Transport Properties Of Rocks Research Articles

Augmenting X-ray micro-CT data with MICP data for high resolution pore-scale simulations of flow properties of carbonate rocks

Pore-scale modeling is essential in understanding and predicting flow and transport properties of rocks. Generally, pore-scale modeling is dependent on imaging technologies such as Micro Computed Tomography (micro-CT), which provides visual confirmation into the pore microstructures of rocks at a representative scale. However, this technique is limited in the ability to provide high resolution images showing the pore-throats connecting pore bodies. Pore scale simulations of flow and transport properties of rocks are generally done on a single 3D pore microstructure image. As such, the simulated properties are only representative of the simulated pore-scale rock volume. These are the technological and computational limitations which we address here by using a stochastic pore-scale simulation approach. This approach consists of constructing hundreds of 3D pore microstructures of the same pore size distribution and overall porosity but different pore connectivity. The construction of the 3D pore microstructures incorporates the use of Mercury Injection Capillary Pressure (MICP) data to account for pore throat size distribution, and micro-CT images to account for pore body size distribution. The approach requires a small micro-CT image volume (7–19 mm3) to reveal key pore microstructural features that control flow and transport properties of highly heterogeneous rocks at the core-scale. Four carbonate rock samples were used to test the proposed approach. Permeability calculations from the introduced approach were validated by comparing laboratory measured permeability of rock cores and permeability estimated using five well-known core-scale empirical model equations. The results show that accounting for the stochastic connectivity of pores results in a probabilistic distribution of flow properties which can be used to upscale pore-scale simulated flow properties to the core-scale. The use of the introduced stochastic pore-scale simulation approach is more beneficial when there is a higher degree of heterogeneity in pore size distribution. This is shown to be the case with permeability and hydraulic tortuosity which are key controls of flow and transport processes in rocks.

Effects of Stress on Transport Properties in Fractured Porous Rocks

Abstract The nonlinear characteristics of the rock transport properties (permeability and electrical conductivity in this study) as a function of stress are closely related to the geometry of the pore space, which consists of stiff pores, microcracks, or microfractures. We consider two behaviors of the pore space, one linear and the other exponential, related to the stiff pores and microfractures, respectively, where the relation between stress and strain can be described by the Two-Part Hooke’s Model. With this model, the relations between porosity, transport properties, and effective stress (confining minus pore pressure) can be obtained and validated with the experimental data of four tight sandstones collected from the Shaximiao Formation of Sichuan Basin, southwest China. The agreement is good. At low effective stresses, the closure of cracks is the main mechanism affecting the transport properties, whose behavior is similar in terms of their parameters. Subsequently, experimental data of nine tight sandstones from the Yanchang Formation, collected from the Ordos Basin, west China, are employed to confirm the previous results, indicating that the fluid and electrical current follow the same path in the pore space.

A Mineralogical Model for Thermal Transport Properties of Rocks: Verification for Low-Porosity, Crystalline Rocks at Ambient Conditions

AbstractThermal conductivity (K) describes the response of matter to temporal or spatial variations in temperature (T). To quantify the effect of varying mineralogy on heat transport of rocks, an accurate (±2%) contact-free heat transfer method was applied at ambient T to multiple sections from 33 different low porosity, continental, igneous and metamorphic rocks. Thermal diffusivity (Dheat) was measured using laser-flash analysis, which was previously used to construct our large mineralogical database and which mitigates spurious radiative transfer found in other techniques. These measurements constrain K, because K is the product of Dheat with the known (or calculable) properties of density and specific heat measured at constant pressure (P). Compositions, proportions, and orientations of minerals, plus rock density, average grain-size (L), and porosity were characterized for 61 sections from 29 silicate rocks plus 5 sections from 3 marbles. Our database was used to evaluate component summation (averaging) formulae that were recently developed by considering Fourier’s laws, and to quantify the dependence of K and/or Dheat on key rock descriptors. We found that: (1) phase proportions and compositions are the main cause of variations; (2) minor porosity and foliation have minor effects; and (3) within ~5%, isotropic rocks follow Dheat = ½{[Σ(fi/Di)]−1 + Σ(fiDi)} where fi is volumetric mineral fraction, analogous to the Voigt-Reuss-Hill average for elastic moduli. Using this formula predictively depends on the accuracy of fi and Di. Quartzo-feldspathic rocks can be described by a new formula that uses only quartz fraction and plagioclase composition. Combining our mineralogical model with a universal formula for Dheat(T) and a thermodynamic identity for K(P) accurately constrains conductive thermal transport for Earth’s low porosity, crystalline rock layers.

