Matrix Compressibility Research Articles

A coated hypotrochoidal compressible liquid inclusion neutral to a hydrostatic stress field after relaxation by interface slip and diffusion

We study the steady-state response of a three-phase composite composed of an internal hypotrochoidal compressible liquid inclusion, an intermediate isotropic elastic coating and an outer isotropic elastic matrix with simultaneous interface slip and diffusion occurring on the solid–solid interface when the matrix is subjected to a uniform hydrostatic stress field. We design a neutral coated hypotrochoidal liquid inclusion that does not disturb the prescribed uniform hydrostatic stress field in the surrounding matrix. The neutrality is achieved when the plane-strain bulk modulus or the compressibility of the elastic matrix is determined by solving a system of simultaneous linear algebraic equations for given geometric and material parameters of the coated liquid inclusion.

Non-invasive regional parameter identification of degenerated human meniscus

Accurate identification of local changes in the biomechanical properties of the normal and degenerative meniscus is critical to better understand knee joint osteoarthritis onset and progression. Ex-vivo material characterization is typically performed on specimens obtained from different locations, compromising the tissue's structural integrity and thus altering its mechanical behavior. Therefore, the aim of this in-silico study was to establish a non-invasive method to determine the region-specific material properties of the degenerated human meniscus. In a previous experimental magnetic resonance imaging (MRI) study, the spatial displacement of the meniscus and its root attachments in mildly degenerated (n = 12) and severely degenerated (n = 12) cadaveric knee joints was determined under controlled subject-specific axial joint loading. To simulate the experimental response of the lateral and medial menisci, individual finite element models were created utilizing a transverse isotropic hyper-poroelastic constitutive material formulation. The superficial displacements were applied to the individual models to calculate the femoral reaction force in an inverse finite element analysis. During particle swarm optimization, the four most sensitive material parameters were varied to minimize the error between the femoral reaction force and the force applied in the MRI loading experiment. Individual global and regional parameter sets were identified. In addition to in-depth model verification, prediction errors were determined to quantify the reliability of the identified parameter sets. Both compressibility of the solid meniscus matrix (+141 %, p ≤ 0.04) and hydraulic permeability (+53 %, p ≤ 0.04) were significantly increased in the menisci of severely degenerated knees compared to mildly degenerated knees, irrespective of the meniscus region. By contrast, tensile and shear properties were unaffected by progressive knee joint degeneration. Overall, the optimization procedure resulted in reliable and robust parameter sets, as evidenced by mean prediction errors of <1 %. In conclusion, the proposed approach demonstrated high potential for application in clinical practice, where it might provide a non-invasive diagnostic tool for the early detection of osteoarthritic changes within the knee joint.

Matrix Compression and Pore Heterogeneity in the Coal-Measure Shale Reservoirs of the Qinshui Basin: A Multifractal Analysis

The application of high-pressure fluid induces the closure of isolated pores inside the matrix and promotes the generation of new fractures, resulting in a compressive effect on the matrix. To examine the compressibility of coal-measure shale samples, the compression of the coal–shale matrix in the high-pressure stage was analyzed by a low-pressure nitrogen gas adsorption and mercury intrusion porosimetry experiment. The quantitative parameters describing the heterogeneity of the pore-size distribution of coal-measure shale are obtained using multifractal theory. The results indicate that the samples exhibit compressibility values ranging from 0.154 × 10−5 MPa−1 to 4.74 × 10−5 MPa−1 across a pressure range of 12–413 MPa. The presence of pliable clay minerals enhances the matrix compressibility, whereas inflexible brittle minerals exhibit resistance to matrix compression. There is a reduction in local fluctuations of pore volume across different pore sizes, an improvement in the autocorrelation of PSD, and a mitigation of nonuniformity after correction. Singular and dimension spectra have advantages in multifractal characterization. The left and right spectral width parameters of the singular spectrum emphasize the local differences between the high- and low-value pore volume areas, respectively, whereas the dimensional spectrum width is more suitable for reflecting the overall heterogeneity of the PSD.

