We study the gas flow processes in ultra-tight porous media in which the matrix pore network is composed of nanometre- to micrometre-size pores. We formulate a pressure-dependent permeability function, referred to as the apparent permeability function (APF), assuming that Knudsen diffusion and slip flow (the Klinkenberg effect) are the main contributors to the overall flow in porous media. The APF predicts that in nanometre-size pores, gas permeability values are as much as 10 times greater than results obtained by continuum hydrodynamics predictions, and with increasing pore size (i.e. of the order of the micrometre), gas permeability converges to continuum hydrodynamics values. In addition, the APF predicts that an increase in the fractal dimension of the pore surface leads to a decrease in Knudsen diffusion. Using the homogenization method, a rigorous analysis is performed to examine whether the APF is preserved throughout the process of upscaling from local scale to large scale. We use the well-known pulse-decay experiment to estimate the main parameter of the APF, which is Darcy permeability. Our newly derived late-transient analytical solution and the late-transient numerical solution consistently match the pressure decay data and yield approximately the same estimated value for Darcy permeability at the typical core-sample initial pressure range and pressure difference. Other parameters of the APF may be determined from independent laboratory experiments; however, a pulse-decay experiment can be used to estimate the unknown parameters of the APF if multiple tests are performed and/or the parameters are strictly constrained by upper and lower bounds.

In this paper we present a partitioning interwell tracer test (PITT) technique for the detection, estimation, and remediation performance assessment of the subsurface contaminated by nonaqueous phase liquids (NAPLs). We demonstrate the effectiveness of this technique by examples of experimental and simulation results. The experimental results are from partitioning tracer experiments in columns packed with Ottawa sand. Both the method of moments and inverse modeling techniques for estimating NAPL saturation in the sand packs are demonstrated. In the simulation examples we use UTCHEM, a comprehensive three‐dimensional, chemical flood compositional simulator developed at the University of Texas, to simulate a hypothetical two‐dimensional aquifer with properties similar to the Borden site contaminated by tetrachloroethylene (PCE), and we show how partitioning interwell tracer tests can be used to estimate the amount of PCE contaminant before remedial action and as the remediation process proceeds. Tracer tests results from different stages of remediation are compared to determine the quantity of PCE removed and the amount remaining. Both the experimental (small‐scale) and simulation (large‐scale) results demonstrate that PITT can be used as an innovative and effective technique to detect and estimate the amount of residual NAPL and for remediation performance assessment in subsurface formations.

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The modes of geologic storage of CO 2 are usually categorized as structural, dissolution, residual, and mineral trapping. Here we argue that the heterogeneity intrinsic to sedimentary rocks gives rise to a fifth category of storage, which we call local capillary trapping. Local capillary trapping occurs during buoyancy-driven migration of bulk phase CO 2 within a saline aquifer. When the rising CO 2 plume encounters a region (10 −2 to 10 +1 m) where capillary entry pressure is locally larger than average, CO 2 accumulates beneath the region. This form of storage differs from structural trapping in that much of the accumulated saturation will not escape, should the integrity of the seal overlying the aquifer be compromised. Local capillary trapping differs from residual trapping in that the accumulated saturation can be much larger than the residual saturation for the rock. We examine local capillary trapping in a series of numerical simulations. The essential feature is that the drainage curves (capillary pressure versus saturation for CO 2 displacing brine) are required to be consistent with permeabilities in a heterogeneous domain. In this work, we accomplish this with the Leverett J -function, so that each grid block has its own drainage curve, scaled from a reference curve to the permeability and porosity in that block. We find that capillary heterogeneity controls the path taken by rising CO 2 . The displacement front is much more ramified than in a homogeneous domain, or in a heterogeneous domain with a single drainage curve. Consequently, residual trapping is overestimated in simulations that ignore capillary heterogeneity. In the cases studied here, the reduction in residual trapping is compensated by local capillary trapping, which yields larger saturations held in a smaller volume of pore space. Moreover, the amount of CO 2 phase remaining mobile after a leak develops in the caprock is smaller. Therefore, the extent of immobilization in a heterogeneous formation exceeds that reported in previous studies of buoyancy-driven plume movement.

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Summary Many naturally fractured reservoirs around the world have depleted significantly, and improved-oil-recovery (IOR) processes are necessary for further development. Hence, the modeling of fractured reservoirs has received increased attention recently. Accurate modeling and simulation of naturally fractured reservoirs (NFRs) is still challenging because of permeability anisotropies and contrasts. Nonphysical abstractions inherent in conventional dual-porosity and dual-permeability models make them inadequate for solving different fluid-flow problems in fractured reservoirs. Also, recent technologies for discrete fracture modeling may suffer from large simulation run times, and the industry has not used such approaches widely, even though they give more-accurate representations of fractured reservoirs than dual-continuum models. We developed an embedded discrete fracture model (DFM) for an in-house compositional reservoir simulator that borrows the dual-medium concept from conventional dual-continuum models and also incorporates the effect of each fracture explicitly. The model is compatible with existing finite-difference reservoir simulators. In contrast to dual-continuum models, fractures have arbitrary orientations and can be oblique or vertical, honoring the complexity of a typical NFR. The accuracy of the embedded DFM is confirmed by comparing the results with the fine-grid, explicit-fracture simulations for a case study including orthogonal fractures and a case with a nonaligned fracture. We also perform a grid-sensitivity study to show the convergence of the method as the grid is refined. Our simulations indicate that to achieve accurate results, the embedded discrete fracture model may only require moderate mesh refinement around the fractures and hence offers a computationally efficient approach. Furthermore, examples of waterflooding, gas injection, and primary depletion are presented to demonstrate the performance and applicability of the developed method for simulating fluid flow in NFRs.

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