Pore Space Topology Controls Ultrasonic Waveforms in Dry Volcanic Rocks

AbstractPore space controls the mechanical and transport properties of rocks. At the laboratory scale, seismic modeling is usually performed in relatively homogeneous settings, and the influence of the pore space on the recorded wavefields is determined by rock‐fluid interactions. Understanding this influence in dry rocks is instrumental for assessing the impact of pore topology on waves propagating in heterogeneous environments, such as volcanoes. Here, we simulated the propagation of shear waves as a function of pore space parameters in computational models built as proxies for volcanic rocks. The spectral‐element simulations provide results comparable with ultrasonic experiments, and the outcome shows that the size, shape, volume, and location of pores impact amplitudes and phases. These variations intensify in waveform coda after multiple scattering. Our results confirm that pore topology is one of the primary regulators of the propagation of elastic waves in dry rocks regardless of porosity.

Increasing Density of 3D-Printed Sandstone through Compaction

The geomechanical and transport properties of rocks are of great importance to geoscience and engineering, as these properties provide responses to external stresses and flow regimes in the subsurface. Typically, experiments conducted on cores from reservoir formations have a degree of uncertainty, due to the heterogeneous characteristics of rock samples. To combat this uncertainty, binder-jet additive manufacturing (3D printing) is an emerging technology to characterize natural porous media in a repeatable fashion. In this study, the 3D printing sandstone analogue involved sand powder and organic binder to mimic silica grains and cement in natural sandstone. The use of compaction rollers and the adjustment of printing parameters allowed one to test how the porosity and strength of 3D-printed samples can replicate the transport and geomechanical properties of natural sandstone. The densities of samples were increased by ~15% and compressive strength by ~65% with the use of the larger roller. This is a promising alternative to experimental testing to calibrate numerical models in geoscience and engineering. The significance of this approach is to allow for customizable porosity, permeability, and strength in rock samples, while preserving scarce natural rock samples.

Microscopy and image analysis of the micro-fabric and composition of saline rocks under different phaseCO2-Brine states

Using different phaseCO2-brine, the effect of stress corrosion on the micro-fabric, topology of the minerals and the elemental composition of saline rock was evaluated, to understand how this affect transport properties of rocks. Image analysis was used to evaluate changes in micro-fabric, topology of mineral and elemental composition from SEM images. The micro-fabric of all the CO2 bearing samples changed significantly according to the different phaseCO2-brine. Grain roundness, grain smoothness, and pore smoothness increased after compression while the roundness of pores reduced. There was a significant change in the weight percentage of silicon, carbon and oxygen in the CO2-bearing samples compared to the brine sample. Change in the shape, solidity and roundness of the pores led to a change in permeability of rocks by altering the tortuosity of the pores. This study provides an understanding of changes in micro-fabric and elemental changes occurring in saline CO2 storage sites under different possible phaseCO2-brine and highlights their implication for storage and properties of the rock.

