Effective Stress Coefficient Research Articles

Experimental Investigation of Depletion- and Injection-Induced Changes in Poromechanical, Transport, and Strength Properties of High-Porosity Sandstone

Summary In this paper, an extensive series of experiments was performed to investigate the evolution of poromechanical (dry, drained, undrained, and unjacketed moduli), transport (permeability), and strength properties during reservoir depletion and injection in a high-porosity sandstone (Castlegate). An overdetermined set of eight poroelastic moduli was measured as a function of confining pressure (Pc) and pore pressure (Pp). The results showed larger effect on pore pressure at low Terzaghi’s effective stress (nonlinear trend) during depletion and injection. Moreover, the rock sample is stiffer during injection than depletion. At the same Pc and Pp, Biot’s coefficient and Skempton’s coefficient are larger in depletion than injection. Under deviatoric loading, absolute permeability decreased by 35% with increasing effective confining stress up to 20.68 MPa. Given these variations in rock properties, modeling of in-situ-stress changes using constant properties could attain erroneous predictions. Moreover, constant deviatoric stress-depletion/injection failure tests showed no changes or infinitesimal variations of strength properties with depletion and injection. It was found that failure of Castlegate sandstone is controlled by simple effective stress, as postulated by Terzaghi. Effective-stress coefficients at failure (effective-stress coefficient for strength) were found to be close to unity (actual numbers, however, were 1.03 for Samples CS-5 and CS-9 and 1.04 for Sample CS-10). Microstructural analysis of Castlegate sandstone using both scanning electron microscope (SEM) and optical microscope revealed that the changes in poroelastic and transport properties as well as the significant hysteresis between depletion and injection are attributed to the existence and distribution of compliant components such as pores, microcracks, and clay minerals.

On the effective stress coefficient of single rough rock fractures

The effective stress coefficient is critical to accurately predict the hydromechanical coupling behavior of single water-bearing rock fractures. The physical meaning of the effective stress coefficient in a rough rock fracture is understood as the ratio of the nominal fracture surface occupied by water to the total fracture surface area. To overcome the difficulty of measuring contact ratio changes in rough rock fractures under normal loading and water pressure, a new effective stress coefficient model for single rough water-bearing fractures is proposed in terms of two mechanical parameters, initial normal stiffness and maximum normal closure. By incorporating the new effective stress coefficient model into the Barton-Bandis constitutive model, a hydromechanical coupling model was built and verified by laboratory and in-situ experimental data. The results indicate that the effective stress coefficient is less than 1 for single rough rock fractures and decreases with increasing difference between normal stress and water pressure. When the normal stress is close to or considerably higher than the fracture water pressure, both the newly built model and Terzaghi's model obtain similar normal displacement. However, for moderate normal stress, the normal displacements predicted by the newly built model and Terzaghi's model differ significantly. The implications of the newly built model in subsurface engineering are discussed.

Bedding Anisotropy and Effective Stress Law for the Permeability and Deformation of Clayey Sandstones

We performed a systematic investigation of the effective stress behaviors for permeability and deformation in relation to bedding anisotropy of two clayey sandstones. Permeability and deformation were measured in samples cored parallel and perpendicular to bedding over a broad range of hydrostatic pressures, covering ‘stage I’ for microcrack closure and ‘stage II’ for pore deformation. Our data show that bedding anisotropy has a significant influence on the effective stress coefficient for permeability, but little effect on the effective stress coefficient for pore volume change. The effective stress coefficient $${\kappa }^{\perp }$$ of permeability for flow perpendicular to bedding was consistently larger than the corresponding $${\kappa }^{||}$$ for parallel flow. The effective stress coefficient $${\beta }^{||}$$ for pore volume changes parallel to bedding and corresponding coefficient $${\beta }^{\perp }$$ values perpendicular to bedding coincided, because the scalar change of pore volume was not sensitive to the orientation of the samples. Furthermore, we confirmed that with the closure of preexisting microcracks, the effective stress coefficients for permeability in stages II were typically larger than the corresponding coefficients in stage I, and that the effective stress coefficients for axial strain and pore volume change decreased for samples both perpendicular and parallel to bedding. Our new results quantified the effect of bedding anisotropy and crack closure on the effective stress behavior of clayey sandstones.

