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ScienceDirectEnergy Procedia 00 (2017) 000–000

www.elsevier.com/locate/procedia

1876-6102 © 2017 The Authors. Published by Elsevier Ltd.Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.

The 15th International Symposium on District Heating and Cooling

Assessing the feasibility of using the heat demand-outdoor temperature function for a long-term district heat demand forecast

I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc

aIN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, PortugalbVeolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France

cDépartement Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France

Abstract

District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heatsales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, prolonging the investment return period. The main scope of this paper is to assess the feasibility of using the heat demand – outdoor temperature function for heat demand forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were compared with results from a dynamic heat demand model, previously developed and validated by the authors.The results showed that when only weather change is considered, the margin of error could be acceptable for some applications(the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations.

© 2017 The Authors. Published by Elsevier Ltd.Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling.

Keywords: Heat demand; Forecast; Climate change

Energy Procedia 143 (2017) 466–474

1876-6102 © 2017 The Authors. Published by Elsevier Ltd.Peer-review under responsibility of the scientific committee of the World Engineers Summit – Applied Energy Symposium & Forum: Low Carbon Cities & Urban Energy Joint Conference.10.1016/j.egypro.2017.12.712

10.1016/j.egypro.2017.12.712 1876-6102

Available online at www.sciencedirect.com

ScienceDirect

Energy Procedia 00 (2017) 000–000 www.elsevier.com/locate/procedia

1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the World Engineers Summit – Applied Energy Symposium & Forum: Low Carbon Cities & Urban Energy Joint Conference.

World Engineers Summit – Applied Energy Symposium & Forum: Low Carbon Cities & Urban Energy Joint Conference, WES-CUE 2017, 19–21 July 2017, Singapore

Modelling clogging dynamism within dual-media pre-treatment rapid filters in seawater desalination

Alvin Wei Ze CHEWa, Adrian Wing Keung LAWa,* aSchool of Civil and Environmental Engineering and Environmental Process Modelling Centre (EPMC)

Nanyang Environment and Water Research Institute (NEWRI), Nanyang Technological University, Singapore

Abstract

The dual-media rapid filtration is a popular pre-treatment technology in seawater desalination industry. However, it is still difficult for operators to optimize both the filtration and backwashing processes, particularly during the rapid filtering of moderate and high turbid (MHT) influents, due to the lack of a good understanding of the clogging dynamism incurred during operations. In this study, we attempt to model the incurred clogging dynamism via both experimental and computational means. For the former, experimental filtering of MHT influents was carried out within a lab-scale dual-media rapid pressure filter under varying experimental conditions. Concurrently, dimensionless analysis of the particle removal constant (RC) parameter was performed by considering the initial influent conditions and media characteristics. Good agreement was achieved between the predicted values from the dimensionless formulation of RC and the respective experimental values, which renders the likelihood of employing the formulation to improve the design of pre-treatment rapid filters for filtering MHT influents. Lastly, we attempt to model the clogging dynamism with the homogenization upscaling approach, by computationally resolving both the macroscale and microscale hydraulic gradient under clean and increasing clogging filter condition respectively to approximate the total clogging hydraulic gradient (CHG). Good agreement between the computational and semi-empirical values was achieved for the clean filter condition. Developing the solver in an open-source Open Field Operation and Manipulation (OpenFOAM) CFD software to investigate the particles’ interactions with a singular collector grain for approximating the microscale CHG is currently in progress. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the World Engineers Summit – Applied Energy Symposium & Forum: Low Carbon Cities & Urban Energy Joint Conference.

Keywords: Dual-media rapid filters; clogging dynamics; seawater desalination pre-treatment

* Corresponding author. Tel.: (+65)6790 5296 E-mail address: [email protected]

2 CHEW, W.Z Alvin, LAW W.K Adrian/ Energy Procedia 00 (2017) 000–000

1. Introduction The dual-media rapid filters are employed extensively to pre-treat seawater influents for mitigating particulate

fouling in the downstream operating reverse osmosis (RO) membranes during seawater reverse osmosis (SWRO) desalination operations. Notwithstanding the advent of membrane pre-treatment technology [1-2], the granular rapid filters are still deployed in many large-scale SWRO desalination plants. Examples of those plants include the current largest SWRO plant in Sorek, Israel (624,000m3/d), Carlsbad, California (328,000m3/d), and Ashkelon, Israel (325,000m3/d). Selection of the pre-treatment technology for any SWRO plant requires a thorough life-cycle analysis (LCA) [2, 4] by considering the following factors: (a) seawater intake quality, (b) availability of funding, (c) level of expertise of operators etc. The conventionality of the granular filtration technology will likely render its continuity as the dominant pre-treatment tool in SWRO desalination operations.

