Monte Carlo simulations of 2D flat-sheet membrane filters for constant-pressure water purification

TL;DR

The paper addresses flux decline and recovery in constant-pressure, dead-end membrane filtration by gases of foulants, introducing a Monte Carlo model that combines advection-diffusion transport with stochastic foulant grafting and backwashing. It captures intermediate blocking as the dominant fouling mechanism and validates the forward filtration and FF-BW cycling against experimental data, using parameter fitting anchored to measurable physical quantities. Key contributions include a tractable 2D domain representation, nondimensionalization to connect to experiments, and a probabilistic grafting/removal framework that reproduces observed flux dynamics and recovery. The approach enables prediction of flux behavior under varied foulant properties and filtration conditions and provides a flexible tool to explore backwashing strategies and their impact on performance in practical water-treatment scenarios.

Abstract

Membrane filtration is widely used in water treatment to remove foulants from contaminated water. Foulant build-up on the membrane occludes the area open for fluid flow, which impairs the efficiency of the filtration operation by decreasing the flux through the membrane. Backwashing is a strategy to restore the membrane, wherein clean water is processed backward through the membrane to dislodge attached foulants. We develop a Monte Carlo model to simulate constant-pressure forward filtration and backwashing through dead-end, flat-sheet membranes, with membrane fouling dominated by intermediate blocking. We validate our model against real-world experiments conducted with different foulant types and concentrations and run under different filtration conditions. Relying primarily on measurable physical parameters and employing easy-to-implement parameter fitting techniques as needed, we show good agreement between experimental data and numerical simulations. We extend these results to predict flux behavior in forward filtration and backwashing when foulant properties or filtration conditions are varied. The newly developed model can be used to further investigate the impact of varying backwashing duration, frequency, and/or pressure on the rate of flux recovery.

Figures (7)

• Figure 1: (a) Schematic of modeled 2D domain. The channel presents solid horizontal boundaries at the top and bottom ($y=h$ and $y=-h$, respectively); it is open at the inlet ($x=0$) and outlet ($x=2\ell$), and includes a cross-sectional flat-sheet porous membrane at ($x = \ell$). The membrane is displayed here with some thickness for visualization purposes but is modeled as a one-dimensional barrier article:PartialDepositionMonteCarlo:VeerapaneniWiesner1994. (b) EMD Millipore 5121 Amicon Stirred Cell Model, produced by the Merck Group. This is the filter used in all experiments referenced in Section \ref{['sec:results_disc']} (without the stirrer). The photo of the stirred cell is from Millipore misc:Model8010:Millipore, edited to include the scale bar.
• Figure 2: Schematic of modeled bacteria species (a) B. diminuta and (b) S. marcescens. Water samples presenting fixed concentrations of one of these species of bacteria at a time are used to benchmark forward filtration operations, as shown in Figures \ref{['subfig:bdimlow']}-\ref{['subfig:smarchigh']}. The average length (from end to end) and diameter dimensions of each bacteria species are reported in article:ConstantPressureDeadEnd:XuChellam2005. Scanning electron microscope (SEM) images of the bacteria are from article:ConstantFluxDeadEnd:ChellamXu2006, used with permission from Elsevier.
• Figure 3: Comparison of simulations run at 0.1%, 1%, 10%, and 100% of the original experimental bacterial concentration size of order $10^{12} \, \textnormal{cells } \per m \cubed$. We include an inset of a zoomed in portion of the full figure to better illustrate the minuscule differences between the curves. We use experimental parameters from Figure \ref{['subfig:smarclow']} for the simulations. The runtime and the normalized residuals relative to the experiments run at full experimental size are given in Table \ref{['tab:scale-stats']}.
• Figure 4: Forward filtration simulations. Each simulation curve is the average of 100 runs. Parameters for each figure are given in Table \ref{['tab:simparams']}. (a) Simulation of feed water with $2.86 \times 10^{12}$ cells m of B. diminuta filtered through membrane with 400-nm pores at a constant TMP of $35.852 \times 10^3 \, Pa$ (5.2 psi) and initial flux of $3.48 \times 10^{-5} \, m \per s$. Experimental data from Figure 4 of article:StokesletsDeadEndMicrofiltration:CoganChellam2008. (b) Simulation of feed water with $1.53 \times 10^{13}$ cells m of B. diminuta filtered through membrane with 200-nm pores at a constant TMP of $33.577 \times 10^3 \, Pa$ (4.87 psi) and initial flux of $2.2 \times 10^{-4} \, m \per s$. Experimental data from Figure 3 of article:ConstantPressureDeadEnd:XuChellam2005. (c) Simulation of feed water with $2.75 \times 10^{12}$ cells m S. marcescens filtered through membrane with 200-nm pores at a constant TMP of $27.165 \times 10^3 \, Pa$ (3.94 psi) and initial flux of $3.49 \times 10^{-5} \, m \per s$. Experimental data from Figure 7 of article:StokesletsDeadEndMicrofiltration:CoganChellam2008. (d) Simulation of feed water with $5.49 \times 10^{12}$ cells m of S. marcescens filtered through membrane with 400-nm pores at a constant TMP of $28.958 \times 10^3 \, Pa$ (4.2 psi) and initial flux of $1.72 \times 10^{-4} \, m \per s$. Experimental data from Figure 3 of article:ConstantFluxDeadEnd:ChellamXu2006.
• Figure 5: Impact of varying a single parameter on the observed flux decline in one phase of forward filtration. (a) Comparing flux decline across simulations of feed water with B. diminuta filtered through a membrane with 400-nm pores at a base concentration of $2.86 \times 10^{12} \, \textnormal{cells} \, \per m \cubed$ ($- \cdot - \cdot$), at half the base concentration ($\cdot \cdot \cdot$), and at double the base concentration using B. diminuta ($\cdot \cdot \cdot$) and at base concentration using S. marcescens (- - -). All other simulations parameters match Figure \ref{['subfig:bdimlow']}. (b) Comparing flux decline across simulations of B. diminuta filtered through 200-nm pores at a base flux of $2.2 \times 10^{-4} \, m \per s$ ($- \cdot - \cdot$), at half the base flux ($\cdot \cdot \cdot$), and at double the base flux ($\cdot \cdot \cdot$). All other parameters are the same as Figure \ref{['subfig:bdimhigh']}.