Investigating the effects of stress creep and effective stress coefficient on stress-dependent permeability measurements of shale rock

Rock permeability is an essential factor for production prediction and economic evaluation, which is often measured based on core samples in laboratory. However, several phenomena such as stress creep and path-dependent stress still present difficulties in correctly measuring and interpreting permeability under varying compaction stresses for core measurements. In this study, an improved stress-dependent permeability model is proposed to consider the effect of time-dependent compaction behavior on permeability measurements by incorporating the stress creep mechanism. Besides, how to correctly interpret stress-dependent permeability results with effective stress coefficient is introduced in detail. A coupled flow-geomechanics model is also developed to investigate the impact of effective stress coefficient on permeability change and cumulative production. Due to the stress creep phenomenon, rock permeability could be significantly overestimated if not enough measurement time is provided. The creep strain is highly related to the content of clay and kerogen. This is because the increasing creep strain over time is mainly from the closure of pre-existed micro-fractures and the compression of Nano-pores inside the soft materials, such as clay and kerogen. The creep strain model and improved stress-dependent permeability model were validated by comparing with multiple experimental data. Effective stress coefficient cannot be simply assumed one for organic-rich or clay-rich shale reservoirs, especially when pore pressure is changed to alter net effective stress in permeability measurements. A large effective stress coefficient amplifies the sensitivity of pore pressure change on the variation of both effective stress and permeability. The simulation results show a larger effective stress coefficient could provide higher cumulative production because of stronger compression from effective stress. The improved knowledge of stress creep and effective stress coefficient enables the development of best practices for permeability measurement of tight rock and provides more accurate permeability results for reservoir management and field development.

Shear Wave Splitting and Polarization in Anisotropic Fluid-Infiltrating Porous Media: A Numerical Study.

The triggering and spreading of volumetric waves in soils, namely pressure (P) and shear (S) waves, developing from a point source of a dynamic load, are analyzed. Wave polarization and shear wave splitting are innovatively reproduced via a three-dimensional Finite Element research code upgraded to account for fast dynamic regimes in fully saturated porous media. The mathematical–numerical model adopts a u-v-p formulation enhanced by introducing Taylor–Hood mixed finite elements and the stability features of the solution are considered by analyzing different implemented time integration strategies. Particularly, the phenomena have been studied and reconstructed by numerically generating different types of medium anisotropy accounting for (i) an anisotropic solid skeleton, (ii) an anisotropic permeability tensor, and (iii) a Biot’s effective stress coefficient tensor. Additionally, deviatoric-volumetric coupling effects have been emphasized by specifically modifying the structural anisotropy. A series of analyses are conducted to validate the model and prove the effectiveness of the results, from the directionality of polarized vibrations, the anisotropy-induced splitting, up to the spreading of surface waves.

Experimental study on the anisotropy of the effective stress coefficient of sandstone under true triaxial stress

The effective stress principle plays an important role in the study of the permeability evolution and mechanical behavior of coal and rocks. A key to evaluating the effective stress is determining the evolution of the effective stress coefficient α. However, conventional triaxial stress-path tests are not suitable for reproducing the actual stress state of coal and rocks and thus determining the effective stress coefficient. Therefore, this study was conducted to investigate the anisotropic characteristics of the effective stress coefficient for sandstone under different true triaxial stress and pore pressure conditions. The results show that the effective stress coefficient exhibits anisotropy due to the different principal strains in three directions and the anisotropy of pore structure, and it is closely linked with the pore pressure and principal stress. An increase in pore pressure causes sandstone particles that block the seepage channel to migrate, which reduces the sensitivity of permeability to principal stress, increasing the effective stress coefficient. When principal stress increases, pores and fractures are compressed, which reduces the sensitivity of permeability to pore pressure, resulting in a decrease in α. However, as principal stress continues to increase, effective stress coefficients can increase in the directions of major and intermediate principal stresses, while an α3 beyond unity appears in the direction of minor principal stress. This is related to the pore fluid flowing through highly compressible clay aggregates, in which the pore area is large, and the sensitivity of permeability to pore pressure is enhanced. The effective stress coefficient increases with an increase in permeability due to the effect of porosity. A new formula for calculating the volumetric strain of a linear elastic isotropic porous medium is established based on the anisotropy of the effective stress coefficient, which can be applied to experimental results.

