Dense Non-aqueous Phase Liquid Migration Research Articles

Control of downward migration of dense nonaqueous phase liquid during surfactant flooding by design simulations

Sand tank experiments have been used to study a surfactant‐enhanced aquifer remediation (SEAR) process during which downward migration of dense nonaqueous phase liquid (DNAPL) has been observed in some of these experiments. Through numerical simulation of one particular sand tank experiment conducted at Sandia National Laboratories we show in this paper that this downward migration of DNAPL can be anticipated and controlled even in a very difficult geosystem environment. The results indicate that design simulations play a significant role in the design of either laboratory column experiments or field SEAR application and that surfactant flooding can be accomplished without loss of hydraulic control of DNAPL under typical alluvial aquifer/aquitard conditions and with only minor vertical mobilization within the aquifer (i.e., <1% of the DNAPL present). The design simulations are considered as a sensitivity analysis exercise in which the heterogeneity in the permeability field and DNAPL saturation and other critical variables are varied to produce a robust design. The simulation results indicate that the significant downward mobilization of DNAPL as observed in the Sandia sand tank experiment is a result of the use of high‐permeability materials, weak viscous (horizontal) forces, and low surfactant solubilization potential. The downward mobilization of DNAPL is a design issue to be evaluated and controlled rather than an inevitable consequence of the use of surfactants to remove DNAPL.

FUNDAMENTAL STUDY ON CHARACTERISTICS OF ENTRAPPED DNAPL DROPLETS IN PORES BASED ON INVASION PERCOLATION THEORY

Characterization of DNAPL (Dense Non-Aqueous Phase Liquids) penetrating process near source zone gives suggestions to make measures against the groundwater contamination and remediation. The study aims at formulating mathematical model for realizing DNAPL droplets behavior using random-walking with entrapped detention factor by capillary pressure. Comparing fingering model based on the invasion percolation theory with experimental data, the results presented that the entrapped coefficient λ, which is a characteristic parameter in the proposed DNAPL migration model, is related to both capillary number and bond number.

Time Scales of DNAPL Migration in Sandy Aquifers Examined via Numerical Simulation

The time required for dense nonaqueous phase liquid (DNAPL) to cease migrating following release to the subsurface is a valuable component of a site conceptual model. This study uses numerical simulation to investigate the migration of six different DNAPLs in sandy aquifers. The most influential parameters governing migration cessation time are the density and viscosity of the DNAPL and the mean hydraulic conductivity of the aquifer. Releases of between 1 and 40 drums of chlorinated solvent DNAPLs, characterized by relatively high density and low viscosity, require on the order of months to a few years to cease migrating in a heterogeneous medium sand aquifer having an average hydraulic conductivity of 7.4 x 10(-3) cm/s. In contrast to this, the release of 20 drums of coal tar (rho(D)= 1061 kg/m(3), micro(D)= 0.161 Pa.s) requires more than 100 years to cease migrating in the same aquifer. Altering the mean hydraulic conductivity of the aquifer results in a proportional change in cessation times. Parameters that exhibit relatively little influence on migration time scales are the DNAPL-water interfacial tension, release volume, source capillary pressure, mean aquifer porosity, and ambient ground water hydraulic gradient. This study also demonstrates that low-density DNAPLs (e.g., coal tar) give rise to greater amounts of lateral spreading and greater amounts of pooling on capillary barriers than high-density DNAPLs such as trichloroethylene or tetrachloroethylene.

Dip-angle influence on areal DNAPL recovery by co-solvent flooding with and without pre-flooding

