Comprehensive comparison of pore-scale models for multiphase flow in porous media.

Multiphase flows in porous media are important in many natural and industrial processes. Pore-scale models for multiphase flows have seen rapid development in recent years and are becoming increasingly useful as predictive tools in both academic and industrial applications. However, quantitative comparisons between different pore-scale models, and between these models and experimental data, are lacking. Here, we perform an objective comparison of a variety of state-of-the-art pore-scale models, including lattice Boltzmann, stochastic rotation dynamics, volume-of-fluid, level-set, phase-field, and pore-network models. As the basis for this comparison, we use a dataset from recent microfluidic experiments with precisely controlled pore geometry and wettability conditions, which offers an unprecedented benchmarking opportunity. We compare the results of the 14 participating teams both qualitatively and quantitatively using several standard metrics, such as fractal dimension, finger width, and displacement efficiency. We find that no single method excels across all conditions and that thin films and corner flow present substantial modeling and computational challenges.

Diffusion-Based Recycling of Flavins Allows Shewanella oneidensis MR-1 To Yield Energy from Metal Reduction Across Physical Separations.

We fabricated a microfluidic reactor with a nanoporous barrier to characterize electron transport between Shewanella oneidensis MR-1 and the metal oxide birnessite across a physical separation. Real-time quantification of electron flux across this barrier by strains with different electron transfer capabilities revealed that this bacterium exports flavins to its surroundings when faced with no direct physical access to an electron acceptor, allowing it to reduce metals at distances exceeding 60 µm. An energy balance indicates that flavins must be recycled for S. oneidensis MR-1 to yield energy from lactate oxidation coupled to flavin reduction. In our system, we find that flavins are recycled between 24 and 60 times depending on flow conditions. This energy saving strategy, which until now had not been systematically tested or captured in environmentally relevant systems, suggests that electron shuttling microorganisms have the capacity to access and reduce metals in physically distant or potentially toxic microenvironments (i.e., pores with soluble and transiently sorbed toxins) where direct contact is limited or unfavorable. Our results challenge the prediction that diffusion-based electron shuttling is only effective across short distances and may lead to improved bioremediation strategies or advance biogeochemical models of electron transfer in anaerobic sediments.

Nanowires of Geobacter sulfurreducens Require Redox Cofactors to Reduce Metals in Pore Spaces Too Small for Cell Passage.

Members of the Geobacteraceae family are ubiquitous metal reducers that utilize conductive "nanowires" to reduce Mn(IV) and Fe(III) oxides in anaerobic sediments. However, it is not currently known if and to what extent the Mn(IV) and Fe(III) oxides in soil grains and low permeability sediments that are sequestered in pore spaces too small for cell passage can be reduced by long-range extracellular electron transport via Geobacter nanowires, and what mechanisms control this reduction. We developed a microfluidic reactor that physically separates Geobacter sulfurreducens from the Mn(IV) mineral birnessite by a 1.4 µm thick wall containing <200 nm pores. Using optical microscopy and Raman spectroscopy, we show that birnessite can be reduced up to 15 µm away from cell bodies, similar to the reported length of Geobacter nanowires. Reduction across the nanoporous wall required reducing conditions, provided by Escherichia coli, and an exogenous supply of riboflavin. Our results discount electron shuttling by dissolved flavins, and instead support their role as bound redox cofactors in electron transport from nanowires to metal oxides. We also show that upon addition of a soluble electron shuttle (i.e., AQDS), reduction extends beyond the reported nanowire length up to 40 µm into a layer of birnessite.

Immobilization of selenite via two parallel pathways during in situ bioremediation.

It is widely understood that selenite can be biologically reduced to elemental selenium. Limited studies have shown that selenite can also be immobilized through abiotic precipitation with sulfide, a product of biological sulfate reduction. We demonstrate that both pathways significantly contribute to selenite immobilization in a microfluidic flow cell having a transverse mixing zone between propionate and selenite that mimics the reaction zone along the margins of a selenite plume undergoing bioremediation in the presence of background sulfate. The experiment showed that red particles of amorphous elemental selenium precipitate on the selenite-rich side of the mixing zone, while long crystals of selenium sulfides precipitate on the propionate-rich side of the mixing zone. We developed a continuum-scale reactive transport model that includes both pathways. The simulated results are consistent with the experimental results, and indicate that spatial segregation of the two selenium precipitates is due to the segregation of the more thermodynamic favorable selenite reduction and the less thermodynamically favorable sulfate reduction. The improved understanding of selenite immobilization and the improved model can help to better design in situ bioremediation processes for groundwater contaminated by selenite or other contaminants (e.g., uranium(IV)) that can be immobilized via similar pathways.