Case Study: Effect of Natural Fracture on Stimulation Strategy in Keshen Tight Gas

Aimed at problems of poor fracturing effects of fracture-network acid fracturing in three wells in the Keshen 5 block, a fractured and tight gas reservoir in Tarim Oilfield, the mechanical activity of natural fractures was studied. The fractures in this block were divided into three types: fully-filled, semi-filled, and unfilled. The analysis of the correlations showed that the correlation of the number of fully-filled fractures and absolute open flows (AOF) is poor, while the correlation between the number of unfilled and semi-filled fractures and AOF is the best. Core samples with different types of fractures were tested using conventional triaxial compression methods, and the experimental results showed that the friction coefficient of the fully-filled fracture is close to that of semi-filled fracture, while the cohesion of fully-filled natural fractures is close to that of intact rocks, which is much greater than that of semi-filled fractures. The effective stress test results shows that the effective stress coefficient of fully-filled natural fracture rock samples is lower than that of semi-filled fractures. Using Mohr–Coulomb theory to calculate the natural fracture mechanics of high-production wells and low-production wells, the results show that low-production wells are mainly fully-filled fractures, most of which are not activated, so the production is low; while high-production wells are semi-filled and unfilled fractures, most of which can be activated, so the production is high. Based on this, for a well dominated by fully-filled fractures, it is recommended to use conventional gel fracturing to replace the fracture-network acid fracturing process. The stimulation practice of two wells has proven the validity of this strategy. The filling degree of natural fractures affects the increasing production and choice of stimulation process. This may be a relatively new understanding and may provide insights to stimulation strategy decisions for other fractured tight reservoirs in the world.

Effective Stress Law for the Permeability and Pore Volume Change of Clayey Sandstones

AbstractThe influence of confining and pore pressures on permeability and pore volume change was studied in two clayey sandstones. The coupling effect is characterized by the effective stress coefficients κ and β, respectively. Hydrostatic compression of a porous rock typically involves an initial nonlinear stage of elastic crack closure and a subsequent linear stage of pore deformation. To elucidate the influence of microcracks on the behavior, we measured the effective stress coefficients in these two stages separately. Our data show that the coefficients κ for permeability of both clayey sandstones are uniformly greater than 1, in agreement with published data and theoretical prediction for a microscopically inhomogeneous assemblage. Our data show that the presence of microcracks may homogenize the pore space, as reflected by a significantly lower κ value during the initial stage of nonlinear compression. We obtained some of the first measurements of the effective stress coefficient β for pore volume change in sandstones, which show values close to but uniformly less than 1. Synthesizing our sandstone data, recently published data on limestones, and theoretical analyses, we propose to define in the β‐κ space two fundamentally different regimes for the effective stress behavior. A comparison of our data with Berryman's model, the clay shell model, and clay particle model indicates apparent discrepancies, which we propose to resolve with a dual equivalent‐channel model based on the spatial partitioning of clayey and clay‐free pore volumes.

Experimental assessment of the stress-sensitivity of combined elastic and electrical anisotropy in shallow reservoir sandstones