A two-dimensional (2D) laboratory model was used to study effects of gravity on areal recovery of a representative dense non-aqueous phase liquid (DNAPL) contaminant by an alcohol pre-flood and co-solvent flood in dipping aquifers. Recent studies have demonstrated that injection of alcohol and co-solvent solutions can be used to reduce in-situ the density of DNAPL globules and displace the contaminant from the source zone. However, contact with aqueous alcohol reduces interfacial tension and causes DNAPL swelling, thus facilitating risk of uncontrolled downward DNAPL migration. The 2D laboratory model was operated with constant background gradient flow and a DNAPL spill was simulated using tetrachloroethene (PCE). The spill was dispersed to a trapped, immobile PCE saturation by a water flood. Areal PCE recovery was studied using a double-triangle well pattern to simulate a remediation scheme consisting of an alcohol pre-flood using aqueous isobutanol (∼ 10% vol.) followed by a co-solvent flood using a solution of ethylene glycol (65%) and 1-propanol (35%). Experiments were conducted with the 2D model oriented in the horizontal plane and compared to experiments at the 15° and 30° dip-angle orientations. Injection was applied either in the downward or upward direction of flow. Experimental results were compared to theoretical predictions for flood front stability and used to evaluate effects of gravity on areal PCE recovery. Sensitivity experiments were performed to evaluate effects of the alcohol pre-flood on PCE areal recovery. For experiments conducted with the alcohol pre-flood and the 2D model oriented in the horizontal plane, results indicate that 89–93% of source zone PCE was recovered. With injection oriented downward, results indicate that areal PCE recovery was 70–77% for a 15° dip angle and 57–59% for a 30° dip angle. With injection oriented upward, results indicate that areal PCE recovery was 57–60% at the 30° dip angle, which was similar to PCE recovery for injection in the downward flow direction. Lower areal PCE recovery at greater dip angles in either direction of flow was attributed to DNAPL swelling and migration, flood front instabilities and bypassing of the displaced fluid past the extraction wells during the alcohol pre-flood. Additional results demonstrate that the use of an alcohol pre-flood can be beneficial in improving DNAPL recovery in the horizontal orientation, but pre-flooding may reduce areal recovery efficiency in dip-angle orientations. This study also demonstrates the use of theoretical perturbation (fingering) analysis in predicting NAPL recovery efficiency for flooding processes in remediating aquifers with dip angles.

Characterization of Tetrachloroethene DNAPL in Low-Permeability Coastal Plain Sediments, North Carolina

The geosystem approach to source-zone characterization was used at a dry cleaners contaminated with tetrachloroethene (PCE) as a dense nonaqueous-phase liquid (DNAPL) within a shallow, low-permeability aquifer. This comprehensive approach to source-zone characterization provided a design-basis level of knowledge of the site geosystem, which includes aquifer heterogeneity, and the volume and spatial distribution of DNAPL. DNAPL was found to occur beneath and adjacent to the dry cleaning building, with both residual and free-phase DNAPL in the bottom 4 ft (1.2 m) of the shallow aquifer. The bottom 2.5 ft (0.76 m) of the aquifer consists of a fining downward sequence that grades from fine sand to clayey silt, with a resulting decrease in permeability in the DNAPL zone by at least one order of magnitude. The DNAPL zone is bounded below by a clay aquitard that serves as an effective capillary barrier to downward DNAPL migration. A partitioning interwell tracer test (PITT) measured approximately 81 ± 7 gallons (280–330 L) of DNAPL in the test zone, with the majority of DNAPL located near the building and decreasing northward away from the building. Soil samples analyzed for PCE show that the DNAPL saturations are greatest vertically from 17 to 18.5 ft (5.2 to 5.6 m) below ground surface (bgs), in the fine-sand to sandy-silt portion of the DNAPL zone. DNAPL saturations generally decrease at greater depths, from approximately 18.5 to 20 ft (5.6 to 6.1 m) bgs, in a silt to clayey silt (i.e., lower permeability) zone, with little or no DNAPL penetration into the underlying clay aquitard. Postremediation soil core analyses indicate that low permeability at depth was a limiting factor in the detection of all the DNAPL within the targeted zone using the PITT. It is concluded that the partitioning interwell tracer test successfully detected DNAPL in the more sandy portions of the aquifer, while not detecting an estimated 23 ± 5 gallons (87 ± 19 L) of DNAPL in the clayey silts below 17.8 ft (5.4 m) bgs.

Guest Editorial: Contaminant Source Zones: Remediation or Perpetual Stewardship?

Guest Editorial: Contaminant Source Zones: Remediation or Perpetual Stewardship?

