscopes coupled with the thin film Energy Dispersed Analysis of X-rays detector (EDAX) were used for
imaging of samples surfaces and X-ray analyses for the identification of minerals presented in fines released due to velocity
alterations. Results of these analyses for fines released from studied samples are presented in Figures 5-6. As follows from these
figures kaolinite and chlorite are major clays presented in all studied rock cores and fragments. Analysis of all presented SEM
photographs showed that clays form the majority of collected fines with EDAX elemental analysis supported observation from
SEM. A reasonable amount of particles on SEM images are smaller than weighted-mean size of fines determined by PAMAS
particles counter/sizer for each sample. This is due to the fact that particles form agglomerates which pass through porous media,
filtered and captured on SEM photographs.
0
10
20
30
0.0E+00 1.0E-03 2.0E-03 3.0E-03 4.0E-03
k, m
D
u, m/s
0
20
40
60
80
10
7
Velocity, m/s
LBrGr-1/core
0
2
4
6
8
10
10
7
Velocity, m/s
LBrGr-1/fragm
Sal-1/fragm
You et al.
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4. MATHEMATICAL MODEL FOR SUSPENSION FLOW TOWARDS WELL
For reservoir simulation purpose, a new mathematical model is developed accounting for both the Damaged Zone and the
Undamaged Zone in the reservoir. In the Damaged Zone, the fluid of suspension flow is considered incompressible and the flow
rate is constant; while in the Undamaged Zone, the fluid is compressible and no fines migration occurs.
Figure 5: SEM-EDAX FOR LBRGR-1/CORE.
Figure 6: SEM-EDAX FOR SAL-1/1.
a) Damaged Zone: rw<r<ri
The system of governing equations in this region includes:
1. Population balance equation accounting for all the suspended, attached and strained particles in the reservoir:
0a s
r c rc Ut r
(4)
2. Attached particle concentration expressed using the maximum retention function:
2
01
a c r
m
UU
U
(5)
3. Particle straining rate proportional to the advective flux of suspended particles:
s
sc U
t
(6)
4. Darcy’s law taking into account of permeability decline due to particle straining:
0
1s s
k pU
r
(7)
Kaolinite Chlorite
Felsdpar
Kaolinite
Chlorite
You et al.
6
In the above system of governing equations (4-7), is the porosity, λs is the filtration coefficient for particle straining, βs is the
formation damage coefficient, k0 is the initial reservoir permeability, is the dynamic viscosity of fluid; c, σa and σs are the
suspended, attached and strained particles, respectively.
The initial condition for suspended concentration is determined by the amount of lifted fines:
,
0 : , 0
,
a i
w m
a i a
m i
r r r
t c rU
r r r
(8)
The critical velocity Ui is reached at the radius
/ 2i i
r q U (9)
This radius ri is the outer boundary of the damaged zone, since it corresponds to the initial concentration of attached fines and no
more fines are lifted at r>ri.
The radius rm is calculated from
/ 2m m
r q U (10)
which corresponds to the maximum velocity that fines can stay attached at. All particles are lifted for U>Um, i.e. for r<rm.
The initial condition for strained particle concentration states that no strained fines are assumed to reside in the reservoir before the
production
0 : 0s
t (11)
The boundary condition for the pressure is set at the outer boundary of the damaged zone
:i i
r r p p (12)
in which the pressure pi is obtained from the solution of diffusivity equation in the undamaged zone.
b) Undamaged Zone: ri<r<re
The linearised equation for slightly compressible fluid flow applies to the pressure field in undamaged zone:
1p k pr
t c r r r
(13)
The initial condition for pressure ensures the constant initial reservoir pressure pres before production
0 :res
t p p (14)
The no-flow condition at the outer boundary of the undamaged zone indicates zero pressure gradient at the drainage radius re
: 0e
pr r
r
(15)
The inner boundary condition for pressure is imposed at the boundary of the damaged and undamaged zones
: 2
i
i
p qr r
r k r
(16)
The above system of equations together with initial and boundary conditions complete the mathematical model for flow with fines
towards well, which is solved numerically in the next section using the finite difference method.
You et al.