Re-Calibrating the Mercury-Intrusion-Porosimetry-Measured Pore Size Distribution of Coals: A Novel Method for Calculating the Matrix Compression Coefficient

Accurate measurement of the pore size distribution (PSD) in coals is crucial for guiding subsequent coalbed methane (CBM) engineering practice. Currently, mercury intrusion porosimetry (MIP) measurement has been widely used as a PSD testing method due to its effectiveness and convenience. Nevertheless, it is worth noting that the elevated pressure during the MIP experiments can lead to matrix compressibility, potentially causing inaccurate estimations of PSD in coals. Therefore, correction methods are used to modify the PSD in the high-pressure segment to improve the accuracy of MIP data. This study proposed a novel method with higher accuracy and convenience for calculating the matrix compressibility coefficient compared to the traditional calculation methods. Firstly, the matrix compressibility coefficients of six coal samples were calculated by using low-temperature nitrogen adsorption (LTNA) data. Subsequently, by utilizing the mathematical correlation between Kc (the compressibility coefficient of the coal matrix) and Ro,max (the maximum vitrinite reflectance) from prior research, a novel statistical method was designed to determine the matrix compressibility coefficient of the samples. Finally, the statistical matrix compressibility coefficient determination method was used to examine the fractal characteristics of the actual PSD. The results indicate that when the pressure exceeds 24 MPa, the volume obtained from mercury intrusion exceeds the pore volume measurement. The Kc calculated using the traditional correction method is in the range of 0.876–1.184 × 10−10 m2/N, while the Kc values of our proposed statistical correction method range from 0.898 × 10−10 to 1.233 × 10−10 m2/N, with a comparison error rate of ~0.11–5.25%. The MIP data greater than 24 MPa were effectively corrected using the statistical correction method, thus reducing the mercury intrusion volume error by 91.75–96.40%. Additionally, the corrected pore fractal dimension (D2) values fall within the range of 2.792 to 2.975, which are closer to the actual values than the pore fractal dimension range of 3.186 to 3.339.

Matrix Compressibility and Multifractal Nature of Nanoporous Shale

Matrix Compressibility and Multifractal Nature of Nanoporous Shale

The impact of vascular volume fraction and compressibility of the interstitial matrix on vascularised poroelastic tissues.

In this work we address the role of the microstructural properties of a vascularised poroelastic material, characterised by the coupling between a poroelastic matrix and a viscous fluid vessels network, on its overall response in terms of pressures, velocities and stress maps. We embrace the recently developed model (Penta and Merodio in Meccanica 52(14):3321-3343, 2017) as a theoretical starting point and present the results obtained by solving the full interplay between the microscale, represented by the intervessels' distance, and the macroscale, representing the size of the overall tissue. We encode the influence of the vessels' density and the poroelastic matrix compressibility in the poroelastic coefficients of the model, which are obtained by solving appropriate periodic cell problem at the microscale. The double-poroelastic model (Penta and Merodio 2017) is then solved at the macroscale in the context of vascular tumours, for different values of vessels' walls permeability. The results clearly indicate that improving the compressibility of the matrix and decreasing the vessels' density enhances the transvascular pressure difference and hence transport of fluid and drug within a tumour mass after a transient time. Our results suggest to combine vessel and interstitial normalization in tumours to allow for better drug delivery into the lesions.

Quantifying and Controller Determination of Shale Matrix Compressibility: Implications for Pore Structure and Gas Flow Behavior Analyses

Quantifying and Controller Determination of Shale Matrix Compressibility: Implications for Pore Structure and Gas Flow Behavior Analyses

Matrix Compressibility and Its Controlling Factors of the Marine Shale Gas Reservoir: A Case Study of the Ning228 Well in the Southwest Sichuan Basin, China