Seismic and electromagnetic properties generally are anisotropic, depending on the microscale rock fabric and the macroscale stress field. We have assessed the stress-dependent anisotropy of poorly consolidated (porosity of approximately 0.35) sandstones (broadly representative of shallow reservoirs) experimentally, combining ultrasonic (0.6 MHz P-wave velocity, [Formula: see text], and attenuation [Formula: see text]) and electrical resistivity measurements. We used three cores from an outcrop sandstone sample extracted at 0°, 45°, and 90° angles with respect to the visible geologic bedding plane and subjected them to unloading/loading cycles with variations of the confining (20–35 MPa) and pore (2–17 MPa) pressures. Our results indicate that stress field orientation, loading history, rock fabric, and the measurement scale all affect the elastic and electrical anisotropies. Strong linear correlations ([Formula: see text]) between [Formula: see text], [Formula: see text], and resistivity in the three considered directions suggest that the stress orientation similarly affects the elastic and electrical properties of poorly consolidated, high-porosity (shallow) sandstone reservoirs. However, resistivity is more sensitive to pore-pressure changes (effective stress coefficients [Formula: see text]), whereas P-wave properties provide simultaneous information about the confining (from [Formula: see text], with n slightly less than 1) and pore pressure (from [Formula: see text], with n slightly greater than 1) variations. We found n is also anisotropic for the three measured properties because a more intense and rapid grain rearrangement occurs when the stress field changes result from oblique stress orientations with respect to rock layering. Altogether, our results highlighted the potential of joint elastic-electrical stress-dependent anisotropy assessments to enhance the geomechanical interpretation of reservoirs during production or injection activities.

Modeling of geomechanics and fluid flow in fractured shale reservoirs with deformable multi-continuum matrix

The Efficient development of shale reservoirs becomes increasingly dependent upon infill wells in China to stabilize the gas production. The accurate calculation of dynamic evolution of stress field is important for the design of fracturing and infill wells. The extraction of gas flow results in stress-sensitive and significantly alters the original in-situ stress field, which brings difficulties on geomechanical design for fracturing treatment. Hitherto, the main factors that affect the principal stress alteration is unclear, especially when considering the interference between fractures and wells. Besides, the transport mechanisms of shale gas flow are complex, which bring difficulties in the modeling of deformable multi-continuum. In this paper, an adaptive model that couples multi-continuum matrix and discrete fractures is developed. According to the effective stress coefficients of matrix pores and natural fractures, the total deformation is decomposed into two parts: matrix pore pressure depletion induced deformation and natural fracture pressure depletion induced deformation. The model is then validated to simulate hydromechanical coupling processes in fractured-shale reservoirs during the production period. Sensitivity analysis of stress alteration is also performed to study the alteration angle of the minimum horizontal principal stress during production. The modeling results show that the pressure depletion in natural fractures is the fastest, which dominates the shale deformation. Besides, the gas desorption in organic matters enlarges the alteration angle of the minimum horizontal principal stress during production. Finally, we find the difference between adsorption rate and desorption rate, instead of the total adsorbed gas amount, determines the adsorbed gas production.

Consolidation responses of rheological aquitards to tide-induced groundwater fluctuations in coastal soft deposits

To investigate the consolidation responses of coastal rheological aquitards to tide-induced groundwater fluctuations, this study adopts a nonlinear 1-D consolidation model considering the rheological properties of the aquitard and non-Darcian flow. In this model, the depth-dependent property of the initial permeability and compressibility of the aquitard are considered using the continuous exponential functions of the vertical coordinate z. Moreover, the stress-dependent property of the permeability and compressibility during consolidation are described using the correlations of the void ratio with effective stress and permeability coefficient. The rheological nature of the aquitard is characterized with the e-log t curve for the secondary consolidation, while the flow in the aquitard is assumed to follow the exponential non-Darcian law. The numerical solutions for the model are obtained using finite volume method and Newton-Raphson iteration method. A comprehensive parametric study is conducted with regard to the mechanical and hydraulic parameters of the aquitard and its burial conditions. The analysis results reveal the generation, accumulation and oscillation mechanisms of pore pressure change and soil skeleton deformation in the aquitard. The proposed model can provide a theoretical foundation for predicting and controlling the deformation of engineering structures in coastal aquitards.