7
5. WELL PRODUCTIVITY ANALYSIS AND FORECAST (FIELD CASE STUDY)
To analyse the well productivity performance, the well impedance index is calculated as the normalised ratio between the pressure
drop and the flow rate:
0
0
p t q
J tp q t
(17)
In the Sal-1 case, the discharge rate varies within the range of 15-25 L/s. The representative flow rate of 20 L/s is taken in this
calculation. The evaluated impedance history for this well (dimensionless impedance index versus dimensionless time) is shown in
Figure (black star points). Values of main parameters used in the model simulation are as follows: the Hamaker constant
A123=5.7510-21 J (present calculations), the surface potentials for particle and grain are ψ1=-18.36 mV and ψ2=-30.20 mV (present
calculations for 0.07 M as NaCl salinity of reservoir water), respectively. Drag and lifting force coefficients ω=60 and χ=650, cake
porosity ϕc=0.1, reservoir temperature T=130 °C, the initial permeability k0=6.5 md, porosity ϕ=0.106, particle radius rs=2.00 μm.
The calculated well impedance from the developed model is plotted as blue curve in Figure , which is in good agreement with field
data. The results show that the well impedance increases with time at early stage during production, and then tends to constant at a
large time. This is a typical phenomenon for the case of productivity decline due to straining of the mobilised fines near the well.
Figure 7: Well impedance growth during well exploitation from the modeled results and field data.
It is necessary to investigate the effect of reservoir temperature on geothermal well performance. Let us start from the analysis of
temperature effect on the maximum retention function. Besides the field temperature T2=130 °C, three other typical values of
temperature are chosen for the calculation of the maximum retention function versus flow velocity: T1=100 °C, T3=200 °C, T4=300
°C. Results shown in Figure indicate that the higher temperature leads to the lower value of maximum retained particle
concentration at a fixed flow velocity. Thus, the larger amount of fines are lifted and released to the carrier water at the higher
temperature. It causes the larger particle straining rate subsequently and results in worse impairment of well. The well impedance as
a function of time at different temperature values is presented in Figure .
Figure 8: Critical retained particle concentration as a function of flow velocity at different temperatures (T1=100 ºC, T2=130
ºC, T3=200 ºC, T4=300 ºC).
Another important parameter affecting geothermal well performance is the production rate. The impedance curves in Figure are
generated from modelling results with three flow rate values: q=20 L/s is the well rate in the field case; 1.5q and 0.5q are chosen for
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60
1
2
3
4
T
J
Field data
Model
0 0.5 1 1.5
x 10-5
0
3
6
9x 10
-3
-U
cr
T1
T2
T3
T4
You et al.
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sensitivity study. It is found that the higher is the rate, the larger is the well impedance (Figure ). This is because a high rate causes
decrease of the maximum retained particle concentration, which leads to more fines detached from rock surface and larger
permeability decline due to particle straining afterwards.
Figure 9: Effect of temperature on the well impedance index profile (T1=100 ºC, T2=130 ºC, T3=200 ºC, T4=300 ºC).
Figure 10: Timely increase of well impedance for different production rates (q=20 L/s).
Based on the reservoir simulation, well productivity forecast is performed by applying the model developed. Result of the
impedance index profile for this particular field case shows that the well impedance is stabilized after eight times of the current
discharge period (around 40 hours). The stable value of the index is 3.0 (Figure ).
Figure 11: Long-term well index forecast.
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60
1
2
3
4
5
T
J
T1
T2
T3
T4
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60
1
2
3
4
5
T
J
q
1.5q
0.5q
0 1 2 3 4 5 6 7 80
1
2
3
4
T
J
Field data
Model
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6. CONCLUSIONS
Experimental studies on fines mobilisation in rock sample of cores and fragments, derivation of governing equations for suspension
flow towards geothermal wells, their numerical solution and comparison with the well production case in geothermal reservoirs
allow drawing the following conclusions:
1. Velocity-induced fines migration is responsible for a significant reduction of rock permeability leading to initial
formation damage in the studied rock samples.