Exploring the compressibility of the deeply buried marine shale matrix and its controlling factors can help achieve efficient petroleum production. Taking ten sets of deeply buried marine shale core samples from Ning228 wells in the Yanjin area as an example, the matrix compressibility and pore characteristics of deeply buried marine shale reservoirs were investigated by applying mercury intrusion porosimetry (MIP) and nitrogen adsorption/desorption isotherms at a low temperature of 77 K. Mathematical models (based on MIP and nitrogen adsorption/desorption isotherms) were established to analyze the effects of TOC, mineral components, and pore structure on matrix compressibility. The relationship between the compressibility coefficient and the brittleness index was also established. The results show that the compressibility of the shale matrix is significant when the mercury injection pressure ranges from 8.66 to 37 MPa. For deeply buried marine shale, the matrix compressibility is in the range of 0.23 × 10−4–22.03 × 10−4 MPa−1. The influence of TOC and minerals on matrix compressibility is mainly reflected in the control effect of pore structure. High TOC content decreases the overall shale elastic modulus, and high clay mineral content enhances shale stress sensitivity, resulting in a significant matrix compressibility effect. For the effect of pore structure on compressibility, the pore content in shale has a positive effect on matrix compressibility. In addition, the pore-specific surface area is critical to the effective variation of shale matrix compressibility, indicating that the complexity of the shale pore structure is a key factor affecting matrix compressibility.

Design of Silicon Rubber/BN Film with High Through-plane Thermal Conductivity and Ultra-low Contact Resistance

Polymer-hexagonal boron nitride (BN) composite has become an ideal thermal interface material (TIM) for electronic devices because of its high thermal conductivity and superior electronic insulation. However, owing to the 2D shape and chemical inertness of BN filler, the vertical alignment of BN and the huge thermal resistance are current challenges, which hinder the efficient heat transfer of polymer/BN composites. Herein, by a novel non-solvent induced phase separation process combined “in-situ welding” strategy, we present the fabrication of silicone rubber film with finger-like continuous BN-welded filler skeleton, which reveals a high through-plane thermal conductivity of 15.4 W m−1K−1 at only ∼ 15 wt% BN. Finite element simulation and nonlinear model analyses theoretically confirm that the filler-to-filler interfacial thermal resistance (ITR) is halved after in-situ welding process. In addition, thanks to the excellent compressibility and conformability of silicon rubber matrix, the contact thermal resistance (<70 Kmm2W−1) of this composite film is much lower than that of the commercial thermal pad under different pressure. The proposed strategy opens up a novel and high-throughput preparation strategy for the high-performance TIM for modern electronic devices.

Feasibility of melt segregation from a crystal mush in response to the 2011–2012 eruption at Cordón Caulle, Chile

SUMMARY The 2011–2012 eruption at Cordón Caulle in Chile produced crystal-poor rhyolitic magma with crystal-rich mafic enclaves whose interstitial glass is of identical composition to the host rhyolite. Eruptible rhyolites are thought to be genetically associated with crystal-rich magma mushes, and the enclaves within the Cordón Caulle rhyolite support the existence of a magma mush from which the erupted magma was derived. Moreover, towards the end of the 2011–2012 eruption, subsidence gave way to inflation that has on average been continuous through at least 2020. We hypothesize that magma segregation from a crystal mush could be the source of the observed inflation. Conceptually, magma withdrawal from a crystal-poor rhyolite reservoir caused its depressurization, which could have led to upward flow of interstitial melt within an underlying crystal mush, causing a new batch of magma to segregate and partially recharge the crystal-poor rhyolite body. Because the compressibility of the crystalline matrix of the mush is expected to be lower than that of the interstitial melt, which likely contains some fraction of volatile bubbles, this redistribution of melt would result in a net increase in volume of the system and in the observed inflation. We use numerical modelling of subsurface magma flow and storage to show under which conditions such a scenario is supported by geodetic and petrologic observations.