Coupling a Borehole Thermal Model and MT3DMS to Simulate Dynamic Ground Source Heat Pump Efficiency.

We present a novel integrated two-region model that couples simulation of local heat transfer processes in borehole heat exchangers (BHEs) with field-scale heat transport simulation using MT3DMS to fulfill the dynamic simulation of the borehole geothermal systems. This includes the prediction of subsurface thermal perturbation induced by BHEs, derivation of the U-pipe circulating fluid temperature profile within boreholes, and the evaluation of the ground source heat pump efficiency based on available time series of building heat load. In our approach, MT3DMS is the simulator for the two-dimensional field-scale heat transport, while new Python modules are developed to analytically solve the thermal transfer process within boreholes and interface iteratively with MT3DMS. A Python package for scripting MODFLOW-based code named Flopy is used to establish the MT3DMS numerical model. The proposed model is validated against analytical solutions and we demonstrate the application to more complex test problems with field-scale heterogeneity and pumping. Instructions are provided to access the source code and example problems which are available online.

Monitoring network design for phytoremediation systems using primary and secondary data sources.

Phytoremediation, or contaminant removal using plants, has been deployed at many sites to remediate contaminated soil and groundwater. Research has shown that trees are low-cost, rapid, and relatively simple-to-use monitoring systems as well as inexpensive alternatives to traditional pump-and-treat systems. However, tree monitoring is also an indirect measure of subsurface contamination and inherently more uncertain than conventional techniques such as wells or soil borings that measure contaminant concentrations directly. This study explores the implications for monitoring network design at real-world sites where scarce primary data such as monitoring wells or soil borings are supplemented by extensive secondary data such as trees. In this study, we combined secondary and primary data into a composite data set using models to transform secondary data to primary, as primary data were too sparse to attempt cokriging. Optimal monitoring networks using both trees and conventional techniques were determined using genetic algorithms, and trade-off curves between cost and uncertainty are presented for a phytoremediation system at Argonne National Laboratory. Optimal solutions found at this site indicate that increasing the number of secondary data sampled resulted in a significant decrease in global uncertainty with a minimal increase in cost. The choice of the data transformation model had an impact on the optimal designs and uncertainty estimated at the site. Using a data transformation model with a higher error resulted in monitoring network designs where primary data were favored over colocated secondary data. The spatial configuration of the monitoring network design was similar with regard to the areas sampled, irrespective of the data transformation model used. Overall, this study shows that using a composite data set, with primary and secondary data, results in effective monitoring designs, even at sites where the only data transformation model available is one with significant error.

Using MODFLOW and RT3D to simulate diffusion and reaction without discretizing low permeability zones.

Low permeability zones (LPZs) are major sources of groundwater contamination after active remediation to remove pollutants in adjacent high permeability zones (HPZs). Slow back diffusion from LPZs to HPZs can extend management of polluted sites by decades. Numerical models are often used to simulate back diffusion, estimate cleanup times, and develop site management strategies. Sharp concentration gradients of pollutants are present at the interface between HPZs and LPZs, and hence accurate simulation requires fine grid sizes resulting in high computational burden. Since the MODFLOW family of codes is widely used in practice, we develop a new approach for modeling pollutant back diffusion using MODFLOW/RT3D that eliminates the need for fine discretization of the LPZ. Instead, the LPZ is treated as an impermeable region in MODFLOW, while in RT3D the LPZ is conceptualized as a series of immobile zones coupled with a mobile zone at the HPZ/LPZ interface. Finite volume discretization of diffusion and reaction within the LPZ is then modeled as mass transfer and reaction among several immobile species. This results in a simulation domain with significantly fewer grid cells compared to that required if all LPZs are discretized, providing potential for improved computational efficiency. Cases, including a layer of HPZ over an LPZ, a thin/thick lens of LPZ embedded in HPZ, and multiple lens of LPZs embedded in HPZ are tested by the new approach for tracer and reactive scenarios.