2. Low-salinity reservoir water leads to an increase of EDL repulsion force between clay particles and sand surface,
further particle mobilisation and formation damage in both Ladbroke Grove-1 and Salamander-1 rock samples, and,
therefore in the respective wells.
3. Kaolinite and chlorite are the major clay minerals presented in fines released from cores and fragments from Ladbroke
Grove-1 and Salamander-1 wells, and are responsible for rock permeability reduction.
4. Developed system of governing equations for water production with fines migration in geothermal reservoir consists
of population balance for suspended, attached and strained fines, the maximum retention function, the rate equation
for mobilised fines straining, and Darcy equation.
5. Numerical modelling reviews two typical stages of well impedance due to fines migration – quasi-steady state
production and straining of mobilised fines, and the asymptotical stabilisation of the productivity.
6. Well productivity history in field measurement and modelling based prediction are in good agreement, which validates
the proposed laboratory-based mathematical model.
7. Increase of the reservoir temperature leading to lower attached particle concentration indicates the higher particle
release with the temperature increase. Fines induced formation damage in geothermal wells is significantly more
probable than that for conventional oil and gas wells.
8. Numerical modelling of water production with fines migration shows that the higher is the temperature, the steeper is
the well impedance growth with time.
ACKNOWLEDGEMENTS
The authors acknowledge the Department for Manufacturing, Innovation, Trade, Resources and Energy (DMITRE), the Plan for
Accelerating Exploration (PACE) scheme, the Australian Renewable Energy Agency (ARENA), and the South Australian Centre
for Geothermal Energy Research (SACGER) for providing research support.
REFERENCES
Badalyan, A., Carageorgos, T. et al., 2012—Critical analysis of uncertainties during particle filtration. Review of Scientific
Instruments, 83, 095106.
Bedrikovetsky, P., 2008—Upscaling of stochastic micro model for suspension transport in porous media. Transport in Porous
Media, 75, 335-369.
Bedrikovetsky, P., Siqueira, F.D., Furtado, C.A. and Souza, A.L.S., 2011—Modified particle detachment model for colloidal
transport in porous media. Transport in Porous Media, 86, 353-383.
Bedrikovetsky, P., Zeinijahromi, A., Siqueira, F. D., Furtado, C. A. and de Souza, A. L. S., 2012—Particle detachment under
velocity alternation during suspension transport in porous media. Transport in Porous Media, 91, 173-197.
Bradford, S., Kim, H., Haznedaroglu, B., Torkzaban, S. and Walker, S., 2009—Coupled factors influencing concentration-
dependent colloid transport and retention in saturated porous media. Environ. Sci. Technol., 43, 6996–7002.
Chalk, P., Gooding, N., Hutten, S., You, Z. and Bedrikovetsky, P., 2012—Pore size distribution from challenge coreflood testing
by colloidal flow. Chem. Eng. Res. Des., 90, 63-77.
Chen, C., Packman, A. I. and Gaillard, J.-F., 2008—Pore-scale analysis of permeability reduction resulting from colloid deposition.
Geophys. Res. Lett., 35, L07404.
Civan, F., 2007—Reservoir Formation Damage: Fundamentals, Modeling, Assessment, and Mitigation. Burlington: Gulf
Professional Publishing, Elsevier.
Derjaguin, B. and Landau, L., 1993—Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly
charged particles in solutions of electrolytes. Progress in Surface Science, 43, 30-59.
Edery, Y., Kostinski, A. and Berkowitz, B., 2011—Record setting during dispersive transport in porous media. Geophys. Res. Lett.,
38, L16403.
Elimelech, M., Gregory, J. et al., 1995—Particle deposition and aggregartion: measurement, modelling, and simulation. New-York,
USA, Butterworth-Heinemann.
You et al.
10
Freitas, A. M. and Sharma, M. M., 2001—Detachment of particles from surfaces: An AFM study, Journal of Colloid and Interface
Science, 233, 73-82.
Geng J., Yan, J., Li, Z. and He, Z., 2010—Mechanisms and prevention of damage for formations with low-porosity and low-
permeability, SPE 130961 presented at the CPS/SPE International Oil & Gas Conference and Exhibition in China, Beijing, China,
8-10 June 2010.
