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Summary This paper presents a theoretically rigorous correlation of the performance of capillary pressure and relative permeability of naturally fractured sandstone and carbonate reservoirs involving saturation shocks and loading/unloading hysteresis under various stress and thermal conditions. The proposed modeling approach accounts for the combined effects of the porousโrock alteration by various processes, including deformation, transformation, deterioration, and collapse of pore structure, under prevailing temperature and stress conditions during loading and unloading processes, and their effect on the capillary pressure and relative permeability of naturally fractured reservoirs. A saturation shock causing a slope discontinuity in the capillary pressure and relative permeability is shown to occur during saturation change in some sandstoneโ and carbonateโreservoir formations at a critical saturation condition. This phenomenon can be triggered by alteration of fluidโpercolation pathways as a result of the transition from open to closed natural or induced fractures and the deformation of pore structure. The effect of the saturation shock and loading/unloading hysteresis on the capillary pressure and relative permeability of reservoirโrock formations is formulated by means of a phenomenological kinetics model and its applicability is demonstrated by analyzing and correlating the available experimental data. In this paper, the proven comprehensive model developed from a kinetics equation is shown to lead to a theoretically meaningful, universal, and practical constitutive equation in the form of a modified power law. This kinetics equation expresses the probability of dependence of a petrophysical property of porous rocks on a variable, such as saturation for capillary pressure and relative permeability, based on the value of the property relative to its lowโ and highโend limit values. The applicability of the modified powerโlaw equation is validated by means of the experimental data of the capillary pressure and relative permeability gathered by testing of representative samples from various sandstone and carbonate reservoirs. The phenomenological parameters of the core samples obtained from sandstone and carbonate reservoirs are determined for best match of the experimental data with the modified powerโlaw equation. The value of the critical fluid saturation is determined by the observance of a slope discontinuity occurring in the measured experimental data of the variation of the capillary pressure and relative permeability with saturation. The scenarios presented in this study indicate that loading/unloading hysteresis and saturation shock have significant effects on the stressโ and temperatureโdependent capillary pressure and relative permeability of the porous reservoirโrock formations. The dataโinferred physicsโbased model presented in this paper is proved to describe the stressโ and temperatureโdependent capillary pressure and relative permeability of sandstone and carbonate rocks with high accuracy while meeting the endpointโlimit conditions satisfactorily.
- North America > United States (1.00)
- Europe > Norway > Norwegian Sea (0.24)
- Asia > Kazakhstan > Aktobe Oblast > Precaspian Basin > Enbeksk-Zharamysskaya Uplift Zone > Kenkiyak Field (0.99)
- Asia > China > Shanxi > Ordos Basin (0.99)
- Asia > China > Shaanxi > Ordos Basin (0.99)
- Asia > China > Gansu > Ordos Basin (0.99)
Summary A critical review, examination, and clarification of the various issues and problems concerning the definition and dependence of the effectiveโstress coefficients of porousโrock formations is presented. The effectiveโstress coefficients have different values for different rock properties because the physical mechanisms of rock deformation can affect the various rock properties differently. The alteration of petrophysical properties occurs by the onset of various rockโdeformation/damaging processes, including pore collapsing and grain crushing, and affects the values of the effectiveโstress coefficients controlling the different petrophysical properties of rock formations. The slope discontinuity observed in the effectiveโstress coefficients of naturally or induced fracturedโrock formations during loading/unloading, referred to as a shock effect, is essentially related to deformation of fractures at less than the critical effective stress and deformation of matrix at greater than the critical effective stress. The hysteresis observed in the effectiveโstress coefficients of heterogeneous porous rocks during loading/unloading is attributed to elastic deformation under the fully elastic predamage conditions, and/or irreversible poreโstructureโalteration/deformation processes. A proper correlation of the BiotโWillis coefficient controlling the bulk volumetric strain is developed using the data available from various sources in a manner to meet the required endpointโlimit conditions of the BiotโWillis coefficient, ranging from zero to unity. The modified powerโlaw equation presented in this paper yields a physically meaningful correlation because it successfully satisfies the lowโendโ and highโendโlimit values of the BiotโWillis coefficient and also provides a better quality match of the available experimental data than the semilogarithmic equation and the popular basic powerโlaw equation. It is shown that the semilogarithmic correlation cannot predict the values of the Biot coefficient beyond the range of the data because it generates unrealistic values approaching the negative infinity for the Biot coefficient for the lowโpermeability/porosity ratio and unrealistically high values approaching the positive infinity for the highโpermeability/porosity ratio. The basic powerโlaw equation is not adequate either because it can only satisfy the lowโend value but cannot satisfy the highโend value of the Biot coefficient. The correlation developed in this paper from the modified power-law equation is effectively applicable over the full range of the BiotโWillis coefficient, extending from zero to unity. To the best of the author's knowledge, this paper is the first to present an effective theory and formulation of the convenient correlation of the BiotโWillis poroelastic coefficient that not only satisfies both of the two endpointโlimit values of the BiotโWillis coefficient but also produces the best match of the available experimental data.
