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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Estimating Watershed Subsurface Permeability From Stream Discharge Data using Deep Neural Networks, Frontiers in Earth Science: Dataset

This data package contains watershed modeling inputs and outputs as well as deep neural networks training and testing results used in "Estimating Watershed Subsurface Permeability From Stream Discharge Data using Deep Neural Networks" (Cromwell et al., 2021). We train various deep neural network models with different architectures to predict subsurface permeability from stream discharge hydrograph at the watershed outlet. The training data are obtained from ensemble simulations of hydrographs corresponding to an permeability ensemble using a fully-distributed, integrated surface-subsurface hydrologic model. The trained model is then applied to estimate the permeability of the real watershed using its observed hydrograph at the outlet. Our study demonstrates that the permeabilities of the soil and geologic facies that make significant contributions to the outlet discharge can be more accurately estimated from the discharge data. Their estimations are also more robust with observation errors. Compared to the traditional ensemble smoother method, DNNs show stronger performance in capturing the nonlinear relationship between permeability and stream hydrograph to accurately estimate permeability. Our study sheds new light on the value of the emerging deep learning methods in assisting integrated watershed modeling by improving parameter estimation, which will eventually reduce the uncertainty in predictive watershed models. For detailed information regarding watershed model description and DNNs setup, please refer to Cromwell et al., 2021. The deep_learning.zip file contains the inputs and outputs for the different deep neural networks. The watershed_model.zip file contains the inputs and outputs for watershed simulation using ATS. The figures.zip file contains raw figures and their corresponding scripts. For a more detailed description, please see the README.md file within each compressed file.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

Gas Flow Tightly Coupled to Elastoplastic Geomechanics for Tight- and Shale-Gas Reservoirs: Material Failure and Enhanced Permeability

We investigate coupled flow and geomechanics in gas production from extremely low permeability reservoirs such as tight and shale gas reservoirs, using dynamic porosity and permeability during numerical simulation. In particular, we take the intrinsic permeability as a step function of the status of material failure, and the permeability is updated every time step. We consider gas reservoirs with the vertical and horizontal primary fractures, employing the single and dynamic double porosity (dual continuum) models. We modify the multiple porosity constitutive relations for modeling the double porous continua for flow and geomechanics. The numerical results indicate that production of gas causes redistribution of the effective stress fields, increasing the effective shear stress and resulting in plasticity. Shear failure occurs not only near the fracture tips but also away from the primary fractures, which indicates generation of secondary fractures. These secondary fractures increase the permeability significantly, and change the flow pattern, which in turn causes a change in distribution of geomechanical variables. From various numerical tests, we find that shear failure is enhanced by a large pressure drop at the production well, high Biot's coefficient, low frictional and dilation angles. Smaller spacing between the horizontal wells also contributes to faster secondary fracturing. When the dynamic double porosity model is used, we observe a faster evolution of the enhanced permeability areas than that obtained from the single porosity model, mainly due to a higher permeability of the fractures in the double porosity model. These complicated physics for stress sensitive reservoirs cannot properly be captured by the uncoupled or flow-only simulation, and thus tightly coupled flow and geomechanical models are highly recommended to accurately describe the reservoir behavior during gas production in tight and shale gas reservoirs and to smartly design production scenarios.

02 PETROLEUM↗
DOE OSTI2023

Pore-Scale Analysis of the Permeability Damage and Recovery during Cyclic Freshwater and Brine Injection in Porous Media Containing Non-Swelling Clays

Permeability damage in subsurface porous media caused by clay mobilization is encountered in many engineering applications, such as geothermal energy, water disposal, oil recovery, and underground CO2 storage. During the freshwater injection into rocks containing brine, the sudden decrease in salinity causes native clay fines to detach and clog pore throats, leading to a significant decline in permeability. The clay fines detach due to weakened net-attractive forces binding them to each other and the grain. Past experiments link this permeability damage on the immediate history of the salinity and the direction of flow. To better understand this phenomenon, we conducted pore-scale simulations of cyclic injection of freshwater and brine into sandstone containing Kaolinite clay. Our simulations establish a link between the clay-fine trajectory and the permeability trend observed by Khilar and Fogler (1983). For a uniform clay size of 3 microns, we observe a permeability decline by two orders of magnitude during freshwater injection with respect to brine injection. Increasing salinity and simultaneously reversing flow direction restores the permeability. The permeability restoration upon reversing the brine flow direction is attributed to the unblocking of pore throats in the reverse direction by the movement of the clay particles along the grain surfaces by the hydrodynamic force and the strong net-attractive force under high salinity.