Optimization of the rapid filtration mode has, however, still been difficult with moderate and high turbid (MHT) influents. Clogging rate within pre-treatment rapid filters (PTRFs) is expected to accelerate during filtering of MHT influents which increases filters’ backwashing frequency. Those operational difficulties have been well-documented for example in the case studies of Doha Research Plant, Jeddah SWRO plant and Addur SWRO plant in the Middle East [1, 5-6]. Traditionally, backwashing of rapid filters is initiated under either of the following conditions [7]: (a) once at every 24 hours of operations, or (b) exceedance in the filter effluent turbidity or filter head loss. For pointer (a), it is possible that the filter has not reached its maximum clogging capacity and is still able to function for an extended period before backwashing. For pointer (b), operational logistical problems may occur if the breakthrough occurs unexpectedly. Those problems are largely attested to the difficulty of predicting or approximating the clogging state within the operational PTRFs.

Attempts to quantify the clogging dynamism incurred during rapid filtration have been extensive. Readers are referred to the following references [8-11] for some examples. Most recently, Dalawadi et al. [12-13] vigorously performed the method of multiple scales via homogenization theory to optimize the engineering design of filters [12] and to quantify filter blockage [13]. In this study, we retain the fundamental principles of the homogenization upscaling approach in attempts to develop a predictive tool to approximate the transient clogging hydraulic gradient (CHG) under increasing clogging conditions. The predictions are compared to the results from the experimental rapid filtering of emulated MHT influents performed in this study. The computational analysis of the physical interactions between a singular filter grain and Lagrangian particles within a periodic microstructure, as part of the homogenization upscaling approach, is currently underway. Lastly, we shall demonstrate that the predicted values of the particle removal constant from its dimensionless formulation agreed well with our experimental values.

Nomenclature

Aj Vector function A Constant B Constant C1, C2 Constants C Concentration value (scalar) Cin Influent turbidity/concentration d50,p Average diameter of influent particles d10,c Effective diameter of dual-media i,j,k Tensor index Kij Permeability tensor Lmedia Depth of dual-media l Characteristic length of unit cell (microstructure) m, n Empirically derived constant p Pressure field (scalar) RC Particle removal constant t time uy Superficial velocity in ballistic flow direction

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Alvin Wei Ze Chew et al. / Energy Procedia 143 (2017) 466–474 467

Available online at www.sciencedirect.com

ScienceDirect

Energy Procedia 00 (2017) 000–000 www.elsevier.com/locate/procedia

1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the World Engineers Summit – Applied Energy Symposium & Forum: Low Carbon Cities & Urban Energy Joint Conference.

World Engineers Summit – Applied Energy Symposium & Forum: Low Carbon Cities & Urban Energy Joint Conference, WES-CUE 2017, 19–21 July 2017, Singapore

Modelling clogging dynamism within dual-media pre-treatment rapid filters in seawater desalination

Alvin Wei Ze CHEWa, Adrian Wing Keung LAWa,* aSchool of Civil and Environmental Engineering and Environmental Process Modelling Centre (EPMC)

Nanyang Environment and Water Research Institute (NEWRI), Nanyang Technological University, Singapore

