Showing papers on "Permeability (earth sciences) published in 2012"

Gas flow in ultra-tight shale strata

Abstract: 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.

Knudsen’s Permeability Correction for Tight Porous Media

Abstract: Various flow regimes including Knudsen, transition, slip and viscous flows (Darcy’s law), as applied to flow of natural gas through porous conventional rocks, tight formations and shale systems, are investigated. Data from the Mesaverde formation in the United States are used to demonstrate that the permeability correction factors range generally between 1 and 10. However, there are instances where the corrections can be between 10 and 100 for gas flow with high Knudsen number in the transition flow regime, and especially in the Knudsen’s flow regime. The results are of practical interest as gas permeability in porous media can be more complex than that of liquid. The gas permeability is influenced by slippage of gas, which is a pressure-dependent parameter, commonly referred to as Klinkenberg’s effect. This phenomenon plays a substantial role in gas flow through porous media, especially in unconventional reservoirs with low permeability, such as tight sands, coal seams, and shale formations. A higher-order permeability correlation for gas flow called Knudsen’s permeability is studied. As opposed to Klinkenberg’s correlation, which is a first-order equation, Knudsen’s correlation is a second-order approximation. Even higher-order equations can be derived based on the concept used in developing this model. A plot of permeability correction factor versus Knudsen number gives a typecurve. This typecurve can be used to generalize the permeability correction in tight porous media. We conclude that Knudsen’s permeability correlation is more accurate than Klinkenberg’s model especially for extremely tight porous media with transition and free molecular flow regimes. The results from this study indicate that Klinkenberg’s model and various extensions developed throughout the past years underestimate the permeability correction especially for the case of fluid flow with the high Knudsen number.

Changes in permeability caused by transient stresses: Field observations, experiments, and mechanisms

Abstract: CHANGES IN PERMEABILITY CAUSED BY TRANSIENT STRESSES: FIELD OBSERVATIONS, EXPERIMENTS, AND MECHANISMS Michael Manga, 1 Igor Beresnev, 2 Emily E. Brodsky, 3 Jean E. Elkhoury, 4 Derek Elsworth, 5 S. E. Ingebritsen, 6 David C. Mays, 7 and Chi-Yuen Wang 1 Received 7 November 2011; revised 15 February 2012; accepted 10 March 2012; published 12 May 2012. [ 1 ] Oscillations in stress, such as those created by earth- quakes, can increase permeability and fluid mobility in geo- logic media. In natural systems, strain amplitudes as small as 10 A6 can increase discharge in streams and springs, change the water level in wells, and enhance production from petroleum reservoirs. Enhanced permeability typically recovers to prestimulated values over a period of months to years. Mechanisms that can change permeability at such small stresses include unblocking pores, either by breaking up permeability-limiting colloidal deposits or by mobilizing droplets and bubbles trapped in pores by capillary forces. The recovery time over which permeability returns to the prestimulated value is governed by the time to reblock pores, or for geochemical processes to seal pores. Monitor- ing permeability in geothermal systems where there is abun- dant seismicity, and the response of flow to local and regional earthquakes, would help test some of the proposed mechanisms and identify controls on permeability and its evolution. Citation: Manga, M., I. Beresnev, E. E. Brodsky, J. E. Elkhoury, D. Elsworth, S. E. Ingebritsen, D. C. Mays, and C.-Y. Wang (2012), Changes in permeability caused by transient stresses: Field observations, experiments, and mechanisms, Rev. Geophys., 50, RG2004, doi:10.1029/2011RG000382. INTRODUCTION [ 2 ] The permeability of Earth’s crust is of great interest because it largely governs key geologic processes such as advective transport of heat and solutes and the generation of elevated fluid pressures by processes such as physical com- paction, heating, and mineral dehydration. For an isotropic Department of Earth and Planetary Science, University of California, Berkeley, California, USA. Department of Geological and Atmospheric Sciences, Iowa State University, Ames, Iowa, USA. Department of Earth and Planetary Sciences, University of California, Santa Cruz, California, USA. Department of Civil and Environmental Engineering, University of California, Irvine, California, USA. Department of Energy and Mineral Engineering, Center for Geomechanics, Geofluids, and Geohazards, EMS Energy Institute, Pennsylvania State University, University Park, Pennsylvania, USA. U.S. Geological Survey, Menlo Park, California, USA. Department of Civil Engineering, University of Colorado Denver, Denver, Colorado, USA. Corresponding author: M. Manga, Department of Earth and Planetary Science, University of California, 307 McCone Hall, Berkeley, CA 94720, USA. (manga@seismo.berkeley.edu) material, permeability k is defined by Darcy’s law that relates the fluid discharge per unit area q to the gradient of hydraulic head h, q ¼A kgr rh; m where r is the fluid density, m the fluid viscosity and g is gravity. The permeability of common geologic media varies by approximately 16 orders of magnitude, from values as low as 10 A23 m 2 in intact crystalline rock, intact shales, and fault cores, to values as high as 10 A7 m 2 in well-sorted gravels. Nevertheless, despite being highly heterogeneous, perme- ability can be characterized at the crustal scale in a manner that provides useful insight [e.g., Gleeson et al., 2011]. [ 3 ] The responses of hydrologic systems to deformation provide some insight into controls on permeability, in par- ticular its evolution in time. For example, the water level in wells and discharge in rivers have both been observed to change after earthquakes. Because earthquakes produce stresses that can change hydrogeologic properties of the crust, hydrologic responses to earthquakes are expected, especially in the near field (within a fault length of the Copyright 2012 by the American Geophysical Union. Reviews of Geophysics, 50, RG2004 / 2012 1 of 24 Paper number 2011RG000382 8755-1209/12/2011RG000382 RG2004