- Europe (1.00)
- North America > United States > Texas (0.67)
- North America > United States > California (0.46)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock (0.47)
- Europe > Norway > North Sea > Central North Sea > Central Graben > Block 2/8 > Valhall Field > Tor Formation (0.99)
- Europe > Norway > North Sea > Central North Sea > Central Graben > Block 2/8 > Valhall Field > Hod Formation (0.99)
- Europe > Norway > North Sea > Central North Sea > Central Graben > Block 2/11 > Valhall Field > Tor Formation (0.99)
- (2 more...)
Summary This paper presents the theory, formulation, and correlation of the compressibility, porosity, and permeability of shale reservoirs by considering the effects of stress shock causing a slope discontinuity and loading/unloading hysteresis. The slope discontinuity occurs because the relative contributions of the matrix or fracture change at a critical effective stress depending on whether the process is loading or unloading. The hysteresis phenomenon occurs because of partially reversible and irreversible deformations of the various shale rock constituents by various processes during loading and unloading. Two successful modeling approaches are developed for describing the stress dependency of the petrophysical properties of porous rock formations. The first approach implements a kinetic model leading to a modified power-law equation, and the second approach applies an elastic cylindrical pore-shell model leading to a semianalytical equation. The primary advantage of the kinetic model is its applicability to any stress-dependent property, including strain, void ratio, porosity, pore compressibility, and permeability, thus making it a universal method. The semianalytical equation derived from an elastic cylindrical pore-shell model is applicable only for correlation of permeability. Both approaches are shown to yield high-quality correlations of the properties of porous rocks with effective stress by honoring the slope discontinuity observed at a critical effective stress.
- North America > United States > Texas (0.68)
- North America > United States > California (0.46)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Mudrock > Shale (1.00)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- North America > United States > New Mexico > San Juan Basin > San Juan Basin Field > Mancos Formation (0.99)
- North America > United States > Kentucky > Illinois Basin (0.99)
- North America > United States > Indiana > Illinois Basin (0.99)
- (7 more...)
Summary Effective theory and methodology are proposed and validated for accurate correlation of stressโdependent petrophysical properties of naturally fractured or inducedโfractured reservoir formations by means of a matrix/fracture dualโcompressibility treatment. Inspection of various experimental data indicates a sudden change in trends at a certain critical net effective stress in the stress dependence of petrophysical properties of porous rocks as a result of a stress shock caused by the opening or closing of fractures. The variation of petrophysical properties in fracturedโrock formations subjected to stress loading/unloading and thermally induced stress occurs mainly by deformation of the fractures below the critical effective stress and the deformation of the matrix above the critical effective stress. The alteration of petrophysical properties and a slope discontinuity might also be experienced when the stress exceeds the onset of other rockโalteration/damaging processes, such as pore collapsing and grain crushing. Proper formulations of the relevant processes and special correlation methods are presented in a manner to capture this nature of the petrophysical experimental data obtained by testing of cores extracted from naturally fractured or inducedโfractured reservoirโrock formations. The dependency of porosity and permeability of fracturedโrock samples under stress because of thermal, hydraulic, and mechanical effects is represented accurately by a modifiedโpowerโlaw equation derived from a kinetics model as confirmed by effective correlations of various experimental data. It is shown that this new model represents the thermal effect better than the frequently used Arrhenius (1889) equation and VogelโTammannโFulcher (VTF) equation (Vogel 1921; Fulcher 1925; Tammann and Hesse 1926).