Abstract

The dual-media rapid filtration is a popular pre-treatment technology in seawater desalination industry. However, it is still difficult for operators to optimize both the filtration and backwashing processes, particularly during the rapid filtering of moderate and high turbid (MHT) influents, due to the lack of a good understanding of the clogging dynamism incurred during operations. In this study, we attempt to model the incurred clogging dynamism via both experimental and computational means. For the former, experimental filtering of MHT influents was carried out within a lab-scale dual-media rapid pressure filter under varying experimental conditions. Concurrently, dimensionless analysis of the particle removal constant (RC) parameter was performed by considering the initial influent conditions and media characteristics. Good agreement was achieved between the predicted values from the dimensionless formulation of RC and the respective experimental values, which renders the likelihood of employing the formulation to improve the design of pre-treatment rapid filters for filtering MHT influents. Lastly, we attempt to model the clogging dynamism with the homogenization upscaling approach, by computationally resolving both the macroscale and microscale hydraulic gradient under clean and increasing clogging filter condition respectively to approximate the total clogging hydraulic gradient (CHG). Good agreement between the computational and semi-empirical values was achieved for the clean filter condition. Developing the solver in an open-source Open Field Operation and Manipulation (OpenFOAM) CFD software to investigate the particles’ interactions with a singular collector grain for approximating the microscale CHG is currently in progress. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the World Engineers Summit – Applied Energy Symposium & Forum: Low Carbon Cities & Urban Energy Joint Conference.

Keywords: Dual-media rapid filters; clogging dynamics; seawater desalination pre-treatment

* Corresponding author. Tel.: (+65)6790 5296 E-mail address: [email protected]


1. Introduction The dual-media rapid filters are employed extensively to pre-treat seawater influents for mitigating particulate

fouling in the downstream operating reverse osmosis (RO) membranes during seawater reverse osmosis (SWRO) desalination operations. Notwithstanding the advent of membrane pre-treatment technology [1-2], the granular rapid filters are still deployed in many large-scale SWRO desalination plants. Examples of those plants include the current largest SWRO plant in Sorek, Israel (624,000m3/d), Carlsbad, California (328,000m3/d), and Ashkelon, Israel (325,000m3/d). Selection of the pre-treatment technology for any SWRO plant requires a thorough life-cycle analysis (LCA) [2, 4] by considering the following factors: (a) seawater intake quality, (b) availability of funding, (c) level of expertise of operators etc. The conventionality of the granular filtration technology will likely render its continuity as the dominant pre-treatment tool in SWRO desalination operations.

Optimization of the rapid filtration mode has, however, still been difficult with moderate and high turbid (MHT) influents. Clogging rate within pre-treatment rapid filters (PTRFs) is expected to accelerate during filtering of MHT influents which increases filters’ backwashing frequency. Those operational difficulties have been well-documented for example in the case studies of Doha Research Plant, Jeddah SWRO plant and Addur SWRO plant in the Middle East [1, 5-6]. Traditionally, backwashing of rapid filters is initiated under either of the following conditions [7]: (a) once at every 24 hours of operations, or (b) exceedance in the filter effluent turbidity or filter head loss. For pointer (a), it is possible that the filter has not reached its maximum clogging capacity and is still able to function for an extended period before backwashing. For pointer (b), operational logistical problems may occur if the breakthrough occurs unexpectedly. Those problems are largely attested to the difficulty of predicting or approximating the clogging state within the operational PTRFs.

Attempts to quantify the clogging dynamism incurred during rapid filtration have been extensive. Readers are referred to the following references [8-11] for some examples. Most recently, Dalawadi et al. [12-13] vigorously performed the method of multiple scales via homogenization theory to optimize the engineering design of filters [12] and to quantify filter blockage [13]. In this study, we retain the fundamental principles of the homogenization upscaling approach in attempts to develop a predictive tool to approximate the transient clogging hydraulic gradient (CHG) under increasing clogging conditions. The predictions are compared to the results from the experimental rapid filtering of emulated MHT influents performed in this study. The computational analysis of the physical interactions between a singular filter grain and Lagrangian particles within a periodic microstructure, as part of the homogenization upscaling approach, is currently underway. Lastly, we shall demonstrate that the predicted values of the particle removal constant from its dimensionless formulation agreed well with our experimental values.