Laboratory Research on Gas Transport in Shale Nanopores Considering the Stress Effect and Slippage Effect

AbstractThe low permeability of shale, in accretionary complexes and passive continental margins, influences pore pressure generation, and thus induces deformation and fault slip behavior. It is also key in hindering the ability to evaluate shale gas production. Gas is commonly used in measuring the permeability of shale and generally yields high values than that of liquids, due to slippage effect. Separation of the slippage effect from gas permeability is a critical task in the study of low‐permeability media. This study measured the gas permeability (Kg) of the Longmaxi shale parallel to bedding (L1P) and perpendicular to bedding (L1V) under different confining pressures (Cp) and pore pressures (Pp), while simultaneously measuring porosity for different values of Cp. Additionally, a new approach is proposed to define the effective stress coefficient and boundary condition for the Klinkenberg correction. The results show that the Kg of L1P is almost unaffected by the slippage effect, while, for L1V, the Klinkenberg correction is required. The Klinkenberg plot of L1V follows the quadratic model from the study by Ashrafi Moghadam and Chalaturnyk (2014, https://doi.org.10/1016/j.coal.2013.10.008), rather than the classic linear Klinkenberg equation. The results also show that, as the Cp increases and/or the Pp decreases, the contribution of the slippage effect to the L1V Kg increased from 20% to 86.5%. Finally, based on the Knudsen number (Kn), the flow regime of L1P changes from Darcy flow (Kn < 0.01) to slip flow (0.01 < Kn < 0.1), and that of L1V is slip flow.

On the effective stress coefficient of saturated fractured rocks

The applicability of the classic Terzaghi or Biot effective stress laws to fractured rocks is not clear. Based on discrete element models, bulk modulus method and equivalent strain method are presented to determine the effective stress coefficient of saturated fractured rocks, and were examined with the regular fracture network I. Two types of discrete fracture networks, including regular and random network models, were built, and a total of over 300 numerical simulations were performed using the equivalent strain method for sensitivity analysis of the effective stress coefficient of fractured rocks to the fracture geometries characteristics, and the mechanical properties of both the intact rock and the fracture. The classic effective stress laws for porous media cannot be extended to fractured rocks, mainly due to the different volumetric deformation behaviors between porous and fractured materials. The effective stress coefficient is the largest in the regular fracture network I and the smallest in the random fracture network. As the normal and shear stiffness of the fracture increase, the effective stress coefficient decreases, while it increases with the increasing elastic modulus and Poisson’s ratio of the intact rock. An empirical model was proposed to predict the effective stress coefficient of saturated fractured rocks.

Effective-Stress Coefficients of Porous Rocks Involving Shocks and Loading/Unloading Hysteresis

SummaryA critical review, examination, and clarification of the various issues and problems concerning the definition and dependence of the effective-stress coefficients of porous-rock formations is presented. The effective-stress 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 rock-deformation/damaging processes, including pore collapsing and grain crushing, and affects the values of the effective-stress coefficients controlling the different petrophysical properties of rock formations. The slope discontinuity observed in the effective-stress coefficients of naturally or induced fractured-rock 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 effective-stress coefficients of heterogeneous porous rocks during loading/unloading is attributed to elastic deformation under the fully elastic predamage conditions, and/or irreversible pore-structure-alteration/deformation processes.A proper correlation of the Biot-Willis coefficient controlling the bulk volumetric strain is developed using the data available from various sources in a manner to meet the required endpoint-limit conditions of the Biot-Willis coefficient, ranging from zero to unity. The modified power-law equation presented in this paper yields a physically meaningful correlation because it successfully satisfies the low-end- and high-end-limit values of the Biot-Willis coefficient and also provides a better quality match of the available experimental data than the semilogarithmic equation and the popular basic power-law 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 low-permeability/porosity ratio and unrealistically high values approaching the positive infinity for the high-permeability/porosity ratio. The basic power-law equation is not adequate either because it can only satisfy the low-end value but cannot satisfy the high-end 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 Biot-Willis 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 Biot-Willis poroelastic coefficient that not only satisfies both of the two endpoint-limit values of the Biot-Willis coefficient but also produces the best match of the available experimental data.