Two-dimensional DNAPL migration affected by groundwater flow in unconfined aquifer

The dense non-aqueous phase liquid (DNAPL) migration process was experimentally investigated in a laboratory-scale tank (150 cm width, 82.5 cm height, and 15 cm depth) to assess a site characterization on DNAPL contamination below a groundwater table. The heterogeneous ground of the tank model consisted of Toyoura sand (hydraulic conductivity, k=1.5×10 −2 cm/s for void ratio, e=0.62) and silica #7 sand ( k=2.3×10 −3 cm/s for e=0.72). A series of experiments was carried out with or without lateral groundwater flow. Hydrofluoroether was used as a representative DNAPL. The main results obtained in this study are as follows: (1) the DNAPL plume does not invade into the less permeable soil layer with higher displacement pressure head; (2) the DNAPL plume migrates faster with lateral groundwater flow than without it; (3) lateral groundwater flow does not affect lateral DNAPL migration; rather, it promotes downward migration; and (4) pore DNAPL pressure without groundwater flow is higher than that with it. The above experimental results were compared with numerical analysis. The fundamental behaviors of DNAPL source migration observed experimentally are expected to be useful for assessing the characteristics of two-dimensional DNAPL migration in an aquifer.

Noninvasive monitoring of DNAPL migration through a saturated porous medium using electrical impedance tomography

Electrical impedance tomography (EIT) was used to monitor the movement of a fluorinated hydrocarbon dense nonaqueous phase liquid (DNAPL) through a saturated porous medium within a laboratory column. Impedance measurements were made using a horizontal plane of 12 electrodes positioned at regular intervals around the centre of the column. A 2D inversion algorithm, which incorporated the cylindrical geometry of the column, was used to reconstruct resistivity and phase images from the measured data. Differential time-lapse images of DNAPL movement past the plane of electrodes were generated by the cell-by-cell subtraction of resistivity and phase baseline models from those associated with the DNAPL release stage of the experiment. The DNAPL pulse was clearly delineated as resistive anomalies in the differential time-lapse resistivity images. The spatial extent of the resistive anomalies indicated that in addition to vertical migration, some lateral spreading of the DNAPL had occurred. Residual contamination could be detected after quasi-static conditions were reestablished. Residual DNAPL saturation was estimated from the resistivity model data by applying Archie's second equation. Despite significant measured phase changes due to DNAPL contamination, the differential phase images revealed only weak anomalies associated with DNAPL flow; these anomalies could be seen only in the initial stages of the experiment during peak flow through the plane of electrodes.

Influence of constitutive model parameters on the predicted migration of DNAPL in heterogeneous porous media

This study examines the influence of constitutive models and their parameters on predictions of the spatial and temporal distribution of a finite release of a dense, nonaqueous phase liquid (DNAPL) into a two‐dimensional, spatially correlated random permeability field. The base case simulation employed a comprehensive constitutive model that was validated against relevant one‐dimensional laboratory experiments. The base case was perturbed in the course of nine individual simulations, where each simulation examined the consequences of simplifying a single model characteristic. None of the nine subsequent simulations was able to reproduce, within ±10%, the spatial and temporal migration characteristics of the nonwetting fluid body at late time predicted by the base case. Capillary pressure‐saturation relationships that do not incorporate specific displacement and terminal pressures are demonstrated to severely overpredict the spatial extent of nonwetting fluid advancement. This suggests that van Genuchten‐based models may not be suitable for predicting DNAPL migration in saturated porous media. Not accounting for any one of hysteresis, nonwetting phase trapping, or the proper curvature or end‐point values of the nonwetting phase imbibition relative permeability curve profoundly influenced the time predicted for all nonwetting fluid movement to cease. The practical implication of this study is that an appropriate, comprehensive constitutive model, characterized with suitable parameter values, is necessary to accurately simulate a complete DNAPL release below the water table in both space and time.

Relative permeability characteristics necessary for simulating DNAPL infiltration, redistribution, and immobilization in saturated porous media

This study presents a relative permeability‐saturation (kr‐S) constitutive model that incorporates the critical phenomena necessary for simulating the rates of nonwetting fluid infiltration, redistribution, and immobilization in a saturated porous medium. To develop a model validation data set, the migration of a dense, nonaqueous phase liquid (DNAPL) pool within a one‐dimensional, 1 m tall, saturated sandpack was monitored under alternating drainage and imbibition conditions. A light transmission/image analysis system, able to distinguish between connected‐phase and residual nonwetting phase (NWP) in the apparatus, measured the elevation of the top of the connected‐phase DNAPL pool as a function of time. Light transmission calibration curves, correlating fluid saturation to transmitted color at the macroscopic scale, were found to exhibit a functional dependence on saturation history that must be taken into account. Applying the calibration curves to captured images of the experiment provided a continuous sequence of fluid saturation profiles. Numerical simulations of the bench‐scale experiment, using model parameters measured independently at the macroscopic scale, predict within measurement uncertainty the observed timescales of DNAPL migration and immobilization. Additional simulations reveal that model validation for imbibition processes depends on properly accounting for NWP kr‐S hysteresis, including imbibition function curvature and the abrupt extinction of NWP relative permeability.