Nomenclature

Aj Vector function A Constant B Constant C1, C2 Constants C Concentration value (scalar) Cin Influent turbidity/concentration d50,p Average diameter of influent particles d10,c Effective diameter of dual-media i,j,k Tensor index Kij Permeability tensor Lmedia Depth of dual-media l Characteristic length of unit cell (microstructure) m, n Empirically derived constant p Pressure field (scalar) RC Particle removal constant t time uy Superficial velocity in ballistic flow direction

468 Alvin Wei Ze Chew et al. / Energy Procedia 143 (2017) 466–474 CHEW, W.Z Alvin, LAW W.K Adrian / Energy Procedia 00 (2017) 000–000 3

ui,j Velocity tensor Vs Superficial velocity xi,j, Xi,j Positional tensor Y1 Depth of macroscopic filter system ϴ Hydraulic retention time µin Influent dynamic viscosity ρ50,p Bulk density of influent particles π Pi-terms ε Small dimensionless parameter Ωf Fluid phase Ωs Solid phase Ωfs, ᴦ Solid-fluid interface Ω Unit-cell (microstructure) θ′ Porosity of unit-cell δij Kronecker delta

2. Proposed methodology

2.1. Coupling homogenization upscaling with computational analysis Referencing to Figure 1, we model the granular filter as a collection of fixed non-overlapping circular objects

which is defined as the porous media domain. By adopting the near-periodic condition, we focus on the cell-problem of a singular rigid sphere. Due to the inherent symmetry of the rigid spheres, the three-dimensional (3D) problem can be reduced to two-dimensional (2D) domain in Figure 1. The pore space within the cell problem (Ω) is defined as the fluid phase (Ωfluid) whereas the solid phase of the singular filter grain is defined as Ωsolid . Lastly, the interface between the solid and liquid phases is defined as Ωfs which is the surface boundary of the filter grain. The characteristic length of the cell problem is defined as l.

Figure 1: Simplified representation of granular filter in two-dimensions (2D) with emphasis of cell problem comprising of a singular circular object for emulating a filter grain.

The pore space within the cell problem in Figure 1 is assumed to be saturated with an incompressible Newtonian fluid which fulfils the Stokes’ problem under steady-state condition.

ρuj∂ui∂xj

= − ∂p∂xi

+ µ∇2ui, xi,j ∊ Ωf (1.1)

∂ui∂xi

= 0, xi,j ∊ Ωf (1.2)

ui = 0, xi,j ∊ Ωfs (1.3)

where p is the fluid pressure, u is the velocity vector, µ is the fluid viscosity, xi,j is the positional tensor where i, j can be x, y or z.


We first derive the homogenized equations for Darcy’s Law from Equations 1.1 to 1.3 with the method of multiple scales via homogenization theory. By introducing a small dimensionless parameter (ε) which links the slow and fast variables with respect to Figure 1, we normalize Equations 1.1, 1.2 and 1.3. We retain the ordering importance for each of the terms in Equation 2.1 and expand Equation 2.4 in accordance to the spatial derivatives, as shown in Equation 2.5, to obtain the PDEs at the different orders.

ρu′j∂u′i∂x′j

= − ∂p∂x′i

+ µ∇′2u′i, xi,j ∊ Ωf (2.1)

∂u′i∂x′i

= 0, xi,j ∊ Ωf (2.2)

u′i = 0, xi,j ∊ Ωfs (2.3)

ɛ2ρuj∂ui∂xj

= − ∂p∂xi

+ ɛµ∇2ui, xi,j ∊ Ωf (2.4)

∇= ∇x + ɛ∇X (2.5)

Order ɛ (0):

0 = ∂p0

∂xi (2.6)

p0 = p0(Xi) (2.7)

0 = ∂ui0

∂xi (2.8)

ui0 = ui

0(Xi) (2.9) Order ɛ (1):

0 = ∂ui0

∂Xi+ ∂ui

1

∂xi (2.10)

0 = − ∂p1

∂xi− ∂p0

∂Xi+ µ ∂2ui

0

∂xi2 (2.11)

Equation 2.11 is a linear problem for its solution can be written in Equations 2.12 and 2.13.

ui0 = −kij

∂p0

∂Xi (2.12)

p1 = −Aj∂p0

∂Xi+ p1 (2.13)

where kij and Aj must satisfy the following conditions, which must be solved within the unit microstructure periodic cell. ∂kij∂xi

= 0 , kij = 0 on Ґ

−∂Aj∂xi

+ µ∇2kij = −δij, Aj and kij are Ω periodic

To obtain the effective flow equation constituting to Darcy’s Law, we take the cell average of Equations 2.12 and 2.13 to obtain Equations 2.14 and 2.15.