Pore-scale study of transverse mixing induced CaCO3 precipitation and permeability reduction in a model subsurface sedimentary system.

A microfluidic pore structure etched into a silicon wafer was used as a two-dimensional model subsurface sedimentary system (i.e., micromodel) to study mineral precipitation and permeability reduction relevant to groundwater remediation and geological carbon sequestration. Solutions containing CaCl(2) and Na(2)CO(3) at four different saturation states (Ω = [Ca(2+)][CO(3)(2-)]/K(spCaCO(3))) were introduced through two separate inlets, and they mixed by diffusion transverse to the main flow direction along the center of the micromodel resulting in CaCO(3) precipitation. Precipitation rates increased and the total amount of precipitates decreased with increasing saturation state, and only vaterite and calcite crystals were formed (no aragonite). The relative amount of vaterite increased from 80% at the lowest saturation state (Ω(v) = 2.8 for vaterite) to 95% at the highest saturation state (Ω(v) = 4.5). Fluorescent tracer tests conducted before and after CaCO(3) precipitation indicate that pore spaces were occluded by CaCO(3) precipitates along the transverse mixing zone, thus substantially reducing porosity and permeability, and potentially limiting transformation from vaterite to the more stable calcite. The results suggest that mineral precipitation along plume margins can decrease both reactant mixing during groundwater remediation, and injection and storage efficiency during CO(2) sequestration.

Flux-Corrected Transport with MT3DMS for Positive Solution of Transport with Full-Tensor Dispersion.

Solute transport is usually modeled by the advection-dispersion-reaction equation. In the standard approach, mechanical dispersion is a tensor with principal directions parallel and perpendicular to the flow vector. Since realistic scenarios include nonuniform and unsteady flow fields, the governing equation has full tensor mechanical dispersion. When conventional grid-based numerical methods are used, approximation of the cross terms arising from the off-diagonal terms cause nonphysical solution with oscillations. As an example, for the common scenario of contaminant input into a domain with zero initial concentration, the cross-dispersion terms can result in negative concentrations that can wreak havoc in reactive transport applications. To address this issue, we use the well-known flux-corrected-transport (FCT) technique for a standard finite volume method. Although FCT has most often been used to eliminate oscillations resulting from discretization of the advection term for explicit time stepping, we show that it can be adapted for full-tensor dispersion and implicit time stepping. Unlike other approaches based on new discretization techniques (e.g., mimetic finite difference, nonlinear finite volume), FCT has the advantage of being flexible and widely applicable. Implementation of FCT requires solving an additional system of equations at each time step, using a modified "low order" matrix and a modified right-hand-side vector. To demonstrate the flexibility of FCT, we have modified the well-known and widely used groundwater solute transport simulator, MT3DMS. We apply the new simulator, MT3DMS-FCT, to several benchmark problems that suffer from negative concentrations when using MT3DMS. The new results are mass conservative and strictly nonnegative.

Contributions of biotic and abiotic pathways to anaerobic trichloroethene transformation in low permeability source zones.