Predicting the saturated hydraulic conductivity of soils: a review

Abstract: This paper examines and assesses predictive methods for the saturated hydraulic conductivity of soils. The soil definition is that of engineering. It is not that of soil science and agriculture, which corresponds to “top soil” in engineering. Most predictive methods were calibrated using laboratory permeability tests performed on either disturbed or intact specimens for which the test conditions were either measured or supposed to be known. The quality of predictive equations depends highly on the test quality. Without examining all the quality issues, the paper explains the 14 most important mistakes for tests in rigid-wall or flexible-wall permeameters. Then, it briefly presents 45 predictive methods, and in detail, those with some potential, such as the Kozeny-Carman equation. Afterwards, the data of hundreds of excellent quality tests, with none of the 14 mistakes, are used to assess the predictive methods with a potential. The relative performance of those methods is evaluated and presented in graphs. Three methods are found to work fairly well for non-plastic soils, two for plastic soils without fissures, and one for compacted plastic soils used for liners and covers. The paper discusses the effects of temperature and intrinsic anisotropy within the specimen, but not larger scale anisotropy within aquifers and aquitards.

Changes in permeability caused by transient stresses: field observations, experiments, and

Abstract: Oscillations in stress, such as those created by earthquakes, can increase permeability and fluid mobility in geologic media. In natural systems, strain amplitudes as small as 10 -6 can increase discharge in streams and springs, change the water level in wells, and enhance production from petroleum reservoirs. Enhanced permeability typically recovers to pre-stimulated values over a period of months to years. Mechanisms that can change permeability at such small stresses include unblocking pores, either by breaking up permeability-limiting colloidal deposits or by mobilizing droplets and bubbles trapped in pores by capillary forces. The recovery time over which permeability returns to the pre-stimulated value is governed by the time to re-block pores, or for geochemical processes to seal pores. Monitoring permeability in geothermal systems where there is abundant seismicity, and the response of flow to local and regional earthquakes, would help test some of the proposed mechanisms and identify controls on permeability and its evolution.

Innovative methods for flow-unit and pore-structure analyses in a tight siltstone and shale gas reservoir

Abstract: Tight gas reservoirs are notoriously difficult to characterize; routine methods developed for conventional reservoirs are not appropriate for tight gas reservoirs. In this article, we investigate the use of nonroutine methods to characterize permeability heterogeneity and pore structure of a tight gas reservoir for use in flow-unit identification. Profile permeability is used to characterize fine-scale (1 in. [2.5 cm]) vertical heterogeneity in a tight gas core; more than 500 measurements were made. Profile permeability, although useful for characterizing heterogeneity, will not provide in-situ estimates of permeability; furthermore, the scale of measurement is much smaller than log scale. Pulse-decay permeability measurements collected on core plugs under confining pressure were used to correct the profile permeability measurements to in-situ stress conditions, and 13-point averages of profile permeability were used to relate to log-derived porosity measurements. Finally, N2 adsorption, a new method for tight gas was used to estimate the pore-size distribution of several tight gas samples. A unimodal or bimodal distribution was observed for the samples, with the larger peak corresponding to the dominant pore-throat size, as confirmed by independent methods. Furthermore, the adsorption-desorption hysteresis loop shape was used to interpret the dominant pore shape as slot-shaped pores, which is typical of many tight gas reservoirs. The N2 adsorption method provides rapid analysis and does not suffer from some of the same limitations of Hg injection. In the future, we hope that the N2 adsorption method may prove useful for flow-unit characterization (based on dominant pore size) of fine-grained (siltstone-shale) tight gas reservoirs.