Estimating Fluid Saturations from Capillary Pressure and Relative Permeability Simulations Using Digital Rock

Direct numerical simulations of fluid flow on three-dimensional pore-scale microstructures derived from images promise more, cheaper, and faster, special core analysis for estimating volumetric and transport properties of rocks. However, the micron-scale X-ray computer tomography images generated by the present imaging technology are limited in resolution, and thus, a significant portion of rock pore volume can remain unresolved. The missing pore volume is not accessible to direct numerical simulations which limits applicability of digital rock physics to infer true residual saturation of reservoir fluids. To derive meaningful results from direct simulations, at minimum, raw fluid saturation inferred from simulations on micron-scale images must be corrected for the missing pore volume. We use concepts of capillary physics in rocks to quantify the impact of image resolution on image-derived fluid saturation and develop novel transforms that compensate for this effect on estimates of fluid saturation from multiphase simulations without the need for higher-resolution imaging. We find that image resolution constraints provide quality indicators when comparing digital rock-derived fluid saturations (e.g., connate water saturation) with those measured in a laboratory.

Enhanced Oil Recovery in the Wolfcamp Shale by Carbon Dioxide or Nitrogen Injection: An Experimental Investigation

SummaryWe present a comprehensive investigation of gas injection for enhanced oil recovery (EOR) in organic-rich shale using 11 coreflooding experiments in sidewall core plugs from the Wolfcamp Shale, and three additional coreflooding experiments using Berea Sandstone. Our work studies the effect of pressure, minimum miscibility pressure (MMP), soak time, injection-gas composition, and rock-transport properties on oil-recovery factor. The injection gases were carbon dioxide (CO2) and nitrogen. The core plugs were resaturated with crude oil in the laboratory, and the experiments were performed at reservoir pressure and temperature using a design that closely replicates gas injection through a hydraulic fracture, minimizes convective flow, and exaggerates the fracture to the reservoir-rock ratio. We accomplished this by surrounding the Wolfcamp reservoir-rock matrix with glass beads. Computed-tomography (CT) scanning enabled the visualization of the compositional changes with time and space during the gas-injection experiments and gas chromatography provided the overall change in composition between the crude oil injected and the oil recovered.As gas surrounds the oil-saturated sample, a peripheral, slow-kinetics vaporization/condensation process is the main production mechanism. Gas flows preferentially through the proppant because of its high permeability, avoiding the formation and displacement of a miscible front along the rock matrix to mobilize the oil. Instead, the gas surrounding the reservoir-core sample vaporizes the light and intermediate components from the crude oil, making recovery a function of the fraction of oil that can be vaporized into the volume of gas in the fracture at the prevailing thermodynamic conditions. The mass transfer between the injected gas and the crude oil is sufficiently fast to result in significant oil production during the first 24 hours, but slow enough to cause the formation of a compositional gradient within the matrix that exists even 6 days after injection has started. The peripheral and the slow-kinetics aspects of the recovery mechanism are a consequence of the low fluid-transport capacity associated with the organic-rich shale that is saturated with liquid hydrocarbons.Our results show CO2 overperforms nitrogen as an EOR injection gas in organic-rich shale, and higher injection pressure leads to higher oil recovery, even beyond the MMP. The gas-injection scheme should allow enough time for the mass transfer to occur between the injected gas and the crude oil; we achieved this in the laboratory with a huff ’n’ puff scheme. Our results advance the understanding of gas injection for EOR in organic-rich shale in a laboratory scale, but additional work is required to rigorously scale up these observations to better design field applications.

Computational topology-based characterization of pore space changes due to chemical dissolution of rocks

In this paper, we present an algorithm for the numerical simulation of reactive transport at the pore scale to facilitate observation of pore space and rock matrix evolution. Moreover, simulation at the pore scale opens up the possibility of estimating changes in the transport properties of rocks, such as permeability and tortuosity. To quantitatively analyze pore space evolution, we developed a numerical algorithm that can be used to construct persistence diagrams of the connectivity components for pore space and the rock matrix, which characterize the topology evolution during rock matrix dissolution. Introducing the “bottle-neck” metric in the space of the persistence diagrams, we cluster the numerical experiments in terms of similarities in topology evolution. We demonstrate that the application of this metric to the persistence diagrams allowed us to distinguish topologically different dissolution scenarios, for instance, the formation of a dissolution front near the inlet, homogeneous dissolution of the matrix inside the core sample, and formation of wormholes. We illustrate that the differences in topology evolution lead to cross-correlations among the transport properties of rocks (porosity-permeability-tortuosity).