⟨ui0⟩ = ⟨kij⟩

∂p0

∂Xi (2.14)

⟨p1⟩ = θp0(1) (2.15)

θ′ = ΩfΩ (2.16)

where ⟨ui0⟩ is the cell-avaerage seepage velocity (m/s), ⟨kij⟩ is the cell average hydraulic conductivity (m/s), ∂p0

∂Xi is

the macroscopic hydraulic gradient (dimensionless), θ′ is the porosity of the cell-analysis (dimensionless).

Alvin Wei Ze Chew et al. / Energy Procedia 143 (2017) 466–474 469 CHEW, W.Z Alvin, LAW W.K Adrian / Energy Procedia 00 (2017) 000–000 3

ui,j Velocity tensor Vs Superficial velocity xi,j, Xi,j Positional tensor Y1 Depth of macroscopic filter system ϴ Hydraulic retention time µin Influent dynamic viscosity ρ50,p Bulk density of influent particles π Pi-terms ε Small dimensionless parameter Ωf Fluid phase Ωs Solid phase Ωfs, ᴦ Solid-fluid interface Ω Unit-cell (microstructure) θ′ Porosity of unit-cell δij Kronecker delta

2. Proposed methodology

2.1. Coupling homogenization upscaling with computational analysis Referencing to Figure 1, we model the granular filter as a collection of fixed non-overlapping circular objects

which is defined as the porous media domain. By adopting the near-periodic condition, we focus on the cell-problem of a singular rigid sphere. Due to the inherent symmetry of the rigid spheres, the three-dimensional (3D) problem can be reduced to two-dimensional (2D) domain in Figure 1. The pore space within the cell problem (Ω) is defined as the fluid phase (Ωfluid) whereas the solid phase of the singular filter grain is defined as Ωsolid . Lastly, the interface between the solid and liquid phases is defined as Ωfs which is the surface boundary of the filter grain. The characteristic length of the cell problem is defined as l.

Figure 1: Simplified representation of granular filter in two-dimensions (2D) with emphasis of cell problem comprising of a singular circular object for emulating a filter grain.

The pore space within the cell problem in Figure 1 is assumed to be saturated with an incompressible Newtonian fluid which fulfils the Stokes’ problem under steady-state condition.

ρuj∂ui∂xj

= − ∂p∂xi

+ µ∇2ui, xi,j ∊ Ωf (1.1)

∂ui∂xi

= 0, xi,j ∊ Ωf (1.2)

ui = 0, xi,j ∊ Ωfs (1.3)

where p is the fluid pressure, u is the velocity vector, µ is the fluid viscosity, xi,j is the positional tensor where i, j can be x, y or z.


We first derive the homogenized equations for Darcy’s Law from Equations 1.1 to 1.3 with the method of multiple scales via homogenization theory. By introducing a small dimensionless parameter (ε) which links the slow and fast variables with respect to Figure 1, we normalize Equations 1.1, 1.2 and 1.3. We retain the ordering importance for each of the terms in Equation 2.1 and expand Equation 2.4 in accordance to the spatial derivatives, as shown in Equation 2.5, to obtain the PDEs at the different orders.

ρu′j∂u′i∂x′j

= − ∂p∂x′i

+ µ∇′2u′i, xi,j ∊ Ωf (2.1)

∂u′i∂x′i

= 0, xi,j ∊ Ωf (2.2)

u′i = 0, xi,j ∊ Ωfs (2.3)

ɛ2ρuj∂ui∂xj

= − ∂p∂xi

+ ɛµ∇2ui, xi,j ∊ Ωf (2.4)

∇= ∇x + ɛ∇X (2.5)

Order ɛ (0):

0 = ∂p0

∂xi (2.6)

p0 = p0(Xi) (2.7)

0 = ∂ui0

∂xi (2.8)

ui0 = ui

0(Xi) (2.9) Order ɛ (1):