A Fully-Coupled Free and Adsorptive Phase Transport Model for Shale Gas Reservoirs Including Non-Darcy Flow Effects

Abstract: Accurate modeling of gas through shale-gas reservoirs characterized by nano-meter pores where the effects of various non-Darcy flow regimes and the adsorbed-layer are important is presented and demonstrated by several examples. Quantification of gas transport may be accomplished using the transport equation that is valid for all flow regimes. This equation though needs further modification when transport is through a media where the gas is adsorbed onto the pore wall. In the presence of adsorption, there is a pore pressure dependent loss of porosity and cross-sectional area to free gas transport. The apparent gas permeability correction is accomplished for various flow regimes using the Knudsen number by consideration of the reduction of the cross-sectional area to free gas transport in the presence of adsorption. We show that transport in the adsorbed layer may contribute significantly in the total gas transport in these nanopores. An effective transport model is presented to account for the impact of adsorption through two mechanisms. First, we modify the transport equation to account for the pore-pressure dependent-reduction in the volume available to free gas transport; second, we model transport through the adsorbed layer using Fick’s law of diffusion. The coupled model is then compared to conventional transport models over a wide range of reservoir properties and conditions.

Numerical Simulation of 3D Hydraulic Fracturing Based on an Improved Flow-Stress-Damage Model and a Parallel FEM Technique

Abstract: The failure mechanism of hydraulic fractures in heterogeneous geological materials is an important topic in mining and petroleum engineering. A three-dimensional (3D) finite element model that considers the coupled effects of seepage, damage, and the stress field is introduced. This model is based on a previously developed two-dimensional (2D) version of the model (RFPA2D-Rock Failure Process Analysis). The RFPA3D-Parallel model is developed using a parallel finite element method with a message-passing interface library. The constitutive law of this model considers strength and stiffness degradation, stress-dependent permeability for the pre-peak stage, and deformation-dependent permeability for the post-peak stage. Using this model, 3D modelling of progressive failure and associated fluid flow in rock are conducted and used to investigate the hydro-mechanical response of rock samples at laboratory scale. The responses investigated are the axial stress–axial strain together with permeability evolution and fracture patterns at various stages of loading. Then, the hydraulic fracturing process inside a rock specimen is numerically simulated. Three coupled processes are considered: (1) mechanical deformation of the solid medium induced by the fluid pressure acting on the fracture surfaces and the rock skeleton, (2) fluid flow within the fracture, and (3) propagation of the fracture. The numerically simulated results show that the fractures from a vertical wellbore propagate in the maximum principal stress direction without branching, turning, and twisting in the case of a large difference in the magnitude of the far-field stresses. Otherwise, the fracture initiates in a non-preferred direction and plane then turns and twists during propagation to become aligned with the preferred direction and plane. This pattern of fracturing is common when the rock formation contains multiple layers with different material properties. In addition, local heterogeneity of the rock matrix and macro-scale stress fluctuations due to the variability of material properties can cause the branching, turning, and twisting of fractures.

A New Analytical Method for Analyzing Linear Flow in Tight/Shale Gas Reservoirs: Constant-Flowing-Pressure Boundary Condition

Abstract: Many tight/shale gas wells exhibit linear flow, which can last for several years. Linear flow can be analyzed using a square-root-oftime plot, a plot of rate-normalized pressure vs. the square root of time. Linear flow appears as a straight line on this plot, and the slope of this line can be used to calculate the product of fracture half-length and the square root of permeability. In this paper, linear flow from a fractured well in a tight/shale gas reservoir under a constant-flowing-pressure constraint is studied. It is shown that the slope of the square-root-of-time plot results in an overestimation of fracture half-length, if permeability is known. The degree of this overestimation is influenced by initial pressure, flowing pressure, and formation compressibility. An analytical method is presented to correct the slope of the squareroot-of-time plot to improve the overestimation of fracture halflength. The method is validated using a number of numerically simulated cases. As expected, the square-root-of-time plots for these simulated cases appear as a straight line during linear flow for constant flowing pressure. It is found that the newly developed analytical method results in a more reliable estimate of fracture half-length, if permeability is known. Our approach, which is fully analytical, results in an improvement in linear-flow analysis over previously presented methods. Finally, the application of this method to multifractured horizontal wells is discussed and the method is applied to three field examples.