Low permeability source zones sustain long-term trichloroethene (TCE) groundwater contamination. In anaerobic environments, TCE is transformed by both biological reductive dechlorination and abiotic reactions with reactive minerals. Little is known about the relative contribution of these two pathways as TCE diffuses from low permeability zones (LPZs) into high permeability zones (HPZs). This study combines a flow cell experiment, batch experiments, and a diffusion-reaction model to evaluate the contributions of biotic and abiotic TCE transformation in LPZs. Natural clay (LPZ) and sand (HPZ) from a former Air Force base were used in all experiments. In batch, the LPZ material transformed TCE and cis-1,2-dichloroethene (cis-DCE) to acetylene with pseudo first-order rate constants of 8.57 × 10-6 day-1 and 1.02 × 10-6 day-1, respectively. Biotic and abiotic pathways were then evaluated together in a bench-scale flow cell (16.5 cm × 2 cm × 16.5 cm) that contained a LPZ layer, with a source of TCE at the base, overlain by a HPZ continuously purged with lactate-amended groundwater. Diffusion controlled mass transfer in the LPZ, while advection controlled migration in the HPZ. The mass discharge rate of TCE and its biotic (cis-DCE and vinyl chloride) and abiotic (acetylene) transformation products were measured over 180 days in the flow cell effluent. Depth profiles of these compounds through the LPZ were determined after terminating the experiment. A one-dimensional diffusion-reaction model was used to interpret the effluent and depth profile data and constrain reaction parameters. Abiotic transformation rate constants for TCE to acetylene, normalized to in situ solids loading, were approximately 13 times greater in batch than in the flow cell. Slower transformation rates in the flow cell indicate elevated TCE concentration and/or further degradation of acetylene to other reduced gas compounds in the flow cell LPZ (thereby partially masking TCE abiotic transformation). Biotic and abiotic parameters used to interpret the flow cell data were then used to simulate a field site with a 300 cm thick LPZ. Abiotic processes contributed to a 2% reduction in TCE flux after 730 days. When abiotic rate constants were changed to that observed in batch, or to rate constants previously reported for a pyrite rich mudstone, the TCE flux reduction was 21% and 53%, respectively, after 730 days. Though biotic processes dominated TCE transformation in the flow cell experiment, the simulations indicate that abiotic processes have potential to significantly contribute to TCE attenuation in electron donor limited environments provided suitable reactive minerals are present.

Impact of nonaqueous phase liquid (NAPL) source zone architecture on mass removal mechanisms in strongly layered heterogeneous porous media during soil vapor extraction.

An existing multiphase flow simulator was modified in order to determine the effects of four mechanisms on NAPL mass removal in a strongly layered heterogeneous vadose zone during soil vapor extraction (SVE): a) NAPL flow, b) diffusion and dispersion from low permeability zones, c) slow desorption from sediment grains, and d) rate-limited dissolution of trapped NAPL. The impacts of water and NAPL saturation distribution, NAPL-type (i.e., free, residual, or trapped) distribution, and spatial heterogeneity of the permeability field on these mechanisms were evaluated. Two different initial source zone architectures (one with and one without trapped NAPL) were considered and these architectures were used to evaluate seven different SVE scenarios. For all runs, slow diffusion from low permeability zones that gas flow bypassed was a dominant factor for diminished SVE effectiveness at later times. This effect was more significant at high water saturation due to the decrease of gas-phase relative permeability. Transverse dispersion contributed to fast NAPL mass removal from the low permeability layer in both source zone architectures, but longitudinal dispersion did not affect overall mass removal time. Both slow desorption from sediment grains and rate-limited mass transfer from trapped NAPL only marginally affected removal times. However, mass transfer from trapped NAPL did affect mass removal at later time, as well as the NAPL distribution. NAPL flow from low to high permeability zones contributed to faster mass removal from the low permeability layer, and this effect increased when water infiltration was eliminated. These simulations indicate that if trapped NAPL exists in heterogeneous porous media, mass transfer can be improved by delivering gas directly to zones with trapped NAPL and by lowering the water content, which increases the gas relative permeability and changes trapped NAPL to free NAPL.

Evaluation of simplified mass transfer models to simulate the impacts of source zone architecture on nonaqueous phase liquid dissolution in heterogeneous porous media.

