Mineral Precipitation Upgradient from a Zero-Valent Iron Permeable Reactive Barrier

Core samples taken from a zero-valent iron permeable reactive barrier (ZVI PRB) at Cornhusker Army Ammunition Plant, Nebraska, were analyzed for physical and chemical characteristics. Precipitates containing iron and sulfide were present at much higher concentrations in native aquifer materials just upgradient of the PRB than in the PRB itself. Sulfur mass balance on core solids coupled with trends in ground water sulfate concentrations indicates that the average ground water flow after 20 months of PRB operation was approximately twenty fold less than the regional ground water velocity. Transport and reaction modeling of the aquifer PRB interface suggests that, at the calculated velocity, both iron and hydrogen could diffuse upgradient against ground water flow and thereby contribute to precipitation in the native aquifer materials. The initial hydraulic conductivity ( K ) of the native materials is less than that of the PRB and, given the observed precipitation in the upgradient native materials, it is likely that K reduction occurred upgradient to rather than within the PRB. Although not directly implicated, guar gum used during installation of the PRB is believed to have played a role in the precipitation and flow reduction processes by enhancing microbial activity.     

High-permeability layers for remediation of ground water; go wide, not deep

A nitrate-reactive porous media layer comprising wood particles with very high hydraulic conductivity (K approximately 1 cm/s) was used to successfully treat nitrate in a shallow sand-and-gravel aquifer in southern Ontario. Nitrate concentrations of 1.3 to 14 mg/L as N in the aquifer were attenuated to <0.5 mg/L as N in the reactive layer. Borehole dilution testing indicated that ground water velocities in the reactive layer, although variable, averaged five times higher than in the surrounding aquifer, suggesting that the layer was capturing ground water flow from deeper in the aquifer. The use of high-K reactive media opens up the possibility of installing permeable reactive barriers as horizontal layers in the shallow water table zone that do not necessarily have to penetrate the full depth of a contaminant plume to be effective. Model simulations show that the depth of capture of a high-K layer increases as the layer width in the direction of flow increases. Shallower emplacement could decrease barrier costs at some sites.     

The Horizontal Reactive Media Treatment Well (HRX Well®) for Passive In‐Situ Remediation

A new in‐situ remediation concept termed a Horizontal Reactive Media Treatment Well (HRX Well®) is presented that utilizes horizontal wells filled with reactive media to passively treat contaminated groundwater in‐situ. The approach involves the use of large‐diameter directionally drilled horizontal wells filled with granular reactive media generally installed parallel to the direction of groundwater flow. The design leverages natural “flow‐focusing” behavior induced by the high in‐well hydraulic conductivity of the reactive media relative to the aquifer hydraulic conductivity to passively capture and treat proportionally large volumes of groundwater within the well. Clean groundwater then exits the horizontal well along its downgradient sections. Many different types of solid granular reactive media are already available (e.g., zero valent iron, activated carbon, ion exchange resins, zeolite, apatite, chitin); therefore, this concept could be used to address a wide range of contaminants. Three‐dimensional flow and transport simulations were completed to assess the general hydraulic performance, capture zones, residence times, effects of aquifer heterogeneity, and treatment effectiveness of the concept. The results demonstrate that capture and treatment widths of up to tens of feet can be achieved for many aquifer settings, and that reductions in downgradient concentrations and contaminant mass flux are nearly immediate. For a representative example, the predicted treatment zone width for the HRX Well is approximately 27 to 44 feet, and contaminant concentrations immediately downgradient of the HRX Well decreased an order of magnitude within 10 days. A series of laboratory‐scale physical tests (i.e., tank tests) were completed that further demonstrate the concept and confirm model prediction performance. For example, the breakthrough time, peak concentration and total mass recovery of methylene blue (reactive tracer) was about 2, 35, and 20 times (respectively) less than chloride (conservative tracer) at the outlet of the tank‐scale HRX Well.     

Analytical expressions for the hydraulic design of continuous permeable reactive barriers

Various analytical expressions describing the hydraulic behavior of a continuous permeable reactive barrier (PRB) are developed based upon a two-dimensional approximation of the local groundwater flow system. The fully penetrating PRB is represented as an arbitrarily oriented elliptical “analytic element” with a hydraulic conductivity different from that of the aquifer. The validity of this elliptical geometry approximation as a surrogate for rectangular PRB performance is evaluated and put into context. Closed-form expressions for solute travel time distributions along the extent of the barrier and PRB capture zone geometry are evaluated for general barrier dimension (length and width), hydraulic conductivity, and orientation with respect to regional flow. These expressions are used as the foundation of a simple PRB design process, and provide some interesting insights into the hydraulic behavior of continuous permeable reactive barriers.     

