[1] This study provides an evaluation of various modifications of the cubic law, expanding upon previous work as follows: (1) Experimentally measured flow rates and apertures are the basis for the evaluation; (2) a rock fracture is used rather than an analog or numerically simulated fracture; (3) the fracture is not disturbed at any point during the testing; and (4) detailed measurements of the apertures and the top and bottom fracture surface profiles (931,988 measurements in total) are obtained, enabling assessment of the impact of fracture surface undulation and model discretization on the simulated flow rates. The cubic law calculated with either the geometric mean aperture or incorporating surface roughness factors provided reasonable (±10%) estimates of the observed flow rates for Re < 1. The cubic law applied locally (LCL) over-predicted the observed flow rates by at least 1.9 times. Modifying the LCL to incorporate a solution for tapered plates and correcting for surface undulation reduced the over-prediction to at least 1.75 times the measured flow rates. The primary conclusions that we can draw from this work are as follows: (1) There appears to be merit to conducting further studies of the cubic law applied at the single-fracture scale to determine whether similar results are achievable in all fracture types; and (2) the current understanding of when the LCL will provide an adequate representation of the true flow behavior is not entirely correct; more investigation into the effect of fracture surface undulation and other causes of abrupt aperture change (e.g., rock debris trapped within the fracture plane) is required.

This paper describes a field experiment involving the release of 230.9 liters of tetrachloroethylene (PCE) below the water table in a naturally occurring, unconfined sand aquifer. The release was executed in a 3 m X 3 m X 3.4 m deep, scalable‐joint steel sheet‐pile cell anchored into an underlying clay aquitard. After allowing 28 days for redistribution, excavation of the upper approximately 0.9 m of the cell revealed PCE pools and residual to be present in relatively coarser grained horizons, with substantial degrees of lateral flow having taken place. This lateral flow was observed in laminations and lenses ranging in thickness from a few mm to a few cm, with only subtle variations in texture separating individual migration pathways. Detailed sampling during the excavation procedure and subsampling of three cores extended down to the clay aquitard revealed a spatially variable distribution of PCE with saturations ranging from 1% to 38% of pore space. Laboratory measurement of a fully hysteretic capillary pressure curve demonstrated that the degree of nonwetting phase residual is a function of the maximum saturation attained along main drainage during the initial infiltration process. Various models for consolidated petroleum reservoir materials did not fit the experimental data well. The theory governing pool formation in heterogeneous porous media is also presented, and it is demonstrated that pools can form in homogeneous media exhibiting a distinct entry pressure.

[1] This study presents a capillary-pressure saturation (P C -S) constitutive model that incorporates the capillary phenomena necessary for simulating the spatial distribution of nonwetting fluid migrating in a saturated porous medium. To develop a model validation data set, a sequence of dense, nonaqueous phase liquid (DNAPL) pools were emplaced, under alternating drainage and imbibition conditions, in a one-dimensional, 1 m tall, saturated sand pack. A light transmission/image analysis system successfully distinguished between connected-phase and residual nonwetting fluid in the apparatus, thereby permitting the accurate measurement of DNAPL pool heights. These heights are found to depend on the nonzero capillary pressure across the fluid-fluid interface at the top of the pool. The terminal pressure is demonstrated to be the minimum sustainable capillary pressure in connected-phase nonwetting fluid experiencing imbibition, below which residual is formed. Additional bench-scale experiments demonstrate that a nonwetting phase pool will penetrate an underlying capillary barrier when the entry pressure is exceeded and that the resulting infiltration will terminate when the capillary pressure at the barrier reduces to the terminal pressure. At the macroscopic scale the terminal pressure corresponds to the extinction saturation (i.e., zero nonwetting phase flow) at the inflection point on the imbibition P C -S curve. A ratio of terminal to entry pressure of approximately 0.6 is found to apply at both bench and macroscopic scales and to be independent of porous media and fluid properties. The developed P C -S constitutive model, which extends the Brooks-Corey function to incorporate the terminal pressure, successfully predicted the behavior observed in the laboratory experiments. Constitutive models that do not incorporate both an entry and a terminal pressure, such as those based upon the standard van Genuchten function, are demonstrated to be unable to predict the observed equilibrium DNAPL pool heights in homogeneous media or above capillary barriers.

A two‐dimensional finite difference model to study the simultaneous movement of a dense, nonaqueous phase liquid and water in heterogeneous porous media is developed. A distinctive feature of the solution is that the primary variables solved for, wetting phase pressure and wetting phase saturation, are both existent throughout the solution domain regardless of whether the nonwetting phase is present. This eliminates the need to specify small, fictitious saturations of nonwetting fluid ahead of the advancing front where only wetting fluid is present, as is often required in conventional simulators. The model is therefore well suited for the simulation of ground water contamination problems involving the advance of immiscible liquids into previously uncontaminated groundwater systems. The finite difference equations are solved fully implicitly using Newton‐Raphson iteration. In order to minimize computer storage and execution time a Dupont‐Kendall‐Rachford iterative solver utilizing Orthomin acceleration has been incorporated. The numerical model is verified against an exact analytical solution which incorporates fully the effects of both relative permeability and capillary pressure. The model is validated through comparison to a parallel‐plate laboratory experiment involving the infiltration of tetrachloroethylene into a heterogeneous sand pack.

This paper examines the behavior of dense, nonaqueous phase liquids (DNAPLs) in fractured clay and rock. The conditions under which a DNAPL will enter an initially water‐saturated, rough‐walled fracture are outlined and expressed in a number of ways, including the height to which a DNAPL pool can accumulate above a fracture prior to initial entry. To study the behavior of DNAPL in a rough‐walled fracture following initial entry, numerical simulations are carried out both in the plane of a fracture using a discrete representation of fracture roughness, and at a larger scale of averaging using an equivalent homogeneous porous media approach. The simulations illustrate that DNAPL will migrate through the larger aperture regions of a fracture plane, and that the DNAPL has the potential to enter progressively smaller aperture fractures with depth as it migrates. Additional numerical simulations indicate that the time taken for a nonaqueous phase liquid to traverse a fractured aquitard is inversely proportional to the fracture aperture, the fracture dip from the horizontal, and the height of the pool collected above the aquitard. It is also demonstrated that upward hydraulic gradients across a fractured aquitard can significantly slow the downward rate of DNAPL migration while downward water gradients enhance the rate of DNAPL migration across the aquitard.