3D printing of rock analogues in sand: a tool for design and repeatable testing of geomechanical and transport properties

Natural rocks can be heterogeneous due to complex diagenetic processes that affect mineralogy and pore architecture. Correlation of geomechanical and transport properties of rocks in three dimensions can lead to large variances in data when tested experimentally. 3D-printing of rock analogues in sand is a promising alternative for experimental testing that can be used to calibrate variables during geotechnical testing. While 3D-printed sand is a homogeneous material, the parameters for creating grain packing and pore infill can be tuned to mimic specific geomechanical and transport properties. Initially, 3D-printed specimens have a low density due to a loose distribution of grains. Herein, we present our efforts at increasing the density through incorporating a roller in the printing process to compact individual layers. We also propose introduction of a more heterogeneous sand mixture that encompasses a wide range of grain-size distributions. Lastly, a discussion between binder saturation (that infills the pore space) of 3D-printed specimens and the axial strength, dimensional control, and porosity is described within. 3D printing of rock analogues is critical in pursuing rigorous destructive tests required for geotechnical and geological engineering because it can provide repeatable, controlled data on rock properties.

Evolution of pore-shape and its impact on pore conductivity during CO2 injection in calcite: Single pore simulations and microfluidic experiments

Injection of CO2 into carbonate rocks causes dissolution and alters rock transport properties. The extent of the permeability increases, due to the increased pore volume and connectivity, strongly depends on the regimes of transport and dissolution reactions. Identification of these regimes and their parametrization at the microscopic scale is required for an understanding of the injection processes, and, afterward, for calculating the effective macroscopic parameters for field-scale simulations. Currently, a commonly used approach for calculating the rock effective parameters is the Pore Network Method, PNM, but a better understanding of the validity of its basic assumptions and their areas of applicability is essential. Here, we performed a combined microscopic experimental and numerical study to explore pore-shape evolution over a wide range of transport and dissolution reaction regimes. Experiments were conducted by flowing an acidic solution through a microscopic capillary channel in a calcite crystal at two different flow rates. The experimental results were used to validate our pore-scale reactive transport model that could reproduce the measured effluent composition as well as pore shape changes. Two key stages in pore shape evolution were observed, a transient phase and a quasi-steady-state phase. During the first stage, the shape of the single pore evolved very fast, depending on the flow regime. Under advective-dominant flow, the pore shape remained nearly cylindrical, while under diffusive-dominant transport, the pore shape developed into a half-hyperboloid shape. During the quasi-steady-state stage, the pore volume continued to increase, however, without or with diminutive change of the pore shape. In this stage, only a long period of injection may result in a significant deviation of the pore shape from its original cylinder shape, which is a common assumption in PNMs. Furthermore, we quantitatively evaluated the impact of evolved pore shape spectrum on the conductance calculations and compared it to the formulations currently used for pore network modeling of reactive transport. Under low flow rates, neglecting the developed non-uniform pore shape during the non-steady stage may lead to an overestimation of pore conductance up to 80%.

Pore-scale heterogeneity, flow channeling and permeability: Network simulation and comparison to experimental data

The flow and transport properties of rocks depend on the statically geometry and topology of the pore space, which can be viewed as a complex network, as well as the characteristics of dynamic fluid flow pathways. The pore-scale heterogeneity (i.e., pore connectivity and pore-size distribution) generates the flow channeling, which can be quantified by the critical radius rc, hydraulic tortuosity τ, and the ratio of effective and non-effective porosity. The rc is defined as the lowest radius in the pathway of flow channeling. The tortuosity τ of the flow channeling can be determined by the Dijkstra algorithm. The “universality” of rc, τ, and the factor σr/z of pore-scale heterogeneity were verified based on network simulations. Since both of the homogeneous and heterogeneous rocks can be reduced as the equivalent channel model (ECM), the new permeability model can be proposed based on the definition of rc. The proposed permeability model is satisfactorily testified against network simulation results, and the published experimental datasets of the different rocks in the literature, including natural and tight sandstone.