Injection-extraction treatment well pairs: an alternative to permeable reactive barriers

Two of the biggest drawbacks of using permeable reactive barriers (PRBs) to treat contaminated ground water are the high capital cost of installation, particularly when the contaminated ground water is deep below ground surface, and the uncertainty of whether or not PRBs remain effective for the long time scales (e.g., decades) needed for many contaminant plumes. The use of an injection-extraction treatment well pair (IETWP) for capture and treatment of contaminated ground water can circumvent these difficulties, while still providing many of the same advantages offered by PRBs. In this paper, the hydraulics of IETWPs and PRBs are compared, focusing primarily on the width of the captured plume. It is demonstrated that IETWPs act as hydraulic barriers in a manner similar to PRBs, and that IETWPs provide excellent plume capture. A mathematical expression is presented for the plume capture width of an IETWP oriented perpendicular to the ground water flow direction in a homogeneous aquifer. Also discussed are other practical considerations that might determine whether an IETWP is better suited than a PRB for a particular contaminated site; these considerations include operating and maintenance costs, and the conditions under which an IETWP system can be used for in situ remediation.     

Mass Discharge in a Tracer Plume: Evaluation of the Theissen Polygon Method

A tracer plume was created within a thin aquifer by injection for 299 d of two adjacent “sub‐plumes” to represent one type of plume heterogeneity encountered in practice. The plume was monitored by snapshot sampling of transects of fully screened wells. The mass injection rate and total mass injected were known. Using all wells in each transect (0.77 m well spacing, 1.4 points/m² sampling density), the Theissen Polygon Method (TPM) yielded apparently accurate mass discharge (M_d) estimates at three transects for 12 snapshots. When applied to hypothetical sparser transects using subsets of the wells with average spacing and sampling density from 1.55 to 5.39 m and 0.70 to 0.20 points/m², respectively, the TPM accuracy depended on well spacing and location of the wells in the hypothesized transect with respect to the sub‐plumes. Potential error was relatively low when the well spacing was less than the widths of the sub‐plumes (>0.35 points/m²). Potential error increased for well spacing similar to or greater than the sub‐plume widths, or when less than 1% of the plume area was sampled. For low density sampling of laterally heterogeneous plumes, small changes in groundwater flow direction can lead to wide fluctuations in M_d estimates by the TPM. However, sampling conducted when flow is known or likely to be in a preferred direction can potentially allow more useful comparisons of M_d over multiyear time frames, such as required for performance evaluation of natural attenuation or engineered remediation systems.     

Analysis of solute transport in flow fields influenced by preferential flowpaths at the decimeter scale

Several recent studies at the Macrodispersion Experiment (MADE) site in Columbus, Mississippi, have indicated that the relative preferential flowpaths and flow barriers resulting from decimeter-scale aquifer heterogeneities appear to have a dominant effect on plume-scale solute transport. Numerical experiments are thus conducted in this study to explore the key characteristics of solute transport in two-dimensional flow fields influenced by decimeter-scale preferential flowpaths. A hypothetical but geologically plausible network of 10 cm wide channels of high hydraulic conductivity is used to represent the relative preferential flowpaths embedded in an otherwise homogeneous aquifer. When the hydraulic conductivity in the channels is 100 times greater than that in the remaining portion of the aquifer, the calculated concentration distributions under three source configurations all exhibit highly asymmetrical, non-Gaussian patterns. These patterns, with peak concentrations close to the source and extensive spreading downgradient, resemble that observed at the MADE site tracer tests. When the contrast between the channel and nonchannel hydraulic conductivities is reduced to 30:1 from 100:1, the calculated mass distribution curve starts to approach a Gaussian one with the peak concentration near the central portion of the plume. Additional analysis based on a field-scale model demonstrates that the existence of decimeter-scale preferential flowpaths can have potentially far-reaching implications for ground water remediation. Failure to account for them in numerical simulation could lead to overestimation of the effectiveness of the remedial measure under consideration.     