Bhuvankar, Pramod (ORCID:000000027739973X)↗
DOE OSTI2020

Enhanced Corneal Penetration of a Poorly Permeable Drug Using Bioadhesive Multiple Microemulsion Technology

Corneal penetration is a key rate limiting step in the bioavailability of topical ophthalmic formulations that incorporate poorly permeable drugs. Recent advances have greatly aided the ocular delivery of such drugs using colloidal drug delivery systems. Ribavirin, a poorly permeable BCS class-III drug, was incorporated in bioadhesive multiple W/O/W microemulsion (ME) to improve its corneal permeability. The drug-loaded ME was evaluated regarding its physical stability, droplet size, PDI, zeta potential, ultrastructure, viscosity, bioadhesion, in vitro release, transcorneal permeability, cytotoxicity, safety and ocular tolerance. Our ME possessed excellent physical stability, as it successfully passed several cycles of centrifugation and freeze–thaw tests. The formulation has a transparent appearance due to its tiny droplet size (10 nm). TEM confirmed ME droplet size and revealed its multilayered structure. In spite of the high aqueous solubility and the low permeability of ribavirin, this unique formulation was capable of sustaining its release for up to 24 h and improving its corneal permeability by 3-fold. The in vitro safety of our ME was proved by its high percentage cell viability, while its in vivo safety was confirmed by the absence of any sign of toxicity or irritation after either a single dose or 14 days of daily dosing. Our ME could serve as a vehicle for enhanced ocular delivery of drugs with different physicochemical properties, including those with low permeability.

Ibrahim, Mohamed Moustafa↗
DOE OSTI2015

Seismic and aseismic deformations and impact on reservoir permeability: The case of EGS stimulation at The Geysers, California, USA

In this paper, we use the Seismicity-Based Reservoir Characterization approach to study the spatiotemporal dynamics of an injection-induced microseismic cloud, monitored during the stimulation of an enhanced geothermal system, and associated with the Northwest Geysers Enhanced Geothermal System (EGS) Demonstration project (California). We identified the development of a seismically quiet domain around the injection well surrounded by a seismically active domain. Then we compare these observations with the results of 3-D Thermo-Hydro-Mechanical simulations of the EGS, which accounts for changes in permeability as a function of the effective normal stress and the plastic strain. The results of our modeling show that the aseismic domain is caused by both the presence of the injected cold water and by thermal processes. These thermal processes cause a cooling-stress reduction, which prevent shear reactivation and favors fracture opening by reducing effective normal stress and locally increasing the permeability. This process is accompanied by aseismic plastic shear strain. In the seismic domain, microseismicity is caused by the reactivation of the preexisting fractures, resulting from an increase in injection-induced pore pressure. Our modeling indicates that in this domain, permeability evolves according to the effective normal stress acting on the shear zones, whereas shearing of preexisting fractures may have a low impact on permeability. We attribute this lack of permeability gain to the fact that the initial permeabilities of these preexisting fractures are already high (up to 2 orders of magnitude higher than the host rock) and may already be fully dilated by past tectonic straining.

58 GEOSCIENCES↗
DOE OSTI2016

High-stress triaxial direct-shear fracturing of Utica shale and in situ X-ray microtomography with permeability measurement

The challenge of characterizing subsurface fluid flow has motivated extensive laboratory studies, yet fluid flow through rock specimens in which fractures are created and maintained at high-stress conditions remains underinvestigated at this time. The studies of this type that do exist do not include in situ fracture geometry measurements acquired at stressed conditions, which would be beneficial for interpreting the flow behavior. Therefore, this study investigates the apparent permeability induced by direct-shear fracture stimulation through Utica shale (a shale gas resource and potential caprock material) at high triaxial stress confinement and for the first time relates these values to simultaneously acquired in situ X-ray radiography and microtomography images. Change in fracture geometry and apparent permeability was also investigated at additional reduced stress states. Finite element and combined finite-discrete element modeling were used to evaluate the in situ observed fracturing process. Results from this study indicate that the increase in apparent permeability through fractures created at high-stress (22.2 MPa) was minimal relative to the intact rock (less than 1 order of magnitude increase), while fractures created at low stress (3.4 MPa) were significantly more permeable (2 to 4 orders of magnitude increase). Here, this study demonstrates the benefit of in situ X-ray observation coupled with apparent permeability measurement to analyze fracture creation in the subsurface. Our results show that the permeability induced by fractures through shale at high stress can be minor and therefore favorable in application to CO 2 sequestration caprock integrity but unfavorable for hydrocarbon recovery from unconventional reservoirs.