Variations in Elastic and Electrical Properties of Crustal Rocks With Varying Degree of Microfracturation

AbstractThis work aims at investigating the effect of varying degrees of microfracturing on the joint elastic and electrical transport properties of rocks. Different crustal rocks were subjected to thermal treatment, expected to induce microfracturing, up to different target temperatures from 100 up to 900 °C. The rocks bulk and pore volumes, P and S wave velocities, and frequency‐dependent electrical impedance were measured before and after the treatment. As the temperature of treatment increased, P and S wave velocities and the electrical formation factor drop and pore and bulk volumes increase. As indicated by the microscopic images, this is consistent with the creation of microcracks. These created microcracks do not affect the properties in the exact same manner, and a strong effect of the initial porosity is observed for electrical formation factor. Extrapolating to low‐frequency field‐scale measurements in water‐saturated reservoir rocks highlights an interesting observation: Both seismic and electrical properties at the field scale might highlight similar variations with increasing damage in all rocks. The maximum amount of decrease expected for all rocks is about 1 order of magnitude in electrical formation factor and 40% decrease in P and S wave velocities. Finally, temperature proved to affect very differently the rocks of varying porosity and mineral content, in ways not fully covered by existing works. Porosity, by increasing the matrix compressibility, damps the degree of microfracturing and crack opening. The distinct behavior in calcite‐pure marble evidences a dominance of anisotropic of thermal expansion over isotropic expansion mismatch.

Joint inversion of nuclear magnetic resonance data from partially saturated rocks using a triangular pore model

Measurement of nuclear magnetic resonance (NMR) relaxation is a well-established laboratory/borehole method to characterize the storage and transport properties of rocks due to its direct sensitivity to the corresponding pore-fluid content (water/oil) and pore sizes. Using NMR, the correct estimation of, e.g., permeability strongly depends on the underlying pore model. Usually, one assumes spherical or cylindrical pores for interpreting NMR relaxation data. To obtain surface relaxivity and thus, the pore-size distribution, a calibration procedure by, e.g., mercury intrusion porosimetry or gas adsorption has to be used. Recently, a joint inversion approach was introduced that used NMR measurements at different capillary pressures/saturations (CPS) to derive surface relaxivity and pore-size distribution (PSD) simultaneously. We further extend this approach from a bundle of parallel cylindrical capillaries to capillaries with triangular cross sections. With this approach, it is possible to account for residual or trapped water within the pore corners/crevices of partially saturated pores. In addition, we have developed a method that allows determining the shape of these triangular capillaries by using NMR measurements at different levels of drainage and imbibition. We show the applicability of our approach on synthetic and measured data sets and determine how the combination of NMR and CPS significantly improves the interpretation of NMR relaxation data on fully and partially saturated porous media.

Permeability of Granite Including Macro-Fracture Naturally Filled with Fine-Grained Minerals

Information on the permeability of rock is essential for various geoengineering projects, such as geological disposal of radioactive wastes, hydrocarbon extraction, and natural hazard risk mitigation. It is especially important to investigate how fractures and pores influence the physical and transport properties of rock. Infiltration of groundwater through the damage zone fills fractures in granite with fine-grained minerals. However, the permeability of rock possessing a fracture naturally filled with fine-grained mineral grains has yet to be investigated. In this study, the permeabilities of granite samples, including a macro-fracture filled with clay and a mineral vein, are investigated. The permeability of granite with a fine-grained mineral vein agrees well with that of the intact sample, whereas the permeability of granite possessing a macro-fracture filled with clay is lower than that of the macro-fractured sample. The decrease in the permeability is due to the filling of fine-grained minerals and clay in the macro-fracture. It is concluded that the permeability of granite increases due to the existence of the fractures, but decreases upon filling them with fine-grained minerals.