Measuring the k– S– p relations on DNAPLs migration

Migration characteristics of dense non-aqueous phase liquids (DNAPLs) in the subsurface can be expressed as a water–DNAPL two-phase system based on mainly the k– S– p relations, which describe the relations among relative permeability ( k), degree of water saturation ( S), and capillary pressure head ( p). The aims of this research are to develop an experimental system with new type of probes, such as the electrical conductivity probe for measuring the degree of water saturation and the hydrophilic and hydrophobic tensiometer for measuring the pore water and DNAPL pressures, and also to estimate the results obtained from the developed experimental system. From these tests, the excellent k– S– p relations were obtained and the efficiency and validity of this developed experimental system have been confirmed in terms of the concept of the scaling coefficient calculated by interfacial tensions.

Scaling DNAPL migration from the laboratory to the field

A particular problem with the release of dense nonaqueous phase liquids (DNAPLs) into the environment is identifying where the DNAPL is and if it is still moving. This question is particularly important at sites where thousands of cubic meters of DNAPLs were disposed of. To date, results from laboratory models have not been scaled to predict analogous migration at the larger length and time scales appropriate for sites where large volumes of DNAPLs were released. Modified inspectional analysis is a technique for developing scaling relationships through nondimensionalizing the governing equations. It was applied in this study to scale observations of DNAPL migration in a laboratory model to four hypothetical scenarios in the field where large volumes of DNAPL were released. One scenario was compared to a large DNAPL spill site. The length and time scales of DNAPL movement predicted from our analysis are consistent with those predicted from a numerical model of this site. To our knowledge, this is the first application of modified inspectional analysis for release of DNAPLs in a laboratory model. This methodology may prove useful for scaling results from other laboratory investigations of DNAPL migration to field-scale systems.

Use of the geotechnical centrifuge as a tool to model dense nonaqueous phase liquid migration in fractures

We describe a study undertaken to investigate the potential of the geotechnical centrifuge as an experimental tool to study dense nonaqueous phase liquid (DNAPL) behavior in fracture systems. Scaling laws are developed that link observations made in a centrifuge model of a fracture system to the full‐scale problem (prototype). Centrifuge experiments carried out in synthetic fractures, described by smooth‐walled vertical capillary tubes, demonstrate for the first time that the geotechnical centrifuge can be used to model DNAPL transport in a simplified system provided that inertial forces are negligible in both the model and the prototype. Experiments also confirm, as predicted by Kueper and McWhorter [1991], that DNAPL invades a smooth‐walled, vertical fracture when the DNAPL pool height at its entrance reaches its entry pressure. A simple mathematical model describing the displacement of the DNAPL‐water interface is also presented. The predictions of this model and the experimental data are in good agreement with each other in the lower half of an invaded fracture. However, at the early stages of DNAPL invasion into the fracture, our observed DNAPL‐water interface velocities are slower than predicted by the model. We attribute this to an apparent dependence of the local capillary pressure on the interface displacement velocity.

Numerical examination of the factors controlling DNAPL migration through a single fracture.

The migration of five dense nonaqueous phase liquids (DNAPLs) through a single fracture in a clay aquitard was numerically simulated with the use of a compositional simulator. The effects of fracture aperture, fracture dip, matrix porosity, and matrix organic carbon content on the migration of chlorobenzene, 1,2-dichloroethylene, trichloroethylene, tetra-chloroethylene, and 1,2-dibromoethane were examined. Boundary conditions were chosen such that DNAPL entry into the system was allowed to vary according to the stresses applied. The aperture is the most important factor of those studied controlling the migration rate of DNAPL through a single fracture embedded in a clay matrix. Loss of mass to the matrix through diffusion does not significantly retard the migration rate of the DNAPL, particularly in larger aperture fractures (e.g., 50 microm). With time, the ratio of diffusive loss to the matrix to DNAPL flux into the fracture approaches an asymptotic value lower than unity. The implication is that matrix diffusion cannot arrest the migration of DNAPL in a single fracture. The complex relationships between density, viscosity, and solubility that, to some extent, govern the migration of DNAPL through these systems prevent accurate predictions without the use of numerical models. The contamination potential of the migrating DNAPL is significantly increased through the transfer of mass to the matrix. The occurrence of opposite concentration gradients within the matrix can cause dissolved phase contamination to exist in the system for more than 1000 years after the DNAPL has been completely removed from the fracture.