Pore‐Fracture Distribution Heterogeneity of Shale Reservoirs Determined by using HPMI and LPN2 GA Tests

AbstractThe compressibility of shale matrix reflects the effects of reservoir lithology, material composition, pore structure and tectonic deformation. It is important to understand the factors that influence shale matrix compressibility (SMC) and their effects on pore size distribution (PSD) heterogeneity in order to evaluate the properties of unconventional reservoirs. In this study, the volumes of pores whose diameters were in the range 6–100 nm were corrected for SMC for 17 shale samples from basins in China using high‐pressure mercury intrusion and low‐temperature nitrogen gas adsorption analyses, in order to investigate the factors influencing the SMC values. In addition, the variations in fractal dimensions before and after pore volume correction were determined, using single and multifractal models to explain the effects of SMC on PSD heterogeneity. In this process, the applicability of each fractal model for characterizing PSD heterogeneity was determined using statistical analyses. The Menger and Sierpinski single fractal models, the thermodynamic fractal model and a multi‐fractal model were all used in this study. The results showed the following. The matrix compression restricts the segmentation of the fractal dimension curves for the single fractal Menger and Sierpinski models, which leads to a uniformity of PSD heterogeneity for different pore diameters. However, matrix compression has only a weak influence on the results calculated using a thermodynamic model. The SMC clearly affects the multifractal value variations, showing that the fractal dimension values of shale samples under matrix compression are small. Overall PSD heterogeneity becomes small for pores with diameters below 100 nm and the SMC primarily affects the PSD heterogeneity of higher pore volume areas. The comparison of fractal curves before and after correction and the variance analysis indicate that the thermodynamic model is applicable to quantitatively characterize PSD heterogeneity of shale collected from this sampling area. The results show that PSD heterogeneity increases gradually as micro‐pore volumes increase.

A fully explicit staggered algorithm for near‐field wave propagation of fluid‐saturated porous media based on u‐p dynamic formulation

AbstractNear‐field wave propagation of the fluid‐saturated porous media (FSPM) is an important issue in soil dynamics and geotechnical earthquake engineering. In the current study, a fully explicit staggered algorithm for the near‐field wave propagation analysis of the FSPM in the time domain is developed based on the u‐p dynamic formulation. The decoupling of dynamic formulation is implemented by the diagonalization of the mass matrix and pore fluid compressibility matrix. The central difference method and Newmark constant average acceleration method are used for the solution of the displacement and velocity of solid skeleton, and the backward difference method is used for the solution of pore fluid pressure in the time domain. The effectiveness and feasibility of the matrix diagonalization are verified by the comparison with the classical numerical algorithm. The proposed algorithm is also validated by the comparison of the numerical results with the corresponding analytical solution results. Combing with the transmitting artificial boundary condition, the proposed algorithm is then applied to investigate the seismic response of a FSPM free field, and its applicability to the typical near‐field wave propagation problems of the FSPM is indicated. The stability analysis of the proposed algorithm is finally conducted, and the corresponding stability criterion is presented. For the proposed algorithm, all the dynamic variables of the FSPM are solved in an iterative way and the coupling dynamic equations need not to be solved at each time step. The computational effort can be reduced considerably, and the computational efficiency can be improved remarkably.

Characterization of Coal Pore Structure and Matrix Compressibility by Water Vapor Injection

Characterization of Coal Pore Structure and Matrix Compressibility by Water Vapor Injection

Characterization of Full Pore and Stress Compression Response of Reservoirs With Different Coal Ranks

The accurate characterization of coal pore structure is significant for coalbed methane (CBM) development. The splicing of practical pore ranges of multiple test methods can reflect pore structure characteristics. The pore\fracture compressibility is the main parameter affecting the porosity and permeability of coal reservoirs. The difference in compressibility of different coal rank reservoirs and pore\fracture structures with changing stress have not been systematically found. The pore structure characteristics of different rank coal samples were characterized using the optimal pore ranges of high-pressure mercury intrusion (HPMI), low-temperature liquid nitrogen adsorption (LT-N2A), low-pressure carbon dioxide adsorption (LP-CDA), and nuclear magnetic resonance (NMR) based on six groups of different rank coal samples. The compressibility of coal matrix and pore\fracture were studied using HPMI data and NMR T2 spectrum under effective stress. The results show that the more accurate full pore characterization results can be obtained by selecting the optimal pore range measured by HPMI, LT-N2A, and LP-CDA and comparing it with the NMR pore results. The matrix compressibility of different rank coal samples shows that low-rank coal &amp;gt; high-rank coal &amp;gt; medium-rank coal. When the effective stress is less than 6 MPa, the microfractures are compressed rapidly, and the compressibility decreases slowly when the effective stress is more than 6 MPa. Thus, the compressibility of the adsorption pore is weak. Nevertheless, the adsorption pore has the most significant compression space because of the largest proportion in different pore structures. The variation trend of matrix compressibility and pore\fracture compressibility is consistent with the increase of coal rank. The compressibility decreases with the rise of reservoir heterogeneity and mechanical strength. The development of pore volume promotes compressibility. The research results have guiding significance for the exploration and development of CBM in different coal rank reservoirs.