Key features of artificial aquifers for use in modeling contaminant transport

Two large-scale (9.5 m long, 4.7 m wide, 2.6 m deep), three-dimensional artificial aquifers were constructed to investigate the influence of spatial variations in aquifer properties on contaminant transport. One aquifer was uniformly filled with coarse sand media (0.6 to 2.0 mm) and the other was constructed as a heterogeneous aquifer using blocks of fine, medium, and coarse sands. The key features of these artificial aquifers are described. An innovative deaeration tower was constructed to overcome a problem of the aquifers becoming blocked with excess air from the ground water source. A series of tracer injection experiments were conducted to test the homogeneity of the first aquifer that was purposely built as a homogeneous aquifer and to calculate values of aquifer parameters. Experimental data show that the aquifer is slightly heterogeneous, and hydraulic conductivity values are significantly higher down one side of the aquifer compared to the mean value. There was very good agreement in estimated dispersivity values between the plume area ratio methods and the curve fitting of tracer breakthrough curves. Dispersivity estimates from a full areal source injection (12.2 m2) experiment using a 1D analytical model were higher than estimates from a limited source injection (0.2 m2) experiment using a 3D model, possibly because the 1D model does not take account of the heterogeneity of hydraulic conductivity in the aquifer, thus overestimating dispersivity. Transverse and vertical dispersivity values were about five times less than the longitudinal dispersivity. There was slight sorption of Rhodamine WT onto the aquifer media.     

The Application of Combined Seismic and Electrical Measurements to the Determination of the Hydraulic Conductivity of a Lake Bed

The hydraulic properties of lake beds control the interactions between lakes and ground water systems, but these properties are normally difficult to measure directly. The authors'method combines seismic reflection and electrical measurements to map the relative hydraulic conductivity of lake bed sediments. A shipboard seismic profiling system provides sediment thickness, while a towed electrical array yields longitudinal conductance and electrical chargeability. The sediment's leakance (hydraulic conductivity/thickness) can be calculated from the longitudinal conductance data. Leakance may then be converted to relative hydraulic conductivity through the seismically derived sediment thicknesses. Simultaneously acquired electrical chargeability provides an independent measure of clay content. The seismic and electrical systems are computer automated and yield production rates of approximately five line-kilometers/hour or 300 electrical soundings/hour. The systems provide continuous hydraulic information along the ship track rather than the point information derived from coring.
The procedure and systems have been used to map the bed of Lake Michigan offshore from an area of heavy pumpage. This location has been chosen to test the method because lake water has intruded the aquifer in plumes largely controlled by lake bed hydraulics. Mapping these plumes onshore permits the inference of the spatial distribution of offshore hydraulic conductivities. Offshore seepage measurements and numerical, chemical transport modeling of this site have confirmed the reliability of the geophysically derived hydraulic conductivities and have also demonstrated the improvement in numerical results achieved through the availability of spatially determined hydraulic conductivities.     

In situ Mixing of Organic Matter Decreases Hydraulic Conductivity of Denitrification Walls in Sand Aquifers

In a previous study, a denitrification wall was constructed in a sand aquifer using sawdust as the carbon substrate. Ground water bypassed around this sawdust wall due to reduced hydraulic conductivity. We investigated potential reasons for this by testing two new walls and conducting laboratory studies. The first wall was constructed by mixing aquifer material in situ without substrate addition to investigate the effects of the construction technique (mixed wall). A second, biochip wall, was constructed using coarse wood chips to determine the effect of size of the particles in the amendment on hydraulic conductivity. The aquifer hydraulic conductivity was 35.4 m/d, while in the mixed wall it was 2.8 m/d and in the biochip wall 3.4 m/d. This indicated that the mixing of the aquifer sands below the water table allowed the particles to re-sort themselves into a matrix with a significantly lower hydraulic conductivity than the process that originally formed the aquifer. The addition of a coarser substrate in the biochip wall significantly increased total porosity and decreased bulk density, but hydraulic conductivity remained low compared to the aquifer. Laboratory cores of aquifer sand mixed under dry and wet conditions mimicked the reduction in hydraulic conductivity observed in the field within the mixed wall. The addition of sawdust to the laboratory cores resulted in a significantly higher hydraulic conductivity when mixed dry compared to cores mixed wet. This reduction in the hydraulic conductivity of the sand/sawdust cores mixed under saturated conditions repeated what occurred in the field in the original sawdust wall. This indicated that laboratory investigations can be a useful tool to highlight potential reductions in field hydraulic conductivities that may occur when differing materials are mixed under field conditions.     