- Europe (1.00)
- North America > United States > Texas (0.28)
- North America > United States > California (0.28)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock (0.33)
- Reservoir Description and Dynamics > Unconventional and Complex Reservoirs > Naturally-fractured reservoirs (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization > Exploration, development, structural geology (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization > Reservoir geomechanics (0.93)
Abstract This paper presents the theory and formulation of the compressibility, porosity, and permeability of shale reservoirs by considering the effects of stress shock causing slope discontinuity and loading/unloading hysteresis. The slope discontinuity happens because the relative contributions of the matrix and fracture change at a critical effective stress at which the fractures close or open depending on whether the process is loading or unloading. The hysteresis phenomenon occurs as a result of partially reversible and irreversible deformations of the various shale rock constituents by various processes during loading and unloading. Two semi-analytical modeling approaches are developed for describing the stress-dependency of the petrophysical properties of porous rock formations. The first approach implements a kinetic model and the second approach applies an elastic cylindrical pore-shell model. Both approaches yield high-quality correlations of the various petrophysical properties of porous rocks with effective stress by honoring the slope discontinuity observed in the compressibility, porosity, and permeability of rocks at critical effective stress. Introduction Shale rock formations include matters of inorganic (quartz, clay, etc.) and organic (kerogen) in the rock matrix, gas at various states (dissolved, adsorbed, and free gases), and brine (water and dissolved salts). The pore system in naturally fractured rocks contains both the matrix and fracture porosity. Some induced fractures are generated in brittle rocks during stress deformation and hydraulic fracturing. The contribution of the interconnectivity of pores and the porosity in the inorganic and organic matters, and the fracture system to the overall effective porosity and permeability of shale rocks depends on the effective stress. The effective stress ฯ acting upon porous rocks is determined by an amended Biot's (1941) law as the difference between the total confining stress ฯc and some degree of participation of the pore fluid pressure p (Biot and Willis, 1957; Kรผmpel, 1991, Kwon et al., 2001, Walls and Nur, 1979, Zimmermann, 1991, Zoback and Byerlee, 1975a, b): (equation) (1)
- North America > United States > Oklahoma (0.46)
- North America > United States > California (0.46)
- North America > United States > Texas > Harris County > Houston (0.28)
- North America > United States > Kentucky > Illinois Basin (0.99)
- North America > United States > Indiana > Illinois Basin (0.99)
- North America > United States > Illinois > Illinois Basin (0.99)
- Asia > China > Sichuan > Sichuan Basin (0.99)
- Well Completion > Hydraulic Fracturing (1.00)
- Reservoir Description and Dynamics > Unconventional and Complex Reservoirs > Naturally-fractured reservoirs (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization > Exploration, development, structural geology (1.00)
Abstract The conventional approach to flow unitsโ characterization according to Amaefule et al. (1993) is based on the Kozeny-Carman equation. Although, the Kozeny-Carman equation has been used widely for relating permeability to other properties of porous materials, it suffers from the assumption of non-interacting flow tubes. In this paper, the effects of pore connectivity, valve action of pore throats, and cementation factor are considered by an interacting bundle of tortuous leaky capillary-tubes model of porous media to derive an improved equation of permeability. The parameters of the power-law form of this equation are related to pore connectivity measured by the coordination number using the functional relationships derived from the phenomenological rate equations. The validity and accuracy of this approach is established by comparison with directly measured core data. This approach allows for incorporation of various data within a single, compact, and simple power-law equation over the full range of porosity and permeability. The power law exponent of the leaky-tubes model is shown to deviate significantly from the unity assumed in the Kozeny-Carman equation. While the Amaefule et al. (1993) approach characterizes the reservoir flow units solely based on a flow-zone indicator (FZI) parameter, the present improved approach adds a power-law exponent which allows for enhanced flow unitsโ characterization using two porosity dependent parameters. The analysis of the permeability vs. porosity data demonstrates that the power law flow unitsโ model alleviates the deficiencies of the classical Kozeny-Carman equation. This model adequately approximates the actual flow patterns in porous media because it allows interactions and cross-flow between the capillary hydraulic paths.