Visualization of DNAPL fingering processes and mechanisms in water-saturated porous media

Groundwater contamination by dense nonaqueous phase liquids (DNAPLs) has received increasing attention in the last decade. The fingering process of DNAPL migration in porous me- dia remains an incompletely understood subject. The main reason is that natural porous media are opaque and hence very few visualizations are available. This paper presents the visual results of two-dimensional experiments in a glass tank in which DNAPL penetrated into water-saturated homogeneous porous media. The results provide a clear reference for conceptual models of DNAPL finger development due to immiscible flow instabilities. The fingering process can be divided into two stages, that is, the finger initiation stage and the finger elongation stage. At the finger initiation stage, many DNAPL protuberances appear at the interface between tetrachloroethylene (PCE) and water along the surface of the porous media. During the finger elongation stage, some relatively larger protuberances develop into primary fingers. Secondary fingers may develop on the existing primary fingers. The fingers grew downwardly in a winding manner with the mechanisms of shielding, tip- growing, splitting, and coalescing. The fingers grew linearly with time and had similar growth rate at the finger elongation stage. The average wavelength (space between fingers) of the primary fingers was 0.051 m and the average PCE content in the region with fingers was 2.5% (7.0% saturation).

Shallow lateral DNAPL migration within slightly dipping limestone, southwestern Kentucky

Dense non-aqueous phase liquid (DNAPL) migration from source areas has mostly been governed by gravitative movement along beds dipping ∼1° NW that show diffuse-flow, semi-confined characteristics. This shallow, phreatic migration has occurred within relatively fractured and vuggy beds of the Mississippian St. Louis Limestone at depths beneath ground of 12–15 m, over lateral distances to 230 m. Near source areas, vertical product migration is occasionally deeper than 21 m beneath ground. Migration along the top-of-bedrock (TOB—generally at depths of 1.5–4.6 m) appears to be restricted to distances of less than 46 m, and therefore is unlikely to foster significant offsite migration. However, opportunely located TOB lows can provide routes for free-product entry, into the main lateral-migration beds, that are not located beneath source areas. Preferred migration along layer diplines appears to reflect: (1) bedding–plane partings; (2) interconnected, layer-bounded joints; (3) minor solutional enhancement of the above two features, especially the first; (4) sufficiently large and interconnected pore spaces, dissolution pits, and vugs; and (5) any possible solution conduits (for which there is no direct evidence, but some local occurrences are hinted at by site hydraulic characteristics). Local deflection of migrating free product away from the bedding dipline can be expected where (1) NW-trending bedding, joint, or vug-network pathways are poorly developed or absent in proximity to such available pathways trending along other directions, or (2) clay-filled depressions in the TOB surface, deeper than about 12 m beneath ground, act as barriers to downdip migration in the uppermost bedrock. Where such critically deep TOB lows might be filled with relatively permeable sands, lateral DNAPL migration from the uppermost bedrock into the soil mantle could occur along the updip slope of the TOB low. The directions of groundwater flow and transport (to the W) and DNAPL migration (to the NW) are divergent, which probably led to a plan-view aqueous plume that, over decades, had advanced toward the NW and W while tapering toward the migration limit to the NW.