Reactive barriers: hydraulic performance and design enhancements

The remediation of contaminated ground water is a multibillion-dollar global industry. Permeable reactive barriers (PRBs) are one of the leading technologies being developed in the search for alternatives to the pump-and-treat method. Improving the hydraulic performance of these PRBs is an important part of maximizing their potential to the industry. Optimization of the hydraulic performance of a PRB can be defined in terms of finding the balance between capture, residence time, and PRB longevity that produces a minimum-cost acceptable design. Three-dimensional particle tracking was used to estimate capture zone and residence time distributions. Volumetric flow analysis was used for estimation of flow distribution across a PRB and in the identification of flow regimes that may affect the permeability or reactivity of portions of the PRB over time. Capture zone measurements extended below the base of partially penetrating PRBs and were measured upgradient from the portion of aquifer influenced by PRB emplacement. Hydraulic performance analysis of standard PRB designs confirmed previously presented research that identified the potential for significant variation in residence time and capture zone. These variations can result in the need to oversize the PRB to ensure that downgradient contaminant concentrations do not exceed imposed standards. The most useful PRB design enhancements for controlling residence time and capture variation were found to be customized downgradient gate faces, velocity equalization walls, deeper emplacement of the funnel than the gate, and careful manipulation of the hydraulic conductivity ratio between the gate and the aquifer.     

Monte Carlo evaluation of microbial-mediated contaminant reactions in heterogeneous aquifers

Monte Carlo simulations are conducted to evaluate microbial-mediated contaminant reactions in an aquifer comprised of spatially variable microbial biomass concentrations, aquifer hydraulic conductivities, and initial electron donor/acceptor concentrations. A finite element simulation model is used that incorporates advection, dispersion, and Monod kinetic expressions to describe biological processes. Comparisons between Monte Carlo simulations of heterogeneous systems and simulations using homogeneous formulation of the same two-dimensional transport problem are presented. For the assumed set of parameters, physical aquifer heterogeneity is found to have a minor effect on the mass of contaminant biodegraded/transformed when compared to a homogeneous system; however, it noticeably changes the dispersion, skewness, and peakness of contaminant concentration distributions. Similarly, for low microbial growth rate, given favorable microbial growth characteristics, biological heterogeneity has minor effect on the mass of contaminant biodegraded/transformed when compared to a homogeneous system. On the other hand, when higher effective growth rates are assumed, biological heterogeneity and spatial heterogeneities in essential electron donor/acceptors reduce the efficiency of biotic contaminant reactions; consequently, model simulations derived from heterogeneous biomass distributions predict remediation time scales that are longer than those simulated for homogeneous systems. When correlations between physical aquifer and biological heterogeneities are considered, the assumed correlation affects predicted mean and variance of contaminant concentration and biomass distributions. For example, an assumed negative correlation between hydraulic conductivity and the initial biomass distribution produces a plume where less efficient biotic contaminant reactions occur at the leading edge of the plume; this is consistent with less degradation/transformation occurring over regions of higher groundwater velocities. However, the presence and absence of these correlations do not appear to affect the efficiency of microbial-mediated contaminant attenuation.     

Combining pump-and-treat and physical barriers for contaminant plume control

A detailed analysis is presented of the hydraulic efficiency of plume management alternatives that combine a conventional pump-and-treat system with vertical, physical hydraulic barriers such as slurry walls or sheet piles. Various design settings are examined for their potential to reduce the pumping rate needed to obtain a complete capture of a given contaminated area. Using established modeling techniques for flow and transport, those barrier configurations (specified by location, shape, and length) that yield a maximum reduction of the pumping rate are identified assuming homogeneous aquifer conditions. Selected configurations are further analyzed concerning their hydraulic performance under heterogeneous aquifer conditions by means of a stochastic approach (Monte Carlo simulations) with aquifer transmissivity as a random space function. The results show that physical barriers are an appropriate means to decrease expected (mean) pumping rates, as well as the variance of the corresponding pumping rate distribution at any given degree of heterogeneity. The methodology presented can be transferred easily to other aquifer scenarios, provided some basic premises are fulfilled, and may serve as a basis for reducing the pumping rate in existing pump-and-treat systems.     