Experimental evaluation of liquid nitrogen fracturing on the development of tight gas carbonate rocks in the Lower Indus Basin, Pakistan

Tight gas carbonate formations have enormous potential to meet the supply and demand of the ever-growing population. However, it is impossible to produce from these formations due to the reduced permeability and lower marginal porosity. Several methods have been used to extract unconventional tight gas from these reservoirs, including hydraulic fracturing and acidizing. However, field studies have demonstrated that these methods have environmental flaws and technical problems. Liquid nitrogen (LN2) fracturing is an effective stimulation technique that provides sudden thermal stress in the rock matrix, creating vivid fractures and improving the petro-physical potential. In this study, we acquired tight gas carbonate samples and thin sections of rock from the Laki limestone formation in the Lower Indus Basin, Pakistan, to experimentally quantify the effects of LN2 fracturing. Initially, these samples were characterized based on mineralogical (X-ray diffraction), petrography, and petro-physical (permeability and porosity) properties. Additionally, LK-18-06 Laki limestone rock samples were exposed to LN2 for different time intervals (30, 60, and 90 mins), and various techniques were applied to comprehend the effects of the LN2 before and after treatment, such as atomic force microscopy, scanning electron microscopy, energy-dispersive spectroscopy, nano-indentation, and petro-physical characterization. Our results reveal that the LN2 treatment was very effective and induced vivid fractures of up to 38 µm. The surface roughness increased from 275to 946 nm, and indentation moduli significantly decreased due to the decreased compressibility of the rock matrix. Petro-physical measurements revealed that the porosity increased by 47% and that the permeability increased by 67% at an optimum LN2 treatment interval of 90 mins. This data can aid in an accurate assessment of LN2 fracturing for the better development of unconventional tight gas reservoirs.

Changes in rock matrix compressibility during deep CO2 storage

AbstractGeologic carbon storage projects aim to permanently trap large volumes of CO2 in reservoir rock sealed with low permeability layers. As high‐pressure supercritical or liquid CO2 is injected, hydromechanical and chemical processes caused by the reaction between the rock and acidic mixture of brine and CO2 are initiated. The compressibility of reservoir rock needs to be properly characterized in order to assess the deformation and stability of the host formations, and there are a number of factors to be considered, including the matrix structure, solid, pores, and fluid. This study triggers from a fundamental question whether CO2 treatment affects the compressibility of the rock matrix and its dominant composing solid minerals. Three different reservoir representatives are selected: Berea sandstone for silica‐rich rock, and Apulian limestone and Indiana limestone for calcite‐rich rock. Quartz and calcite are the main composing minerals of the reservoir rock, and their crystals are separately examined. Experimental methods are introduced for high‐pressure CO2 treatment of water‐saturated materials, and measurements of the unjacketed and solid compressibilities are conducted. No change in the solid compressibility of the sandstone and quartz after CO2 treatment is observed, whereas it increases by 18–21% for the limestones and by 15% for calcite. The latter observation is inconsistent with the ultrasonic wave velocities measurements and is believed to be due to the local dissolution of the calcite crystal surface. The results show that only the solid matrix of the limestones becomes more compressible after CO2 treatment. Consequent microimaging and mercury intrusion porosimetry analyses allowed observations of dissolution and precipitation of calcite, and creation of new connected and non‐connected pores. Finally, the changes in limestone solid compressibilities and pore structure could significantly affect the rock properties and behavior during and after CO2 injection and should be accounted for in the reservoir models. © 2021 Society of Chemical Industry and John Wiley &amp; Sons, Ltd.