0 = ∂ui0

∂Xi+ ∂ui

1

∂xi (2.10)

0 = − ∂p1

∂xi− ∂p0

∂Xi+ µ ∂2ui

0

∂xi2 (2.11)

Equation 2.11 is a linear problem for its solution can be written in Equations 2.12 and 2.13.

ui0 = −kij

∂p0

∂Xi (2.12)

p1 = −Aj∂p0

∂Xi+ p1 (2.13)

where kij and Aj must satisfy the following conditions, which must be solved within the unit microstructure periodic cell. ∂kij∂xi

= 0 , kij = 0 on Ґ

−∂Aj∂xi

+ µ∇2kij = −δij, Aj and kij are Ω periodic

To obtain the effective flow equation constituting to Darcy’s Law, we take the cell average of Equations 2.12 and 2.13 to obtain Equations 2.14 and 2.15.

⟨ui0⟩ = ⟨kij⟩

∂p0

∂Xi (2.14)

⟨p1⟩ = θp0(1) (2.15)

θ′ = ΩfΩ (2.16)

where ⟨ui0⟩ is the cell-avaerage seepage velocity (m/s), ⟨kij⟩ is the cell average hydraulic conductivity (m/s), ∂p0

∂Xi is

the macroscopic hydraulic gradient (dimensionless), θ′ is the porosity of the cell-analysis (dimensionless).


By applying the Gauss theorem and the boundary conditions, the cell average of Equation 2.8 results in Equation 2.17. Substituting Equation 2.14 into Equation 2.17 yields Equation 2.18. If the porous media domain is assumed to be homogeneous and isotropic on the macroscale, ⟨kij⟩ becomes a constant on the macroscale which results in Equation 2.19. The value of p0 can then be solved on the macroscale with the appropriate boundary conditions. ∂⟨ui

0⟩∂Xi

= 0 (2.17)

∂∂Xi

[⟨kij⟩∂p0

∂Xi] = 0 (2.18)

∂∂Xk

[∂p0

∂Xk] = 0 (2.19)

Equation 2.20 will be employed to approximate the total CHG under the increasingly clogging conditions, which will then be compared with the experimental values at a specific degree of clogging. p~ p0 + ɛp1 (2.20)

where p is the total clogging hydraulic gradient (CHG) (dimensionless), p0 is the clean bed hydraulic gradient (dimensionless), ɛ is the small parameter value (dimensionless) and p1 is the computationally derived microscale hydraulic gradient value (dimensionless) under increasing clogging conditions.

The value of p0 was either approximated by finding its exact analytical solution or resolving the cell problem computationally in Open-Source Open Field and Operations Manipulation (OpenFOAM) by analysing the clean filter conditions with no introduction of Lagrangian particles into the numerical domain. To emulate the increasing clogging conditions for approximating p1, we propose to inject Lagrangian particles into the numerical domain in OpenFOAM by considering the physical interactions between the emulated filter grain and the Lagrangian particles for 3 distinct cases in Figure 2.

Figure 2: Forces considerations in simplified computational model. (left) approaching particle towards grain, (middle) attachment of particle on grain, (right) detachment of particle from grain

2.2. Experimental filtering of MHT influents Rapid filtering of emulated MHT influents was carried within a lab-scale dual-media pressure filter setup as

schematically represented in Figure 3. The respective depth and effective size of the deployed dual-media (GAC and sand) were fixed at 30cm and 1.0mm, and 30cm and 0.425mm. Before each experimental run, appropriate amounts of particle image velocimetry (PIV) particles, having bulk density of 1030kgm−3 and average sizes of 50µm, 20µm and 5µm, were mixed with tap water to achieve the desired turbidity value for each of the monodisperse and polydisperse suspensions synthesized. No chemical pre-treatment was adopted for the synthesized PIV suspensions. A total of 20 rapid filtration experiments having varying initial turbidity value and average particle size (d50) was carried out at 2 different hydraulic loading rate of 20.0m/h and 27.1m/h. During the entire 42 minutes for each experimental run, 250ml of samples were extracted at sampling ports 4, 6, 7 and 8 at every 6-minute interval for immediate turbidity measurements upon extraction. The remaining samples of ports 6, 7 and 8 were kept properly for total suspended solids (TSS) and particle size analyses at the end of each experimental run. Pressure head measurements were taken at sampling ports 2, 4, 6, 7 and 8 for filter head loss measurements. Lastly, backwashing of the filter will be carried out upon the attainment of any of following conditions: (a) total head loss incurred


exceeded 2m, (b) turbidity of effluent was approximately less than 90% removal of the influent turbidity, or (c) at the end of the pre-designated experimental run of 42 minutes.