Multiphase flow and transport in fractured clay/sand sequences

A numerical model (Queen's University Multi-Phase Flow Simulator, QUMPFS) was used to assess the rate of trichloroethylene (TCE) dense, non-aqueous phase liquid (DNAPL) migration through fractured clay, with special attention focused on the influence of interbedded sand lenses. The presence of these sand lenses was found to increase the time required for the non-wetting phase to migrate through the full 30 m vertical extent of the clay sequence from a few days to several years. Applied vertical hydraulic gradients were found to be moderately influential in systems consisting solely of fractured clays, yet one of the dominant factors controlling speed of vertical migration when sand lenses were present. Larger displacement pressure of the sands relative to that of the fractures leads to slower DNAPL migration rates, due to the delays that occur during build-up of capillary pressures. Dissolution of DNAPL and subsequent matrix diffusion of the aqueous phase has little effect on the rate of DNAPL migration through systems consisting of fractured clay only, yet slows the rate of migration in systems containing sand lenses. In all cases examined, the rate of DNAPL loading to the lower aquifer far exceeded the rate of aqueous phase mass loading. It was also found that DNAPL reaches the lower aquifer at approximately the same time as the aqueous phase plumes even for systems experiencing downward groundwater flow due to the attenuation of the aqueous phase through matrix diffusion.

The significance of buried landscape in subsurface migration of dense non-aqueous phase liquids; the case of perchloroethylene in the Sussex Aquifer, New Brunswick

Abstract At Sussex, New Brunswick, dissolved perchloroethylene (PCE) as high as 28.0 mu g/liter, was detected within the upper aquifer and in concentrations to 1.6 mu g/liter within the lower aquifer that serves as the main source of municipal water supply. Predominantly formed as an esker ridge, the lower aquifer consists of well-sorted, glaciofluvial/ice-contact, sand and gravel layers mostly confined by underlying till and/or bedrock and an overlying unit of laminated silt-clay glaciolacustrine sediments (middle aquitard). The middle aquitard is in turn overlain by an upper aquifer of variable thickness, extending from a depth of about 18 m to near surface, consisting of coarsening-upward sand and gravel, with occasional lenses of clay, silt and diamicton. A dispersal plume was identified by contouring PCE concentrations from 72 samples from the upper aquifer; PCE was not detected in 16 surface soil samples. The highest concentrations imply that the PCE originated from a surface spill near the urban business center and that subsurface migration was influenced significantly by a buried relict river channel cut into the middle aquitard. Scouring along the channel bottom cut through the middle aquitard and intersected the esker ridge of the underlying water supply aquifer, forming windows through the aquitard. Contamination of the lower aquifer has likely originated from the PCE being drawn through these windows during pumping of a water-supply well that is now out of service. Results indicate that withdrawal rates and placement of original municipal water wells, as well as the stratigraphy, conductivity and topography of subsurface units are controlling factors in Dense Non-Aqueous Phase Liquid migration at this site.

Stochastic pore-scale growth models of DNAPL migration in porous media

Stochastic models that account for a wide range of pore-scale effects are discussed in the context of two-phase, immiscible displacement problems in natural porous media. We focus on migration of dense, nonaqueous phase liquids (DNAPLs) through water-saturated geological materials. DNAPL movement is governed by buoyancy, capillary, and viscous forces, as well as by the details of the porous medium. We examine key issues relevant to development of stochastic growth models. We then present a particular stochastic growth model, based on a generalization of invasion percolation and Eden growth approaches, which realistically simulates two-phase flows in a computationally efficient manner. Fingering patterns are shown to depend critically on the competing buoyancy, capillary, and viscous forces between the DNAPL and the water, and their interactions with the porous medium at the local scale. We conclude with recommendations for future research.

Gravity‐destabilized nonwetting phase invasion in macroheterogeneous porous media: Experimental observations of invasion dynamics and scale analysis

We designed and conducted experiments in a heterogeneous sand pack where gravity‐destabilized nonwetting phase invasion (CO2 and trichloroethylene) could be recorded using high‐resolution light transmission methods. The heterogeneity structure was designed to be reminiscent of fluvial channel lag cut‐and‐fill architecture and to contain a series of capillary barriers. As invasion progressed, nonwetting phase structure developed a series of fingers and pools; behind the growing front we found nonwetting phase saturation to pulsate in certain regions when viscous forces were low. Through a scale analysis we derive a series of length scales that describe finger diameter, pool height and width, and regions where pulsation occurs within a heterogeneous porous medium. In all cases we find that the intrinsic pore‐scale nature of the invasion process and resulting structure must be incorporated into our analysis to explain experimental results. We propose a simple macroscale structural growth model that assembles length scales for substructures to delineate nonwetting phase migration from a source into a heterogeneous domain. For such a model applied at the field scale for dense nonaqueous phase liquid migration, we expect capillary and gravity forces within the complex subsurface lithology to play the primary roles with viscous forces forming a perturbation on the inviscid phase structure.