Uncertainty and Sensitivity Analysis of In-Situ Stress in Deep Inclined Strata

In the development process of oil and gas field, the dip angles generally exist in deep strata, and the variability and dispersion in the mechanics parameters of the formation make the computation model of in situ stress for a gentle structure no longer applicable. In light of the fact that the dip angle was large and the geological structure was complex in Sichuan basin and Xinjiang basin, uncertainty of mechanical parameters and tectonic stress coefficients of the formation were analyzed by the Monte Carlo method based on acoustic logging data and stratigraphic dipmeter log data. Taking dip angle and dip direction into account, the uncertainty calculation method for in situ stress in deep inclined strata was proposed. Multi-factor analysis was used to analyze the sensitivity of various factors affecting the in situ stress in deep inclined strata. The results show that, the horizontal in situ stress calculation model adopted in this paper is more suitable for structurally intense areas. The horizontal stress confidence interval is more significant for oil and gas field engineering than single principal stress value. For PY gas field and TLM oil field with different geological conditions and rocks mechanical parameters of formation, the dip angle and effective stress coefficient are the most sensitive to the horizontal in situ stress.

Calculating Components of the Effective Tensors of Elastic Moduli and Biot’s Parameter of Porous Geocomposites

Methods of composite mechanics were used to evaluate the effective elastic moduli and Biot’s parameter of porous media. Natural composites — dolomites and hyaloclastites — were considered as examples, which were also examined experimentally. The microscopic structure of the rocks was studied under a microscope, and their mineral composition was determined by the X-ray diffractometry. A comparison of experimental and calculated elastic moduli of dolomites showed their good agreement, which proved that the averaging method can be used to rapidly evaluate their effective elastic properties. For dolomites, Young’s modulus and Biot’s parameter were determined as functions of porosity using the calculation results and experimental data. The computation method described in this paper allows one to calculate Biot’s tensor in the general case of an anisotropic and inhomogeneous matrix and to evaluate the influence of pore shape on stresses and strains at the microlevel, which is not possible by experimental methods. Using samples of hyaloclastites with round and angular pores, the effect of pore shape on the elastic moduli and the effective stress coefficient was investigated. The effect of pore orientation was also studied using anisotropic dolomite samples with elongated pores.

Experimental efforts to access 4D feasibility and interpretation issues of Brazilian presalt carbonate reservoirs

Brazilian presalt reservoirs comprise carbonate rocks saturated with light oil with different amounts of [Formula: see text] and excellent productivity. The occurrence of giant-size accumulations with such productivity generates the interest in production monitoring tools, such as time-lapse seismic. However, time-lapse seismic may present several challenges, such as imaging difficulties, repeatability, and detectability of small variations of reservoir properties. In addition, when assessing time-lapse seismic feasibility, the validity of Gassmann’s modeling for complex, heterogeneous carbonate rocks is arguable. Other questions include the pressure variation effects on the seismic properties of competent rocks. The effective stress is a linear combination of confining stress and pore pressure that governs the behavior of physical properties of rocks. Many applications assume that the effective stress for elastic-wave velocity is given by the difference between confining stress and pore pressure, whereas another common approach uses the Biot-Willis coefficient as a weight applied to the pore pressure to estimate the effective stress. Through a series of experiments involving ultrasonic pulse transmission on saturated core plugs in the laboratory, we verified the applicability of Gassmann’s fluid substitution and estimated the empirical effective stress coefficients related to the P- and S-wave velocities for rock samples from two offshore carbonate reservoirs from the presalt section, Santos Basin. We observed that Gassmann’s equation predicts quite well the effects of fluid replacement, and we found that the effective stress coefficient is less than one and not equal to the Biot-Willis coefficient. Moreover, there is a good agreement between the static and dynamic Biot-Willis coefficient, which is a suggestion that the presalt rocks behave as a poroelastic media. These observations suggest that more accurate time-lapse studies require the estimation of the effective stress coefficient for the particular reservoir of interest.