Pressure‐Dependent Elastic and Transport Properties of Porous and Permeable Rocks: Microstructural Control

AbstractAlthough several studies aimed at linking electrical and hydraulic transport properties in rocks, the existing models remain at most incomplete. Based on this observation, in addition to the transport properties, this contribution investigates the pressure dependence of P wave velocities and porosity for three porous rocks. Apart from hydraulic conductivity, all physical properties show an important dependence to the confining pressure. In particular, electrical resistivity reaches an asymptote at low confining pressures. Using the measured P wave velocities and effective medium theories, the microcrack density (ρ) and its evolution with confining pressure are estimated. For the three rocks, the microcrack density at which electrical resistivity reaches a plateau is of ρ ~0.13. This value corresponds to the threshold for crack percolation in media containing microcracks exclusively. This suggests that in porous and microcracked rocks, electrical resistivity is controlled by two independent hydraulic pathways of tubes and cracks acting in parallel. In contrast, this percolation threshold is not observed in the permeability data. A simple conceptual model is finally introduced that explains the fundamental differences between transport properties.

Pore Space Connectivity and the Transport Properties of Rocks

Pore connectivity is likely one of the most important factors affecting the permeability of reservoir rocks. Furthermore, connectivity effects are not restricted to materials approaching a percolation transition but can continuously and gradually occur in rocks undergoing geological processes such as mechanical and chemical diagenesis. In this study, we compiled sets of published measurements of porosity, permeability and formation factor, performed in samples of unconsolidated granular aggregates, in which connectivity does not change, and in two other materials, sintered glass beads and Fontainebleau sandstone, in which connectivity does change. We compared these data to the predictions of a Kozeny-Carman model of permeability, which does not account for variations in connectivity, and to those of Bernabe et al . (2010, 2011) model, which does [Bernabe Y., Li M., Maineult A. (2010) Permeability and pore connectivity: a new model based on network simulations, J. Geophys. Res. 115 , B10203; Bernabe Y., Zamora M., Li M., Maineult A., Tang Y.B. (2011) Pore connectivity, permeability and electrical formation factor: a new model and comparison to experimental data, J. Geophys. Res. 116 , B11204]. Both models agreed equally well with experimental data obtained in unconsolidated granular media. But, in the other materials, especially in the low porosity samples that had undergone the greatest amount of sintering or diagenesis, only Bernabe et al. model matched the experimental data satisfactorily. In comparison, predictions of the Kozeny-Carman model differed by orders of magnitude. The advantage of the Bernabe et al. model was its ability to account for a continuous, gradual reduction in pore connectivity during sintering or diagenesis. Although we can only speculate at this juncture about the mechanisms responsible for the connectivity reduction, we propose two possible mechanisms, likely to be active at different stages of sintering and diagenesis, and thus allowing the gradual evolution observed experimentally.

Micro-crack enhanced permeability in tight rocks: An experimental and microstructural study

The elastic and hydraulic response of a rock and its stress sensitivity are strongly affected by the presence of micro-cracks. Therefore, a full characterization and quantification of cracks at the micro-scale is essential for understanding the physical and transport properties of rocks under stress. As yet, there is no uniquely accepted method to precisely quantify the density and geometrical characteristics of such microstructural features. In this contribution, we present results of quantitative analyses of 2D scanning electron microscopy (SEM) images and 3D X-ray microtomograms acquired on three samples of Carrara Marble artificially cracked by thermal shock. New semi-automatic workflows have been developed to perform these 2D and 3D analyses. The main outcome is the quantification of average length, aspect ratio, and density per unit surface (2D) or volume (3D) of micro-cracks observed. The thermal treatment only opens grain boundaries and does not result in the creation of new intragranular cracks. The results are consistent with the degree of thermal cracking artificially induced on the rock sample prior to the imaging/analysis procedure, i.e., more and wider micro-cracks are measured on samples heated to higher temperatures. The results of these quantitative microstructural analyses are also consistent with nuclear magnetic resonance (NMR) data independently acquired on the same samples saturated with water.