Nonaqueous phase liquid (NAPL) dissolution was studied in three-dimensional (3D) heterogeneous experimental aquifers (25.5 cm x 9 cm x 8.5 cm) with two different longitudinal correlation lengths (2.1 cm and 1.1 cm) and initial spill volumes (22.5 ml and 10.5 ml). Spatial and temporal distributions of NAPL during dissolution were measured using magnetic resonance imaging (MRI). At high NAPL spill volume, average effluent concentrations initially increased during dissolution, as NAPL pools transitioned to NAPL ganglia, and then decreased as the total NAPL-water interfacial area decreased over time. Experimental results were used to test six dissolution models: (i and ii) a one-dimensional (1D) model using either specific NAPL-water interfacial area values estimated from MR images at each time step (i.e., 1D quasi-steady state model), or an empirical mass transfer (Sh') correlation (i.e., 1D transient model), (iii and iv) a multiple analytical source superposition technique (MASST) using either the NAPL distribution determined from MR images at each time step (i.e., MASST steady state model), or the NAPL distribution determined from mass balance calculations (i.e., MASST transient model), (v) an equilibrium streamtube model, and (vi) a 3D grid-scale pool dissolution model (PDM) with a dispersive mass flux term. The 1D quasi-steady state model and 3D PDM captured effluent concentration values most closely, including some concentration fluctuations due to changes in the extent of flow reduction. The 1D transient, MASST steady state and transient, and streamtube models all showed a monotonic decrease in effluent concentration values over time, and the streamtube model was the most computationally efficient. Changes during dissolution of the effective NAPL-water interfacial area estimated from imaging data are similar to changes in effluent concentration values. The 1D steady state model incorporates estimates of the effective NAPL-water interfacial area directly at each time point; the 3D PDM does so indirectly through mass balance and a relative permeability function, which causes reduced water flow through high saturation NAPL regions. Hence, when model accuracy is required, the results indicate that a surrogate of this effective interfacial area is required. Approaches to include this surrogate in the MASST and streamtube models are recommended.

Lattice Boltzmann simulations of liquid CO2 displacing water in a 2D heterogeneous micromodel at reservoir pressure conditions.

We employed the color-fluid lattice Boltzmann multiphase model to simulate liquid CO2 displacing water documented in experiments in a 2D heterogeneous micromodel at reservoir pressure conditions. The main purpose is to investigate whether lattice Boltzmann simulation can reproduce the CO2 invasion patterns observed in these experiments for a range of capillary numbers. Although the viscosity ratio used in the simulation matches the experimental conditions, the viscosity of the fluids in the simulation is higher than that of the actual fluids used in the experiments. Doing so is required to enhance numerical stability, and is a common strategy employed in the literature when using the lattice Boltzmann method to simulate CO2 displacing water. The simulations reproduce qualitatively similar trends of changes in invasion patterns as the capillary number is increased. However, the development of secondary CO2 pathways, a key feature of the invasion patterns in the simulations and experiments, is found to occur at a much higher capillary number in the simulations compared with the experiments. Additional numerical simulations were conducted to investigate the effect of the absolute value of viscosity on the invasion patterns while maintaining the viscosity ratio and capillary number fixed. These results indicate that the use of a high viscosity (which significantly reduces the inertial effect in the simulations) suppresses the development of secondary CO2 pathways, leading to a different fluid distribution compared with corresponding experiments at the same capillary number. Therefore, inertial effects are not negligible in drainage process with liquid CO2 and water despite the low Reynolds number based on the average velocity, as the local velocity can be much higher due to Haines jump events. These higher velocities, coupled with the low viscosity of CO2, further amplifies the inertial effect. Therefore, we conclude that caution should be taken when using proxy fluids that only rely on the capillary number and viscosity ratio in both experiment and simulation.

Effect of soil moisture dynamics on dense nonaqueous phase liquid (DNAPL) spill zone architecture in heterogeneous porous media.

The amount, location, and form of NAPL in contaminated vadose zones are controlled by the spatial distribution of water saturation and soil permeability, the NAPL spill scenario, water infiltration events, and vapor transport. To evaluate the effects of these processes, we used the three-phase flow simulator STOMP, which includes a new permeability-liquid saturation-capillary pressure (k-S-P) constitutive model. This new constitutive model considers three NAPL forms: free, residual, and trapped. A 2-D vertical cross-section with five stratigraphic layers was assumed, and simulations were performed for seven cases. The conceptual model of the soil heterogeneity was based upon the stratigraphy at the Hanford carbon tetrachloride (CT) spill site. Some cases considered co-disposal of NAPL with large volumes of wastewater, as also occurred at the Hanford CT site. In these cases, the form and location of NAPL were most strongly influenced by high water discharge rates and NAPL evaporation to the atmosphere. In order to investigate the impact of heterogeneity, the hydraulic conductivity within the lower permeability layer was modeled as a realization of a random field having three different classes. For six extreme cases of 100 realizations, the CT mass that reached the water table varied by a factor of two, and was primarily controlled by the degree of lateral connectivity of the low conductivity class within the lowest permeability layer. The grid size at the top boundary had a dramatic impact on NAPL diffusive flux just after the spill event when the NAPL was present near the ground surface. NAPL evaporation with a fine grid spacing at the top boundary decreased CT mass that reached the water table by 74%, compared to the case with a coarse grid spacing, while barometric pumping had a marginal effect for the case of a continuous NAPL spill scenario considered in this work. For low water infiltration rate scenarios, the distribution of water content prior to a NAPL spill event decreased CT mass that reached the water table by 98% and had a significant impact on the formation of trapped NAPL. For all cases simulated, use of the new constitutive model that allows the formation of residual NAPL increased the amount of NAPL retained in the vadose zone. Density-driven advective gas flow from the ground surface controlled vapor migration in strongly anisotropic layers, causing NAPL mass flux to the lower layer to be reduced. These simulations indicate that consideration of the formation of residual and trapped NAPLs and dynamic boundary conditions (e.g., areas, rates, and periods of different NAPL and water discharge and fluctuations of atmospheric pressure) in the context of full three-phase flow are needed, especially for NAPL spill events at the ground surface. In addition, NAPL evaporation, density-driven gas advection, and NAPL vertical movement enhanced by water flow must be considered in order to predict NAPL distribution and migration in the vadose zone.