Pore Pressure Prediction in Onshore West Niger Delta Using Inverted Seismic Velocity and Derived Velocity (Vp) - Vertical Effective Stress (VES) Coefficients

In this study, pore pressure has been predicted using seismic data and derived compressional wave velocity (V p ) - Vertical Effective Stress (VES) coefficients. Post Stack Time Migration (PSTM), angle stack gathers, seismic horizons, checkshot, wireline logs, drilling and pressure data from six wells in the Onshore West Niger Delta, Nigeria were analysed and interpreted. Using generated velocity and density crossplots, the active overpressure generating mechanisms for the studied area were deduced. The V p -VES coefficients were modelled using the direct pressure data and the overburden profile computed from density log. Post stack seismic inversion was performed to improve the seismic resolution as well as derive acoustic impedance using well velocities and stacking velocities from velocity analysis of the 3-D seismic data. The derived V p -VES coefficients were used to transform the seismic acoustic impedance velocity into seismic pore pressure volume. Pore pressure profiles were accordingly extracted along well paths so as to test the accuracy of the model. Interpreted density-velocity crossplots revealed a decrease in velocity at constant density of 2.4 g/cc, an indication that unloading mechanisms contribute to overpressure in the field. The Bowers’ V p -VES coefficients of 7.43 and 0.77 were determined for A and B parameters respectively. Based on the results obtained, the top of overpressure occurred at a depth of 3750 ft and 3800 ft in UMO-001 and UMO-002 wells respectively with a corresponding average pore pressure gradient of 0.47 psi/ft for both wells, indicating that the wells are mildly overpressured. Onsets of unloading were observed in UMO-001 and UMO-002 wells at depths of 6250 ft and 6800 ft with pore pressure gradients of 0.51 psi/ft and 0.60 psi/ft respectively. The Derived Seismic Pore Pressure (DSPP) matched the measured pressure value (kick) of 5300 psi at a depth of 7450 ft and this validated and further increased confidence on the values of the V p -VES coefficients derived. These results show that the derived seismic acoustic impedance volume, vertical effective stress and overburden model produce high resolution seismic pore pressure cube in both time and space. The derived models when applied especially, with seismic acoustic impedance volume can be used to plan and drill future wells with great successes in the studied area. Keywords: pore pressure, vertical effective stress, seismic velocity, acoustic impedance DOI : 10.7176/JEES/9-10-07 Publication date :October 31 st 2019

Experimental study of the effective stress coefficient for coal permeability with different water saturations

The effect of effective stress on coal reservoir permeability is inevitable during coalbed methane (CBM) production. Studying the effective stress coefficient for permeability (ESCK) is crucial because it determines the effective stress and stress sensitivity of a coal reservoir. Considering the actual drainage process of a CBM well, a series of stress sensitivity experiments with different water saturations were designed and implemented. The experimental results show that the gas measured permeability of the coal sample decreased with increasing water saturation. The change in permeability with different water saturations had a significant power relationship with increasing net pressure. Using the response surface method (RSM), ESCK values with different water saturations were obtained. The ESCK value, regardless of the stress conditions, is a constant at a certain water saturation, and it shows an increasing trend with increasing water saturation. The ESCK values with different water saturations indicate that the effective stress decreases with increasing water saturation. The stress sensitivity and dynamic change in coal reservoir permeability were also analyzed using ESCK values with different water saturations. The stress sensitivity coefficient decreased with increased water saturation, and the reservoir permeability decreased more obviously with an ESCK value of 0.7675 than that with a value of 1.0. During CBM well production, water saturation decreases, and the stress sensitivity of coal reservoir permeability increases.

Thermal effective stress in shales

Calculating velocities in shales in thermal production settings is important to refine time-lapse reservoir characterization from seismic. The effective stress concept is attractive to potentially reduce the amount of expensive core calibration data required. We propose a formulation for thermal effective stress in shales based on the idea of balancing undrained pore pressure increments from thermal expansion with an increase in the matrix stress to minimize pore deformation. This formulation is motivated by a desire to simplify forward modeling, reduce the number of dimensions that must be experimentally calibrated through core testing, and to leverage existing velocity-stress relations for thermal applications. The concept was tested on data from a well-known set of experiments consisting of two North Sea Kimmeridge shale core samples, which displayed a linear dependence of velocity on pressure and temperature. These data were found to be consistent with the proposed thermal effective stress model with a constant effective stress coefficient when considering elastic changes but do not prove that the concept is universally valid. Thermal effective stress coefficients were calculated for P- and S-wave velocities from the data and were found to lie from 0.66 to 1.22, demonstrating reasonable scaling for the proposed model.