58 GEOSCIENCES↗
DOE OSTI2017

Steady-state supercritical CO 2 and brine relative permeability in Berea sandstone at different temperature and pressure conditions

In this study, we measure steady-state two-phase supercritical CO 2 -brine relative permeabilities in a 61 cm-long Berea sandstone core at three different conditions (408C and 12.41 MPa, 408C and 8.27 MPa, and 608C and 12.41 MPa) under primary drainage. We use pressure taps to obtain pressure drops of individual sections of the core, and X-ray Computed Tomography (CT) to obtain in situ saturation profiles, which together help to mitigate the capillary end effect. We include previously measured relative permeabilities at 208C and 10.34 MPa, and compare all the data using both an eye-test and a statistical test. We find no appreciable temperature and pressure dependence of CO 2 relative permeability within 20–608C and 8.27–12.41 MPa. We find slight changes in the brine relative permeability between supercritical CO 2 conditions (40–608C and 8.27–12.41 MPa) and the liquid CO 2 condition (208C and 10.34 MPa). The temperature and pressure independence of CO 2 relative permeability has been previously recognized and reassured in this work using a capillary-effect-free method. This allows one to use a single CO 2 relative permeability curve in modeling two-phase CO 2 flow within 20–608C and 8.27–12.41 MPa.

58 GEOSCIENCES↗
DOE OSTI2023

A data-driven framework for permeability prediction of natural porous rocks via microstructural characterization and pore-scale simulation

Understanding the microstructure–property relationships of porous media is of great practical significance, based on which macroscopic physical properties can be directly derived from measurable microstructural informatics. However, establishing reliable microstructure–property mappings in an explicit manner is difficult, due to the intricacy, stochasticity, and heterogeneity of porous microstructures. In this paper, a data-driven computational framework is presented to investigate the inherent microstructure–permeability linkage for natural porous rocks, where multiple techniques are integrated together, including microscopy imaging, stochastic reconstruction, microstructural characterization, pore-scale simulation, feature selection, and data-driven modeling. A large number of 3D digital rocks with a wide porosity range are acquired from microscopy imaging and stochastic reconstruction techniques. A broad variety of morphological descriptors are used to quantitatively characterize pore microstructures from different perspectives, and they compose the raw feature pool for feature selection. Here high-fidelity lattice Boltzmann simulations are conducted to resolve fluid flow passing through porous media, from which reliable permeability references are obtained. The optimal feature set that best represents permeability is identified through a performance-oriented feature selection process, upon which a cost-effective surrogate model is rapidly fitted to approximate the microstructure-permeability mapping via data-driven modeling. This surrogate model exhibits great advantages over empirical/analytical formulas in terms of prediction accuracy and generalization capacity, which can predict reliable permeability values spanning four orders of magnitude. Besides, feature selection also greatly enhances the interpretability of the data-driven prediction model, from which new insights into the mechanism of how microstructural characteristics determine intrinsic permeability are obtained.

58 GEOSCIENCES↗
DOE OSTI2018

Multiphysics Lattice Discrete Particle Modeling (M-LDPM) for the Simulation of Shale Fracture Permeability

A three-dimensional multiphysics lattice discrete particle model (M-LDPM) framework is formulated to investigate the fracture permeability behavior of shale. The framework features a dual lattice system mimicking the mesostructure of the material and simulates coupled mechanical and flow behavior. The mechanical lattice model simulates the granular internal structure of shale, and describes heterogeneous deformation by means of discrete compatibility and equilibrium equations. The network of flow lattice elements constitutes a dual graph of the mechanical lattice system. A discrete formulation of mass balance for the flow elements is presented to model fluid flow along cracks and intact materials. The overall computational framework is implemented with a mixed explicit–implicit integration scheme and a staggered coupling method that makes use of the dual lattice topology enabling the seamless two-way coupling of the mechanical and flow behaviors. The proposed model is used for the computational analysis of shale fracture permeability behavior by simulating triaxial direct shear tests on Marcellus shale specimens under various confining pressures. The simulated mechanical response is calibrated against the experimental data, and the predicted permeability values are also compared with the experimental measurements. Moreover, the paper presents the scaling analysis of both the mechanical response and permeability measurements based on simulations performed on geometrically similar specimens with increasing size. The simulated stress strain curves reflect a significant size effect in the post-peak due to the presence of localized fractures. The scaling analysis of permeability measurements enables prediction of permeability for large specimens by extrapolating the numerical results of small ones.