Matrix diffusion and sorption of Cs+, Na+, I– and HTO in granodiorite: Laboratory-scale results and their extrapolation to the in situ condition

Matrix diffusion and sorption are important processes controlling radionuclide transport in crystalline rocks. Such processes are typically studied in the laboratory using borehole core samples however there is still much uncertainty on the changes to rock transport properties during coring and decompression. It is therefore important to show how such laboratory-based results compare with in situ conditions. This paper focuses on laboratory-scale mechanistic understanding and how this can be extrapolated to in situ conditions as part of the Long Term Diffusion (LTD) project at the Grimsel Test Site, Switzerland. Diffusion and sorption of 137Cs+, 22Na+, 125I– and tritiated water (HTO) in Grimsel granodiorite were studied using through-diffusion and batch sorption experiments. Effective diffusivities (De) of these tracers showed typical cation excess and anion exclusion effects and their salinity dependence, although the extent of these effects varied due to the heterogeneous pore networks in the crystalline rock samples. Rock capacity factors (α) and distribution coefficients (Kd) for Cs+ and Na+ were found to be sensitive to porewater salinity. Through-diffusion experiments indicated dual depth profiles for Cs+ and Na+ which could be explained by a near-surface Kd increment. A microscopic analysis indicated that this is caused by high porosity and sorption capacities in disturbed biotite minerals on the surface of the samples. The Kd values derived from the dual profiles are likely to correspond to Kd dependence on the grain sizes of crushed samples in the batch sorption experiments. The results of the in situ LTD experiments were interpreted reasonably well by using transport parameters derived from laboratory data and extrapolating them to in situ conditions. These comparative experimental and modelling studies provided a way to extrapolate from laboratory scale to in situ condition. It is well known that the difference in porosity between laboratory and in situ conditions is a key factor to scale laboratory-derived De to in situ conditions. We also show that cation excess diffusion is likely to be a key mechanism in crystalline rocks and that high Kd in the disturbed surfaces is critically important to evaluate transport in both laboratory and in situ tests.

Nonlinear diffusion-based interpretation of induced microseismicity: A Barnett Shale hydraulic fracturing case study

For the successful development and operation of hydrocarbon or geothermal reservoirs, knowledge of the hydraulic transport is of crucial importance. Because fundamental physical processes of borehole fluid injections are still insufficiently understood, gathering information about transport properties of rocks under field conditions is quite difficult. However, a substantial contribution in determining the permeability evolution can be obtained by understanding the distribution of induced seismicity in space and time. We have analyzed spatio-temporal characteristics of seismicity recorded during a hydraulic fracturing treatment in the Barnett Shale. In this study, we show that the fluid-rock interaction is nonlinear. To explain corresponding spatio-temporal features of induced seismicity, we considered pore pressure diffusion based on a power-law pressure dependence of permeability. A scaling approach was used to transform clouds of hypocenters of events obtained in a hydraulically anisotropic nonlinear medium into a cloud which would be obtained in an equivalent isotropic but still nonlinear medium. For this, we used a concept of a factorized anisotropic pressure dependence of permeability and found that it is in agreement with the microseismic data under consideration. We used a numerical modeling approach to generate synthetic seismicity by solving nonlinear diffusion equations. The pore-pressure field obtained from flow rates was calibrated with the pore-pressure field computed for injection pressures. This yielded an estimate of the uniaxial storage coefficient and permitted us to compute the permeability evolution inside the fracture stimulated reservoir. Following our modeling, we generated synthetic seismicity whose spatio-temporal features are similar to the ones observed in the case study. This indicates that a nonlinear diffusion with a pressure-dependent permeability seems to provide a reasonable model of the hydraulic-fracture stimulation under consideration. A power-law pressure dependence of stimulated permeability may be a more general characteristic for shales.