Use of Improved Hydrologic Testing and Borehole Geophysical Logging Methods for Aquifer Characterization

Depth-discrete aquifer in formal ion was obtained using recently developed adaptations and improvements to conventional characterization techniques. These improvements included running neutron porosity and hulk density geophysical logging tools through a cased hole, performing an enhanced point-dilution tracer test for monitoring tracer concentration as a function of Lime and depth, and using pressure derivatives for diagnostic and quantitative analysis of constant rate discharge lest data. Data results from the use of these techniques were used to develop a conceptual model of a heterogeneous aquifer. Depth-discrete aquifer information was required to effectively design field-scale deployment and monitoring of an in situ bioremediation technology.
Geophysical logging and point-dilution tracer test results provided the relative distribution of porosity and horizontal hydraulic conductivity, respectively, with depth and correlated well. Hydraulic pumping tests were conducted to estimate mean values for transmissivity and effective hydraulic conductivity, Tracer lest and geophysical logging results indicated that ground water flow was predominant in the upper approximate 10 feet of the aquifer investigated. These results were used to delineate a more representative interval thickness for estimating effective hydraulic conductivity. Hydraulic conductivity, calculated using this representative interval, was estimated lo be 73 ft/d, approximately three limes higher than that calculated using the full length of the screened test interval.     

The effects of vertical barrier walls on the hydraulic control of contaminated groundwater

We present explicit analytic solutions describing the hydraulic head and discharge vector for two-dimensional, steady groundwater flow past an impermeable barrier embedded in a regional flow field. We use the solution to investigate the effects of open vertical barriers on the flow field; in particular, we examine the hydraulic containment of contaminant plumes or source zones by combination of a vertical barrier wall and extraction wells. We quantify the local reduction in discharge rates due to the barrier wall and the local increase in the size of the capture zone of an extraction well near an open, up-gradient barrier. We find that the combination of an open vertical barrier with down-gradient extraction wells can be very effective in decreasing the well discharge rate necessary to control a contaminant plume or source area. Design charts are presented for quantifying the effects of the barrier wall on the hydraulic control of the groundwater flow field and for estimating the jump in head across a barrier. The charts are appropriate for use in the preliminary design and cost estimating of remedial systems, and for the design of dewatering systems.     

Biogeochemical evolution of a landfill leachate plume, Norman, Oklahoma

Leachate from municipal landfills can create groundwater contaminant plumes that may last for decades to centuries. The fate of reactive contaminants in leachate-affected aquifers depends on the sustainability of biogeochemical processes affecting contaminant transport. Temporal variations in the configuration of redox zones downgradient from the Norman Landfill were studied for more than a decade. The leachate plume contained elevated concentrations of nonvolatile dissolved organic carbon (NVDOC) (up to 300 mg/L), methane (16 mg/L), ammonium (650 mg/L as N), iron (23 mg/L), chloride (1030 mg/L), and bicarbonate (4270 mg/L). Chemical and isotopic investigations along a 2D plume transect revealed consumption of solid and aqueous electron acceptors in the aquifer, depleting the natural attenuation capacity. Despite the relative recalcitrance of NVDOC to biodegradation, the center of the plume was depleted in sulfate, which reduces the long-term oxidation capacity of the leachate-affected aquifer. Ammonium and methane were attenuated in the aquifer relative to chloride by different processes: ammonium transport was retarded mainly by physical interaction with aquifer solids, whereas the methane plume was truncated largely by oxidation. Studies near plume boundaries revealed temporal variability in constituent concentrations related in part to hydrologic changes at various time scales. The upper boundary of the plume was a particularly active location where redox reactions responded to recharge events and seasonal water-table fluctuations. Accurately describing the biogeochemical processes that affect the transport of contaminants in this landfill-leachate-affected aquifer required understanding the aquifer's geologic and hydrodynamic framework.     