58 GEOSCIENCES↗
DOE OSTI2019

Analysis of the Pressure-Pulse Propagation in Rock: a New Approach to Simultaneously Determine Permeability, Porosity, and Adsorption Capacity

Permeability estimation from pressure-pulse decay method is complicated by two facts: (1) the decay curve often deviates from the single-exponential behavior in the early time period and (2) possible existence of gas adsorption. Both the two factors cause significant permeability error in most of pressure-pulse decay methods. In this paper, we first present a thorough analysis of pressure-pulse propagation process to reveal the mechanism behind the early time and later time behaviors of pressure decay curve. Inspired by the findings from these analyses, a new scaled pressure is proposed which can: (1) be easily used to distinguish the early time and later time data and (2) make the decay curves of all cases into a single 1:1 straight line for later time. A new data-proceeding method, which calculates the apparent porosity and permeability using the same set of measured data, is then developed. The new method could not only remove the effects of the adsorption on the permeability estimation, but also identify the apparent porosity as well as proper adsorption model and parameters. The proposed method is verified by comparing with true values and calculated values through numerical simulations that cover variations in typical rock properties (porosity, permeability, slippage, and adsorption) and the experiment configurations. It is found that the new method is accurate and reliable for all test cases, whereas the Brace’s and Cui’s approaches may cause permeability error in some cases. Lastly, the new method has been successfully applied to real data measured in pressure-pulse decay experiments involving different types of rocks and gases.

58 GEOSCIENCES↗
DOE OSTI2019

Bayesian and LASSO Regressions for Comparative Permeability Modeling of Sandstone Reservoirs

In this research, Bayesian model averaging (BMA) and least absolute shrinkage and selection operator regression (LASSO) algorithms were adopted for the core permeability modeling as a function of well log and core measurements. More specifically, the core permeability (dependent factor) was modeled given the well log and core data (independent variables) and then predicted in non-cored intervals of a well in a sandstone formation. The BMA is a stochastic linear modeling and a Bayesian parameter selection. Among 50 linear models generated as a function of the independent variables and depicted in Occam’s window, the best model of the highest posterior probability is determined. The best model has the optimal subset parameters that most influences the response factor. The core permeability modeling was again conducted using the LASSO algorithm, which adopts a completely different way of modeling and subset selection by using the penalized least-squared equation. Both BMA and LASSO resulted in a very accurate prediction of the core permeability by achieving perfect measured and calculated permeability matching. Matches for the two algorithms were quantified by computing the adjusted R-squared and root-mean-squared prediction error. In addition, results of the BMA and LASSO were compared to the conventional multiple linear regression (LM). The LASSO algorithm led to an accurate matching similar to LM, but slightly better than BMA. Therefore, both BMA and LASSO represent integrated procedures for accurate permeability estimation similar to conventional regression analysis.

58 GEOSCIENCES↗
DOE OSTI2017

The effects of nearby fractures on hydraulically induced fracture propagation and permeability changes

Fracture propagation caused by hydraulic fracturing operations can be significantly influenced by adjacent fractures. In this paper, we present a detailed coupled hydro-mechanical analysis to study the effects of nearby natural fractures on hydraulically induced fracture propagation and changes in fracture permeability. Two rock domains were considered in comparison: FD1, with one fracture, and FD2, with two adjacent parallel or non-parallel fractures. It was assumed that water injection occurred in a borehole that intersected the single fracture in FD1 and one of the two fractures in FD2. Simulations were made for a time period of 3 h with an injection period of 2 h followed by 1 h of shut-in. An elastic-brittle model based on the degradation of material properties was implemented in a 2D finite-difference scheme and used for elements of the intact rock subjected to tension and shear failure. The intact rock was considered to have a low but non-negligible permeability. A verification study against analytical solutions showed that the fracture propagation and stress concentrations due to differential boundary stresses could be accurately represented by our model. Next, a base case was considered, in which the stress ratio (SR) between the magnitudes of the maximum and minimum boundary stresses, the permeability k R of the intact rock and the initial permeability k TF of the tension failure regions were fixed. In FD2, the distance d F between the two natural fractures defined by the closest distance was also fixed. The results showed that in both rock domains, the fracture started to propagate when the pore pressure was approximately 85% of the magnitude of the minimum boundary stress. The propagation of a single fracture was significantly greater than the propagation of a double fracture system because, in the latter case, the pore pressure decreased when the two fractures connected. As a result, changes in permeability in FD2 were smaller than in FD1. At the end of injection, the maximum ratios between the final and initial permeability of the natural fractures were found to be approximately 3 and 2 for rock domains FD1 and FD2, respectively. For non-parallel fractures, the controlling factor for fracture propagation was the separation between the tips of the pressurised fracture and the neighbouring non-pressurised fracture. A sensitivity study was conducted to study the influence of the key parameters d F , SR, k R and k TF on the simulation results. Lastly, fracture propagation showed more sensitivity to dF and SR than to the other parameters.