- North America > United States > Texas (0.69)
- North America > United States > Louisiana (0.47)
- North America > United States > Texas > Travis Peak Formation (0.99)
- North America > United States > Mississippi > Travis Peak Formation (0.99)
- North America > United States > Louisiana > Travis Peak Formation (0.99)
- (5 more...)
Abstract Transport of gas in nano-permeability shale-gas reservoirs involves complex processes of absorption, adsorption, poroelasticity, alterations of gas properties by pore-confinement, and significant deviations from Darcy-type flow. While recent modifications of Darcyโs law can account for molecular transport in shale depending on the Knudsen conditions, they nevertheless omit the corrections due to convective acceleration and inertial flow occurring through natural fractures and induced fractures formed by hydraulic fracturing and the threshold pressure gradient below which reservoir fluids cannot flow. This paper presents a physically rigorous modeling of shale-gas transport by considering the relevant effects in nanopores and fractures to derive a proper gas storage and transport model. This provides an improved model accounting for complex transport processes in organic and inorganic materials intersected by natural and induced fractures. A non-Darcy equation, comprehensive gas storage model, and quantification of relevant parameters are developed. The model is used to simulate gas transport in laboratory shale-core tests conducted under near-real shale-gas reservoir conditions.
- Europe (0.93)
- North America > United States > New Jersey (0.28)
Summary Transport of gas in extremely-low permeability shale-gas reservoirs involves complex processes of absorption, adsorption, and pore-confinement effect in nanopores; significant deviations occur from Darcy-type flow; and gas properties such as real gas deviation factor and viscosity are significantly altered compared to conventional reservoir conditions. This paper presents a physically rigorous modeling of shale gas transport by considering the various effects of importance in nanopores to derive the proper equations of gas storage and transport, and to demonstrate various applications of practical interest. First, previous approaches are critically reviewed to delineate their outstanding features and shortcomings. Then, a non-Darcy gas transfer equation, comprehensive gas storage model, and quantification of the relevant parameters including permeability are developed. Next, the improved model is used to simulate gas transport in laboratory tests conducted under near-real shale-gas reservoir conditions. Improved non-Darcy nanopore gas storage and flow model describes the shale gas transport properly and can be used satisfactorily in shale-gas reservoir simulation. 1 Introduction Although the theory of gas transport through extremely narrow flow paths in porous media have been reasonably well established, the analyses of experimental data have not been quite successful judging by the results reported in the literature. For example, Javadpour (2009) had to adjust the values of three empirical parameters to be able to achieve a matching of experimental data. Darabi et al. (2012) applied the apparent permeability function (APF) concept which was originally formulated by Ertekin et al. (1986). Darabi et al. (2012) also have three adjustable parameters. Unique determination of these three adjustable parameter values is questionable. Because of the error as pointed out in this paper, the model given by Javadpour (2009) did not match the measured data. The simulation results presented by Roy et al. (2003) and Veltzke and Thรถming (2012) also deviate significantly from their own experimental data. These papers attempted to determine the values of their adjustable parameters using only one set of experimental data. Civan et al. (2012) explained that "one must run a minimum number of tests that is more than the number of adjustable parameters with the same system but conducted under different conditions to achieve uniqueness."