Unconventional Reservoirs: Basic Petrophysical Concepts for Shale Gas

Abstract: Unconventional reservoirs have burst with considerable force in oil and gas production worldwide. Shale Gas is one of them, with intense activity taking place in regions like North America. To achieve commercial production, these reservoirs should be stimulated through massive hydraulic fracturing and, frequently, through horizontal wells as a mean to enhance productivity. In sedimentary terms, shales are fine-grained clastics rocks formed by consolidation of silts and clays. In log interpretation of conventional reservoirs, it is very common to observe that the clay parameters used to correct porosity and resistivity logs for clay effects are in fact read in shaly intervals rather than in pure clay. Although no considerable deviation have been observed in shaly sandstones, anyway these concepts and procedures must be reviewed to run log analysis in shale gas. Organic matter deposited with shales containing kerogen that matured as a result of overburden pressure and temperature, giving rise to source rocks that have yielded and expulsed hydrocarbons. Shale gas reservoir type is a source rock that has retained a portion of the hydrocarbon yielded during its geological history so that to evaluate the current hydrocarbon storage and production potential it is necessary to know the kerogen type and the level of TOC - total organic carbon - in the rock. Produced gas comes from both adsorbed gas in the organic matter and "free" gas trapped in the pores of the organic matter and in the inorganic portions of the matrix, i.e. quartz, calcite, dolomite. In these unconventional reservoirs, gas volumes are estimated through a combination of geochemical analysis and log interpretation techniques. TOC, desorbed total gas content, adsorption isotherms, and kerogen maturity among other things can be measured in cores, sidewall samples and cuttings, in the laboratory. These data are used to estimate total desorbed gas content and adsorbed gas content which is part of the total gas. Also in laboratory, porosity, grain density, water saturation, permeability, mineral composition and elastic modules of the rock are measured. Laboratory measurement uncertainty is high and consistency between different providers appears to be low, with serious suspicions that procedures followed by different laboratories are the source of such differences. The permeability is one of the most important parameters, but at the same time, one of the most difficult to measure reliably in a shale gas. Core calibrated porosity, mineral composition, water saturation and elastic modules can be obtained through electric and radioactive logs. All these information is used to estimate log derived total gas volume which results are also subject to a high degree of uncertainty that must be overcome. Once this key information is obtained, it is possible to estimate different gas in-situ volumes. Indeed, an estimate of porosity-resistivity based total gas in-situ and, on the other hand, geochemical based adsorbed gas in-situ can be performed. Log total gas in-situ can be, and it is advisable to do, compared with adsorbed gas estimations and also with another gas measurement called direct method - total gas desorption performed on formation samples. The difference between log total gas in-situ and adsorbed gas in situ should be the "free" gas in situ. Free gas occupies the pores of kerogen and matrix; also it can be stored in open natural fractures if such fractures are present. The main objective of this paper is to discuss the state-of-the-art in petrophysical evaluation of shale gas reservoirs, to summarize the experiences of operators and researchers, and to bring some views on the criteria and techniques for the evaluation of cores and logs. An inventory of laboratory tests and results, log responses in the presence of kerogen, log interpretation techniques and estimation methods for different volumes of gas in-situ, together with important aspects of the use of analogy in shale gas reservoirs has been done. At the end, a basic petrophysical workflow is outlined for the volumetric determination of gas in situ.

Modelling Water Flow in Unsaturated Porous Media: Accounting for Nonlinear Permeability and Material Heterogeneity

Abstract: Introduction.- Mathematical Models of Flow in Porous Media.- Numerical Solution of Flow Equations.- Computation of Inter-Nodal Permeabilities for Richards Equation.- Upscaling from Darcy Scale to Field Scale.- Flow in Binary Media with Heterogenous Hydraulic Diffusivity.- Flow in Binary Media with Heterogenous Air-Entry Pressure.