Figure 3: Schematic representation of lab-scale dual-media rapid pressure filter setup

3. Results and discussions

3.1. Approximation of 𝑝𝑝0 and 𝑝𝑝1 Due to the inherent symmetry adopted in Figure 1, the Laplace equation of (2.19) is resolved two-dimensionally

in Equations 3.1 to 3.3 by adopting the boundary conditions for a representative macroscopic filter system having unidirectional flow in Figure 4. Alternatively, the cell problem in Figure 1 is resolved computationally by adopting 2 numerical domains of 10 and 20 idealized rigid spheres in Figure 5a (i to ii). Proper numerical meshing procedures were adopted to mitigate the contact points issue in both domains, and the simulations were carried out at varying superficial velocities till steady-state condition was attained. Good agreement between the computational and semi-empirical values was achieved as shown in Figure 5a (iii). The author is currently developing the solver in OpenFOAM which is able to accommodate to the 3 distinct cases in Figure 2 as part of approximating the p1 microscale value at a specific degree of clogging within the computational domain.

∂∂Xy

[∂p0

∂Xy] = 0, p(x, 0) = C1, p(x, y) = C2 (3.1)

p0(y) = Ay + B, A and B are constants (3.2)

p0(y) = (C2 − C1Y1 )y + C1 (3.3)

3.2. Spatiotemporal variation of particle removal constant (𝑅𝑅𝐶𝐶) By assuming ballistic flow direction of the influent particles within the rapid filter setup and neglecting the

diffusive transport of particles due to the adopted hydraulic loading rate and particle size distribution in this study, the analytical solution to the one-dimensional (1D) transport equation of 3.4 can be approximated in Equation 3.5. Dimensionless formulation of RC parameter was carried out in Equations 3.4 to 3.9. To establish a close relationship to the analytically derived solution in Equation 3.5, we assumed the form of Equation 3.10 for predictive purpose. The n power parameter in Equation 3.10 will be calibrated accordingly to assume 90% removal of the initial turbidity value during the rapid filtering of MHT influents in this study. By adopting a value of 0.01 for n parameter in Equation 3.10, good agreement between the predicted values and experimental values for the RC parameter was achieved for all experimental runs as exemplified by the comparison made for the experimental filtering of 50µm particles suspensions in Figure 6. ∂C∂t + uy. ∂C

∂y = Rc, C(0, t) = Cin, Rc(0, t) = 0, C(y, 0) = 0, Rc(y, 0) = 0 (3.4)

|[C(y, t) − C(y(0), 0)]

Δt | = Rc(y(t), t) (3.5)

Rc = f(Vs, Lmedia, d50,p, d10,c, ρ50,p, µin, Cin) (3.6)π1 = f(π2, π3, π4, π5, π6) (3.7)


π1 = Rc · Lmedia2

µin, π2 = Cin · Lmedia

2

µin. t , π3 =ρ50,p · Lmedia

2

µin. t , π4 = d10,cLmedia

π5 =d50,p

Lmedia, π6 = Vs · t

Lmedia (3.8)

Rc. Lmedia2

µin= C1 (Cin. Lmedia

2

µin. t )a

· (ρ50,p. Lmedia

2

µin. t )b

( d10,cLmedia

)c

· (d50,p

Lmedia)

d· ( Vs. t

Lmedia)

e (3.9)

Rc = Cin · (1t) · (

Ѳ · ρ50,p · d50,p · Lmedia2

t2 · d10,c · µin)

n

(3.10)

Figure 4: Simplified representation of two-dimensional (2D) macroscopic filter system

(i)