Bioenhancement of NAPL pool dissolution: experimental evaluation.

Experiments were conducted to quantify nonaqueous phase liquid (NAPL) pool dissolution and its enhancement by in situ biodegradation. The experiments were performed using square cross-section, glass-bead packed column reactors with a small pool of a toluene-in-dodecane mixture (toluene mole fraction, X(tol) approximately 0.02 or 0.09). Experimental quasi-steady-state toluene dissolution fluxes were determined using a 14C-carbon mass-balance approach during water flushing with and without biodegradation. The experiments demonstrated a statistically significant bioenhancement of the toluene dissolution flux of up to roughly twofold at average pore water velocities of approximately 0.1 and 1 m/day when the toluene mole fraction was low ( approximately 0.02); however, little or no bioenhancement was observed with the higher mole fraction ( approximately 0.09). Although it cannot be determined conclusively, the weight of evidence based on biomass measurements and model analyses suggests that the reduced bioenhancement for the high mole fraction was due to higher dissolved toluene concentrations, which may have caused toxicity effects. Importantly, even though NAPL dissolution was not bioenhanced in every case, the biodegradation reduced toluene concentrations to low levels in the reactor effluents.

Magnetic resonance imaging of nonaqueous phase liquid during soil vapor extraction in heterogeneous porous media.

Soil vapor extraction (SVE) is commonly used to remediate nonaqueous phase liquids (NAPLs) from the vadose zone. This paper aims to determine the effect of grain size heterogeneity on the removal of NAPL in porous media during SVE. Magnetic resonance imaging (MRI) was used to observe and quantify the amount and location of NAPL in flow-through columns filled with silica gel grains. MRI is unique because it is nondestructive, allowing three-dimensional images to be taken of the phases as a function of space and time. Columns were packed with silica gel in three ways: coarse grains (250-550 microm) only, fine grains (32-63 microm) only, and a core of fine grains surrounded by a shell of coarse grains. Columns saturated with water were drained under a constant suction head, contaminated with decane, and then drained to different decane saturations. Each column was then continuously purged with water-saturated nitrogen gas and images were taken intermittently. Results showed that at residual saturation, a sharp volatilization front moved through the columns filled with either coarse-grain or fine-grain silica gel. In the heterogeneous columns, the volatilization front in the core lagged just behind the shell because gas flow was greater through the shell and decane in the core diffused outward to the shell. When decane saturation in the core was above residual saturation, decane volatilization occurred near the inlet, the relative decane saturation throughout the core dropped uniformly, and decane in the core flowed in the liquid phase to the shell to replenish volatilized decane. These results indicate that NAPL trapped in low-permeability zones can flow to replenish areas where NAPL is lost due to SVE. However, when residual NAPL saturation is reached, NAPL flow no longer occurs and diffusion limits removal from low-permeability zones.

Use of machine learning methods to reduce predictive error of groundwater models.