58 GEOSCIENCES↗
DOE OSTI2024

Relative permeabilities for two-phase flow through wellbore cement fractures

Multiple fluids are likely to exist in fractures and flow paths associated with leaky wellbores, including liquids (e.g., crude oil) and gases (e.g., gas exsolved from liquid). These fluids occupy and move through different portions of the pore spaces within the fractures depending on many factors, including fluid properties, fracture size, and the amount of the different fluids. Upward leakage of any phase, through the fracture, can contaminate water-bearing formations, create hazardous surface conditions, and compromise the functionality of the wellbore. Early signs of wellbore leaks may be expressed by anomalous pressure behavior at surface monitoring points on cavern storage wells. These pressure anomalies are difficult to interpret, necessitating knowledge of the factors that affect the multiphase flow in fractures and porous media. These parameters are critical to modeling multiphase flow in fractures. This insight can guide further diagnosis and maximize leak remediation. Here, our study focuses on the relationship of the liquid–gas relative permeabilities for representative variable-aperture wellbore cement fracture. To obtain the relative permeability of each phase, two-phase flow tests were conducted where both fluids were flowing simultaneously through a fractured wellbore cement specimen under a range of factors, namely (1) aperture size, (2) capillary numbers, and (3) viscosity ratio. The flow experiments were conducted under a range of confining stresses and flow velocities, using nitrogen gas and silicone oils (of different viscosities) in a specially designed pressure vessel. The sum of gas and oil relative permeabilities were found to be less than one under all conditions, which indicates that the presence of one phase affects the permeability of the other phase, and vice versa. Since the gas phase flow conditions include a significant inertial flow component in addition to viscous flow, the inertial flow coefficients at different saturation states are presented. The factors affecting the relationship between the relative permeabilities are discussed in detail. A new mathematical model for estimating the relative permeability of wellbore cement fracture is presented and experimentally validated.

58 GEOSCIENCES↗
DOE OSTI2020

Scaling of two-phase water-steam relative permeability and thermal fluxes in porous media

Two-phase water-steam flow conditions are frequently encountered in many engineering applications, including geothermal reservoirs. Although routine calculations are based on the multiphase Darcy’s law, the role of the topology of the flowing phases at the pore-scale is usually neglected in the estimation of relative permeabilities. Instead, the latter are frequently computed using empirical models like the Corey correlation. In this work, we first apply the model for relative permeabilities based on pore-scale flow regimes developed by Picchi and Battiato (2019), Relative permeability scaling from pore-scale flow regimes, Water Resour. Res. 55, 3215–3233, to scenarios typical of geothermal reservoirs and then extend it by deriving the scaling laws for the transmissibilities and the thermal properties as a function of temperature. First, we discuss the scaling behavior of normalized relative permeabilities in terms of viscosity ratio and capillary number of water-steam systems and, then, we provide a validation of the model against experimental data available in the literature. The model captures well the data trends collected in real 3D porous media. These results suggest that water-steam relative permeabilities follow the same scaling behavior of gas-liquid systems where the non-wetting phase is much less viscous than the wetting phase. Finally, we investigate the impact that relative permeabilities have on heat transfer rates at two-phase flow conditions and the scaling of mass and energy transmissibility and thermal properties of the mixture. An estimation of the exergy carried by the two-phase water-steam mixture is also included.