(ii)

(iii)

Figure 5: (i) Numerical domain of 10 ideal spheres in OpenFOAM, (ii) Numerical domain of 20 ideal spheres in OpenFOAM and (iii) comparison between semi-empirical values and numerical values in OpenFOAM


(i)

(ii)

(iii)

Figure 6: Comparison between experimental and predicted values for RC incurred during the rapid filtering of 50µm particles suspensions

4. Conclusion and further works Both experimental and computational methods were attempted to model the clogging dynamism incurred during

the rapid filtering of MHT influents. Dimensionless formulation of the particle removal constant (RC) parameter was first established for predictive purpose. Experimental filtering of emulated MHT influents was then carried out under varying experimental conditions. Good agreement was achieved when comparing the experimental and predicted values for the RC parameter in all experimental runs. Lastly, we computationally approximated the macroscopic pressure gradient under the clean filter condition as part of the homogenization upscaling approach to estimate the total CHG incurred at a clogging stage. Current works involve the development of the computational


solver in OpenFOAM to approximate the microscale CHG by simulating the particles’ physical interactions with a singular collector grain.

Acknowledgements

The lab-scale rapid pressure filter setup employed in this study was funded by Singapore-MIT Alliance for Research and Technology (SMART). All other experimental materials used were provided by Nanyang Technological University (NTU) School of Civil and Environmental Engineering Environment Lab 1. The computational resources are currently provided by NTU Nanyang Environment and Water Research Institute (NEWRI) Environmental Process Modelling Centre (EPMC). The first author is grateful to NTU for the 4-year Nanyang President Graduate Scholarship (NPGS) for his PhD study.

References

[1] N. Prihasto, Q.F. Liu, and S.-H. Kim (2009), "Pre-treatment strategies for seawater desalination by reverse osmosis system," Desalination, vol. 249 (1), pp. 308-316.

[2] N. Voutchkov (2010), "Considerations for selection of seawater filtration pretreatment system," Desalination, vol. 261 (3), pp. 354-364. [3] Water Technology. [Online]. Available: http://www.water-technology.net/projects/sorek-desalination-plant/. [4] N. Voutchkov (2009), "SWRO pre-treatment systems: Choosing between conventional and membrane filtration," Filtration & Separation, vol.

46 (Supplement 1), pp. 5-8. [5] A. H. H. Al-Sheikh (1997), "Seawater reverse osmosis pretreatment with an emphasis on the Jeddah Plant operation experience,"

Desalination, vol. 110 (1-2), pp. 183-192. [6] S. Ebrahim, M. Abdel-Jawad, S. Bou-Hamad, and M. Safar (2001), "Fifteen years of R&D program in seawater desalination at KISR part I.

Pretreatment technologies for RO systems," Desalination, vol. 135 (1-3), pp. 141-153. [7] MWH Water Treatment: Principles and Design, John Wiley & Sons, Hoboken, New Jersey, 2005, ch.11. [8] C. R. O'Melia and W. All (1978), “The role of retained particles in deep bed filtration,” Prog. Wat. Tech. vol. 10 (5-6), pp. 167-182. [9] J. R. Hunt, B. C. Hwang, and L. M. McDowell-Boyer (1993), "Solids accumulation during deep bed filtration," Environmental Science &

Technology, vol. 27 (6), pp. 1099-1107. [10] D. C. Mays and J. R. Hunt (2005), "Hydrodynamic Aspects of Particle Clogging in Porous Media," Environmental Science & Technology,

vol. 39 (2), pp. 577-584. [11] D. C. Mays and J. R. Hunt (2007), "Hydrodynamic and Chemical Factors in Clogging by Montmorillonite in Porous Media," Environmental

Science & Technology, vol. 41 (16), pp. 5666-5671. [12] M. P. Dalwadi, I. M. Griffiths, and M. Bruna (2015), "Understanding how porosity gradients can make a better filter using homogenization

theory," Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, vol. 471 (2182). [13] M. P. Dalwadi, M. Bruna, and I. M. Griffiths (2016), "A multiscale method to calculate filter blockage," Journal of Fluid Mechanics, vol.

809, pp. 264-289.

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