Development of a Simpler but Accurate Free Gas Deviation Factor for Fractured (Dual-Porosity) Volumetric Gas Reservoir Fluid

Gas compressibility factor, also known as gas deviation factor or Z-factor, is a thermodynamic correction factor which describes the deviation of a real gas from ideal gas behaviour. The, free gas Z-factor in the Material Balance Equation (MBE) of single-porosity gas reservoirs with insignificant rock (matrix) compaction (after pressure depletion) does not reflect cases in low-permeability gas reservoirs having remarkable rock compaction. Through gas MBE modifications, previous researchers developed Z-factors for dual-porosity (fractured) low permeability gas reservoirs by incorporating gas desorption; however, their approaches create complexity for routine calculations. Therefore this study was designed with the purpose of deriving a free gas Z-factor for single-porosity low-permeability gas reservoirs and further modifying it for more simplicity and accuracy in a dual-porosity scenario. The free gas Z-factor derived for single-porosity low-permeability gas reservoirs is expressed as: where , , , , and are single-porosity Z-factor without rock compaction at pressure , water compressibility, initial water saturation, matrix compressibility, initial gas saturation and pressure depletion, respectively. However, the developed dual porosity free gas Z-factor model incorporates ratio of dual porosity to initial matrix porosity, and it is expressed as: where and are initial matrix porosity and fracture porosity, respectively. The Z-factor model was graphically and statistically correlated with an existing free gas Z-factor model for dual porosity reservoirs. For all the hydraulically fractured shale gas formations considered, the correlations yield R2 values of 1.000.

Integrated characterization of the fracture network in fractured shale gas Reservoirs—Stochastic fracture modeling, simulation and assisted history matching

The large uncertainty in fracture characterization for shale gas reservoirs seriously affects the confidence in making forecasts, fracturing design, and taking recovery enhancement measures. It is of significance to make the most of multiple data in fracture characterization, including the measurements of hydraulic fracturing treatment, core, microseismic, production data, etc. Besides, handling the complex fracture networks (CFNs) explicitly is demanded in large-scale field case studies. This paper presents an efficient method to characterize the complex fracture networks (CFNs) and reduce the uncertainties by integrating stochastic CFNs modeling, reservoir simulation, and assisted history matching. In CFNs modeling, the geometry of CFNs is generated stochastically constrained by the measurements of hydraulic fracturing treatment, core, and microseismic data, and a stochastic parameterization model is used to generate an ensemble of initial realizations of the stress-dependent fracture conductivities. To efficiently simulate the discrete fractures in field cases, the edge-based Green Element Method (eGEM) is modified by applying a steady-state fundamental solution and the technique of local grid refinement (LGR). Assisted-history-matching based on EnKF is implemented to calibrate the CFNs models and further quantify the uncertainties. The proposed method is applied to a field case from a multi-fractured horizontal shale gas well. The results show that the computation of the modified eGEM is much cheaper than the original eGEM when the steady-state fundamental solution and the technique of LGR are applied. Besides, acceptable precision can be obtained with relative coarse grids, for example, 50 m primary grids and 25 m refined grids near the fractures can be used in the test case. These advantages make the modified eGEM quite efficient in assisted history matching of large-scale field applications. The history matching results and EUR distributions show that the uncertainties are significantly reduced after 5 steps assimilation, and good results can be obtained after 10 steps assimilation. The distribution ranges of the matrix permeability and porosity are significantly narrowed down after history matching, while the matrix compressibility is hard to be determined because the rock compressibility is so small comparing to gas compressibility that gas production is not sensitive to it. The results also show that only part of the fractures are well-propped because only the fractures in a certain range of the wellbore are with good properties, that is high initial fracture conductivities and low conductivity moduli. • An integrated method for complex fracture networks (CFNs) characterization. • Geological, seismic, fracturing and production data can be assimilated. • An efficient froward model for field-scale reservoir simulation with CFNs. • Property calibration and uncertainty quantification of CFNs.