Gitis, V., Rubinstein, I., Livshits, M. and Ziskind, G., 2010—Deep-bed filtration model with multistage deposition kinetics. Chem.
Eng. J., 163, 78-85.
Gregory, J., 1975—Interaction of unequal double layers at constant charge. Journal of Colloid and Interface Science, 51, 44-51.
Gregory, J., 1981—Approximate expressions for retarded van der Waals interactions. Journal of Colloid and Interface Science, 83,
138-145.
Hunter, R. J., 1981—Zeta potential in colloid science: principles and applications. Sydney, Academic Press.
Israelachvili, J. N., 2011—Intermolecular and surface forces. Sydney, Academic Press.
Khilar, K. and Fogler, S., 1983—Water sensitivity of sandstones. SPE Journal, 55-64.
Khilar, K. and Fogler, S., 1998—Migration of Fines in Porous Media, Kluwer Academic Publishers, Dordrecht, The Netherlands.
Lever, A. and Dawe, R., 1984—Water-sensitivity and migration of fines in the hopeman sandstone. J. Petro. Geology, 7, 97-107.
Milsch, H., Seibt, A. and Spangenberg, E., 2009—Long-term petrophysical investigations on geothermal reservoir rocks at
simulated In situ conditions. Transport in Porous Media, 77, 59-78.
Muecke, T.W., 1979—Formation fines and factors controlling their movement in porous media. J. Petro. Tech., 31, 144-150.
Ochi, J. and Vernoux, J.-F., 1998—Permeability decrease in sandstone reservoirs by fluid injection hydrodynamic and chemical
effects. J. Hydrol., 208, 237-248.
Rosenbrand, E., Fabricius, I. L. et al., 2013—Kaolinite mobilisation in sandstone pore filling vs suspended particles. Proceedings,
Thirty-Eight Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, CA.
Rosenbrand, E., Fabricius, I.L. and Yuan, H., 2012—Thermally induced permeability reduction due to particle migration in
sandstones: the effect of temperature on kaolinite mobilisation and aggregation. Proceedings, Thirty-Seventh Workshop on
Geothermal Reservoir Engineering, Stanford University, Stanford, CA.
Ruckenstein, E. and Prieve, D. C., 1976—Adsorption and desorption of particles and their chromatographic separation. American
Institute of Chemical Engineers Journal, 22, 276-283.
Sarkar, A. and Sharma, M., 1990—Fines migration in two-phase flow. J. Petro. Tech., 42, 646-652.
Sharma, M. M. and Yortsos, Y. C., 1987—Fines migration in porous media. American Institute of Chemical Engineers Journal, 33,
1654-1662.
Shapiro, A. and Bedrikovetsky, P., 2010—A stochastic theory for deep bed filtration accounting for dispersion and size
distributions. Physica A, 389, 2473-2494.
Stacey, R.W., Sanyal, S., Potter, J. and Wideman, T., 2011—Effectiveness of selective borehole enlargement to improve flow
performance of geothermal wells. Transactions - Geothermal Resources Council, 35, 239-245.
Tiab, D. and Donaldson, E. C., 2004—Petrophysics (2nd ed.), Elsevier, Burlington, MA, USA.
Tomas ewska, . and a a k, L., 2012—Dynamics of clogging processes in injection wells used to pump highly mineralized
thermal waters into the sandstone structures lying under the polish lowlands, Archives of Environmental Protection, 38, 105-117.
Ungemach, P., 2003—Reinjection of cooled geothermal brines into sandstone reservoirs. Geothermics, 32, 743-761.
Verwey, E. J. W. and Overbeek, J. T. G., 1999—Theory of the stability of lyophobic colloids. Toronto, Canada, General Publishing
Company.
You, Z., Badalyan, A. and Bedrikovetsky, P., 2013—Size-exclusion colloidal transport in porous media–stochastic modeling and
experimental study. SPE Journal, 18, 620-633.
Yuan, H, Shapiro, A., You, Z. and Badalyan, A., 2012—Estimating filtration coefficients for straining from percolation and random
walk theories. Chem. Eng. J., 210, 63-73.