Quantitative analyses of groundwater flow and transport typically rely on a physically-based model, which is inherently subject to error. Errors in model structure, parameter and data lead to both random and systematic error even in the output of a calibrated model. We develop complementary data-driven models (DDMs) to reduce the predictive error of physically-based groundwater models. Two machine learning techniques, the instance-based weighting and support vector regression, are used to build the DDMs. This approach is illustrated using two real-world case studies of the Republican River Compact Administration model and the Spokane Valley-Rathdrum Prairie model. The two groundwater models have different hydrogeologic settings, parameterization, and calibration methods. In the first case study, cluster analysis is introduced for data preprocessing to make the DDMs more robust and computationally efficient. The DDMs reduce the root-mean-square error (RMSE) of the temporal, spatial, and spatiotemporal prediction of piezometric head of the groundwater model by 82%, 60%, and 48%, respectively. In the second case study, the DDMs reduce the RMSE of the temporal prediction of piezometric head of the groundwater model by 77%. It is further demonstrated that the effectiveness of the DDMs depends on the existence and extent of the structure in the error of the physically-based model.

An improved cellular automaton method to model multispecies biofilms.

Biomass-spreading rules used in previous cellular automaton methods to simulate multispecies biofilm introduced extensive mixing between different biomass species or resulted in spatially discontinuous biomass concentration and distribution; this caused results based on the cellular automaton methods to deviate from experimental results and those from the more computationally intensive continuous method. To overcome the problems, we propose new biomass-spreading rules in this work: Excess biomass spreads by pushing a line of grid cells that are on the shortest path from the source grid cell to the destination grid cell, and the fractions of different biomass species in the grid cells on the path change due to the spreading. To evaluate the new rules, three two-dimensional simulation examples are used to compare the biomass distribution computed using the continuous method and three cellular automaton methods, one based on the new rules and the other two based on rules presented in two previous studies. The relationship between the biomass species is syntrophic in one example and competitive in the other two examples. Simulation results generated using the cellular automaton method based on the new rules agree much better with the continuous method than do results using the other two cellular automaton methods. The new biomass-spreading rules are no more complex to implement than the existing rules.

Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows.

A phase-field-based hybrid model that combines the lattice Boltzmann method with the finite difference method is proposed for simulating immiscible thermocapillary flows with variable fluid-property ratios. Using a phase field methodology, an interfacial force formula is analytically derived to model the interfacial tension force and the Marangoni stress. We present an improved lattice Boltzmann equation (LBE) method to capture the interface between different phases and solve the pressure and velocity fields, which can recover the correct Cahn-Hilliard equation (CHE) and Navier-Stokes equations. The LBE method allows not only use of variable mobility in the CHE, but also simulation of multiphase flows with high density ratio because a stable discretization scheme is used for calculating the derivative terms in forcing terms. An additional convection-diffusion equation is solved by the finite difference method for spatial discretization and the Runge-Kutta method for time marching to obtain the temperature field, which is coupled to the interfacial tension through an equation of state. The model is first validated against analytical solutions for the thermocapillary driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then used to simulate thermocapillary migration of a three-dimensional deformable droplet and bubble at various Marangoni numbers and density ratios, and satisfactory agreement is obtained between numerical results and theoretical predictions.

Three-dimensional lattice Boltzmann model for immiscible two-phase flow simulations.

We present an improved three-dimensional 19-velocity lattice Boltzmann model for immisicible binary fluids with variable viscosity and density ratios. This model uses a perturbation step to generate the interfacial tension and a recoloring step to promote phase segregation and maintain surfaces. A generalized perturbation operator is derived using the concept of a continuum surface force together with the constraints of mass and momentum conservation. A theoretical expression for the interfacial tension is determined directly without any additional analysis and assumptions. The recoloring algorithm proposed by Latva-Kokko and Rothman is applied for phase segregation, which minimizes the spurious velocities and removes lattice pinning. This model is first validated against the Laplace law for a stationary bubble. It is found that the interfacial tension is predicted well for density ratios up to 1000. The model is then used to simulate droplet deformation and breakup in simple shear flow. We compute droplet deformation at small capillary numbers in the Stokes regime and find excellent agreement with the theoretical Taylor relation for the segregation parameter ß=0.7. In the limit of creeping flow, droplet breakup occurs at a critical capillary number 0.35