42 ENGINEERING↗
DOE OSTI2025

Supported ionic liquid membranes (SILMs) with exceptional selectivity and permeability for dilute CO 2 separations

Supported ionic liquid membranes (SILMs), containing phosphonium ionic liquids with aprotic N-heterocyclic anions (AHA ILs) in an inert inorganic support, were tested under both dry and humidified (40 % RH) mixed-gas conditions down to 420 ppm CO 2 in N 2 at 35 °C. In the dry case, the best performing IL, triethyl(octyl)phosphonium 4-bromopyrazolide ([P 2228 ][4-BrPyra]) exhibited mixed-gas CO 2 permeabilities and CO 2 /N 2 permeability selectivities as high as 26,800 barrer and 7,000, respectively. In the presence of humidity, the CO 2 permeability and CO 2 /N 2 selectivity increased to 49,100 barrer and 13,200, respectively, and these are the highest reported combination in the literature. Humidity amplifies CO 2 permeabilities and CO 2 /N 2 permeability selectivities through increases in CO 2 capacity due to bicarbonate formation and through faster mobility of the mobile carrier from decreased viscosity. Furthermore, N 2 permeability stayed roughly invariant in the presence of humidity, likely from competing effects of viscosity reduction and lower N 2 solubility.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

On the Relationship Between Fault Permeability Increases, Induced Stress Perturbation, and the Growth of Aseismic Slip During Fluid Injection

Fluid injections into the deep subsurface can, at times, generate earthquakes, but often, they only produce aseismic deformations. Here we analyze the influence of fault hydromechanical properties on the growth of injection-induced aseismic slip. Using hydromechanical modeling, we show how permeability enhancement in addition to the background stress and frictional weakening has an important effect on the pressure diffusion and slip growth during injection. We find that the more pronounced the fault permeability enhancement, the stronger is the growth of the aseismic slip zone. The effect of enhanced permeability is more pronounced when the fault is initially close to failure. Our results show that aseismic slip grows beyond the pressurized zone when the fault permeability increases, while slip remains behind the pressurized zone when permeability does not vary from its initial preslip value. Furthermore, fault permeability increases should be considered as complementary mechanism to current models of fluid-induced aseismic slip.

58 GEOSCIENCES↗
DOE OSTI2018

Friction-Stability-Permeability Evolution of a Fracture in Granite

The evolution of frictional strength, stability, and fracture permeability is intimately linked both to the seismic cycle and to the impact of hydraulic stimulation for fractured reservoirs. However, despite this importance, the poromechanical relationships between fault permeability and strength remain unclear. The present study explores this relationship via laboratory experiments for concurrent shear-flow on smooth fractures of Westerly granite. The novelty of these experiments is that the shear velocity is precisely controlled during the measurement of fracture permeability. Results indicate permeability enhancement during velocity-weakening (potentially unstable) frictional slip. To decipher key processes contributing to this response, we evaluate the state of contacting asperities and of fracture surface asperities via digital rock fracture modeling of statistically equivalent surfaces. We propose two plausible mechanisms constraining the relationship between friction and permeability evolution—one based on changes in asperity contact distribution and one on shear-induced dilation triggered by changes in fault slip velocity. Finally, these mechanisms should be taken into account in interpreting field observation such as the abrupt permeability increase of natural faults at the onset of seismic slip.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Scaling Analysis of Two–Phase Flow in Fractal Permeability Fields

Fluid mixing in permeable media is essential in many practical applications. The mixing process is a consequence of velocity fluctuations owing to geological heterogeneities and mobility contrast of fluids. Heterogeneities in natural rocks are often spatially correlated, and their properties, such as permeability, may be described using fractal distributions. This work models the fractal characteristics of such permeability fields in which the covariance function is expressed as a power-law function. A generalized scaling relation is derived relating various fractal permeability fields using the magnitude of their fluctuations. Here, this relation reveals the self-similar behavior of two-phase flow in such permeable media. To that end, a recently developed, high-resolution numerical simulator is employed to validate the analytically derived scaling relations. Two flow problems are considered in which flow is governed by 1) a linear, and 2) a nonlinear transport equation. Due to the probabilistic representation of the fractal permeability fields, a sensitivity study is conducted for each flow scenario to determine the number of realizations required for statistical convergence. Scaling analysis is performed using ensemble averages of simulated saturation profiles and their mixing lengths. Results support the validity of the developed scaling relation across the range of investigated flow conditions at intermediate times. The dynamics of linear flow in the asymptotic regime is affected by the correlation structure of heterogeneity. In nonlinear flow, scaling behavior appears to be dominated by the degree of nonlinearity.

58 GEOSCIENCES↗