Comprehensive evaluation and interpretation of mercury intrusion porosimetry data of coals based on fractal theory, Tait equation and matrix compressibility

Accurate characterization of coal pore structure is vital for understanding the mechanism of gas storage and migration. As an effective method for pore evaluation, mercury intrusion porosimetry (MIP) remains questionable without addressing the effects of interparticle voids filling and matrix compression properly. In this study, three intact coal samples with different metamorphic grades, one tectonic coal sample and two activated carbon (AC) samples were selected. Fractal theory was applied to identify the three stages of MIP test and to simulate the interparticle voids volume quantitatively using extrapolation method. Compared with the conventional matrix compressibility (MC) method for MIP data correction, we put forward the semi-empirical Tait equation (TE) method to compensate for the deficiencies of MC method. The results indicate that the simultaneous mercury filling of interparticle voids account for 1.9–3.4% of the total intrusion volumes for coals and 8.3% for AC. However, the proportions of matrix compression could reach 46.72–80.41% for coals and 14.30% for AC. In combination with low pressure N2 gas adsorption (LPN2GA) method, total pore volume (TPV) in the range of 33–320 nm from TE method is in closer proximity to the results using Barret-Joyner-Halenda (BJH) model. Whereas, MC method is superior in correcting MIP data of smaller pore sizes (7–33 nm). Overlapped pore size distributions (PSD) indicate that peak numbers, peak positions and incremental pore volumes of MIP corrected data show good consistency with LPN2GA measurement. For samples of low strength and with abundant ink-bottle shaped pores, it is inappropriate to correct their MIP data.

Shale Poroelastic Effects on Well Performance Analysis of Shale Gas Reservoirs

The effect of poroelastic properties of the shale matrix on gas storage and transport mechanisms has gained significant attention, especially during history-matching and hydrocarbon production forecasting in unconventional reservoirs. The common oil and gas industry practice in unconventional reservoir simulation is the extension of conventional reservoir simulation that ignores the dynamic behavior of matrix porosity and permeability as a function of reservoir effective net stress. This approach ignores the significant impact of the poroelastic characteristics of the shale matrix on hydrocarbon production. The poroelastic characteristics of the shale matrix highly relate to the shale matrix geomechanical properties, such as the Young’s Modulus, Poisson’s ratio, bulk modulus, sorption behavior, total organic content (TOC), mineralogy and presence of natural fractures in the multi-scale shale structure. In this study, in order to quantify the effect of the poroelasticity of the shale matrix on gas production, a multi-continuum approach was employed in which the shale matrix was divided into organic materials, inorganic materials and natural fractures. The governing equations for gas transport and storage in shale were developed from the basic fundamentals of mass and momentum conservation equations. In this case, gas transport in organics was assumed to be diffusive, while gas transport in inorganics was governed by convection. Finally, a fracture system was added to the multi-scale shale gas matrix, and the poroelastic effect of the shale matrix on transport and storage was investigated. A modified Palmer and Mansoori model (1998) was used to include the pore compression, matrix swelling/shrinkage and desorption-induced deformation of shale organic matter on the overall pore compressibility of the shale matrix. For the inorganic part of the matrix, relations between rock mechanical properties and the pore compressibility were obtained. A dual Langmuir–Henry isotherm was also used to describe the sorption behavior of shale organic materials. The coupled governing equations of gas storage and transport in the shale matrix were then solved using the implicit finite difference approach using MATLAB. For this purpose, rock and fluid properties were obtained using actual well logging and core analysis of the Marcellus gas well. The results showed the importance of the poroelastic effect on the pressure response and rate of gas recovery from the shale matrix. The effect was found to be mainly due to desorption-induced matrix deformation at an early stage. Coupling the shale matrix gas production including the poroelastic effect in history-matching the gas production from unconventional reservoirs will significantly improve engineering completion design optimization of the unconventional reservoirs by providing more accurate and robust production forecasts for each hydraulic fracture stage.