- North America > United States > Texas (0.28)
- North America > United States > Oklahoma (0.28)
Summary Determination of the nanodarcy gas permeability and other parameters of naturally and hydraulically fractured shale formations by pressure-pulse transmission testing of core plugs, drill cuttings, and crushed samples is discussed. The methods available for interpretation of pressure tests are reviewed and modified with emphasis on difference between the intrinsic and apparent permeability. Improved formulations and analysis methods which honor the relevant physics of fluid and transport, and interactions with shale are presented. Better design and analysis of experiments for simultaneous determination of several unknown parameters that impact the transport calculations, including deformation, adsorption, diffusion, and deviation from Darcy flow are described. The permeability and other parameters of shale samples are recommended to be determined by simultaneous analysis of multiple pressure tests conducted under different conditions to accommodate for temporally and spatially variable conditions. The inherent limitations of the methods relying on the analytical solutions of the diffusivity equation based on the Darcy's law are explained. Introduction The permeability measured using a Darcy-like equation is not the intrinsic permeability but the apparent permeability which depends on the prevailing conditions of fluid, transport, and shale. The intrinsic permeability of shale depends on the temperature and effective stress conditions and therefore the conditions of a particular intrinsic value should also be specified. The primary reason for the contradictory values of permeability measured by application of the analytical models is explained by dependence of measured permeability of shale on particular testing conditions over which only a certain average permeability value is obtained from most analytical solutions. Crushed samples have different size particles. The permeability of a particle depends on its size. Large particles are likely to have both the matrix porosity and fracture porosity. Consequently, it is not correct to assume all the particles of different sizes to have the same permeability. Whereas, most attempts in calculating the permeability using the pressure tests on crushed samples assume the same permeability for all particles. This assumption can only be applicable for samples of uninform particle sizes.
- North America > United States > Texas (1.00)
- Europe (0.68)
Abstract Determination of the nanodarcy gas permeability and other parameters of shale by pressure-pulse transmission testing of core plugs, drill cuttings, and crushed samples is discussed. The methods available for interpretation of pressure-pulse decay tests are reviewed with emphasis on the difference between the intrinsic and apparent permeability. Improved formulation and analysis which honor the relevant physics of gas transport and interactions of flowing gas with the shale under the pore-proximity and elevated pressure conditions are presented. Modification of the shale and fluid properties under prevailing stress, and pore-size distribution, connectivity, and confinement conditions is shown to be important under any pressure conditions while the gas rarefaction and slippage effects diminish essentially at high pressures but become important at low pressures. The permeability and other parameters of shale samples are determined by numerical modeling and analysis of the pressure tests conducted under different conditions in order to accommodate for temporally and spatially variable conditions. Better design and analysis of experiments for simultaneous determination of several unknown parameters that impact transport calculations, including stress-deformation, adsorption, diffusion, and deviation from Darcy flow are described. The inherent limitations of the earlier methods which rely on the approximate analytical solutions of the simplified diffusivity equation based on the Darcy's law are delineated. It is pointed out that the permeability measured using a Darcy-type equation is the apparent permeability and not the intrinsic permeability. Thus, the primary reason for the contradictory values of permeability measured by application of the analytical models is explained by dependence of the permeability of shale to different testing conditions over which only different average permeability values can be obtained when applying the approximate analytical solutions obtained based on the assumption of a constant permeability value.
- North America > United States > Texas (1.00)
- Europe (1.00)
- Asia (1.00)
- North America > Canada (0.93)
- North America > United States > West Virginia > Appalachian Basin (0.99)
- North America > United States > Virginia > Appalachian Basin (0.99)
- North America > United States > Texas > Fort Worth Basin > Barnett Shale Formation (0.99)
- (12 more...)