A Leaky Aquifer below Champlain Sea Clay: Closed‐Form Solutions for Natural Seepage

Closed‐form solutions are proposed for natural seepage in semiconfined (leaky) aquifers such as those existing below the massive Champlain Sea clay layers in the Saint‐Lawrence River Valley. The solutions are for an ideal horizontal leaky aquifer below an ideal aquitard that may have either a constant thickness and a constant hydraulic head at its surface, or a variable thickness and a variable hydraulic head at its surface. A few simplifying assumptions were needed to obtain the closed‐form solutions. These have been verified using a finite element method, which did not make any of the assumptions but gave an excellent agreement for hydraulic heads and groundwater velocities. For example, the difference between the two solutions was smaller than 1 mm for variations in the 5 to 8 m range for the hydraulic head in the semiconfined aquifer. Note that fitting the hydraulic head data of monitoring wells to the theoretical solutions gives only the ratio of the aquifer and aquitard hydraulic conductivities, a clear case of multiple solutions for an inverse problem. Consequently, field permeability tests in the aquitard and the aquifer, and pumping tests in the aquifer, are still needed to determine the hydraulic conductivity values.     

Evaluation of Combined Direct-Push Methods Used for Aquifer Model Generation

Most established methods to characterize aquifer structure and hydraulic conductivities of hydrostratigraphical units are not capable of delivering sufficient information in the spatial resolution that is desired for sophisticated numerical contaminant transport modeling and adapted remediation design. With hydraulic investigation methods based on the direct-push (DP) technology such as DP slug tests, DP injection logging, and the hydraulic profiling tool, it is possible to rapidly delineate hydrogeological structures and estimate their hydraulic conductivity in shallow unconsolidated aquifers without the need for wells. A combined application of these tools was used for the investigation of a contaminated German refinery site and for the setup of hydraulic aquifer models. The quality of DP investigation and the models was evaluated by comparisons of tracer transport simulations using these models and measured breakthroughs of two natural gradient tracer tests. Model scenarios considering the information of all tools together showed good reproduction of the measured breakthroughs, indicating the suitability of the approach and a minor impact of potential technical limitations. Using the DP slug tests alone yielded significantly higher deviations for the determined hydraulic conductivities compared to considering two or three of the tools. Realistic aquifer models developed on basis of such combined DP investigation approaches can help optimize remediation concepts or identify flow regimes for aquifers with a complex structure.     

Exceptionally Long MTBE Plumes of the Past Have Greatly Diminished

Studies published in the late 1990s and early 2000s identified the presence of exceptionally long methyl tert‐butyl ether (MTBE) plumes (more than 600 m or 2000 feet) in groundwater and have been cited in technical literature as characteristic of MTBE plumes. However, the scientific literature is incomplete in regard to the subsequent behavior and fate of these MTBE plumes over the past decade. To address this gap, this issue paper compiles recent groundwater monitoring records for nine exceptional plumes that were identified in prior studies. These nine sites exhibited maximum historical MTBE groundwater plume lengths ranging from 820 m (2700 feet) to 3200 m (10,500 feet) in length, exceeding the lengths of 99% of MTBE plumes, as characterized in multiple surveys at underground storage tank sites across the United States. Groundwater monitoring data compiled in our review demonstrate that these MTBE plumes have decreased in length over the past decade, with five of the nine plumes exhibiting decreases of 75% or more compared to their historical maximum lengths. MTBE concentrations within these plumes have decreased by 93% to 100%, with two of the nine sites showing significant decreases (98% and 99%) such that the regulatory authority has subsequently designated the site as requiring no further action.     

Analytical Solutions for Flow Fields near Drain-and-Gate Reactive Barriers

Permeable reactive barriers (PRBs) are a popular technology for passive contaminant remediation in aquifers through installation of reactive materials in the pathway of a plume. Of fundamental importance are the degree of remediation inside the reactor (residence time) and the portion of groundwater intercepted by a PRB (capture width). Based on a two-dimensional conformal mapping approach (previously used in related work), the latter is studied in the present work for drain-and-gate (DG) PRBs, which may possess a collector and a distributor drain (“full” configuration) or a collector drain only (“simple” configuration). Inherent assumptions are a homogeneous unbounded aquifer with a uniform far field, in which highly permeable drains establish constant head boundaries. Solutions for aquifer flow fields in terms of the complex potential are derived, illustrated, and analyzed for doubly symmetric DG configurations and arbitrary reactor hydraulic resistance as well as ambient groundwater flow direction. A series of practitioner-friendly charts for capture width is given to assist in PRB design and optimization without requiring complex mathematics. DG PRBs are identified as more susceptible to flow divergence around the reactor than configurations using impermeable side structures (e.g., funnel-and-gate), and deployment of impermeable walls on drains is seen to mitigate this problem under certain circumstances.