Characterizing permeability-porosity relationships of porous rocks using a stress sensitivity model in consideration of elastic-structural deformation and tortuosity sensitivity

Clarifying the relationship between stress sensitivities of permeability and porosity is of great significance in guiding underground resource mining.More and more studies focus on how to construct stress sensitivity models to describe the relationship and obtain a comprehensive stress sensitivity of porous rock.However,the limitations of elastic deformation calculation and incompleteness of considered tortuosity sensitivity lead to the fact that the existing stress sensitivity models are still unsatisfactory in terms of accuracy and generalization.Therefore,a more accurate and generic stress sensitivity model considering elastic-structural deformation of capillary cross-section and tortuosity sensitivity is proposed in this paper.The elastic deformation is derived from the fractal scaling model and Hooke's law.Considering the effects of elastic-structural deformation on tortuosity sensitivity,an empirical formula is proposed,and the conditions for its applicability are clarified.The predictive performance of the proposed model for the permeability-porosity relationships is validated in several sets of publicly available experimental data.These experimental data are from different rocks under different pressure cycles.The mean and standard deviation of relative errors of predicted stress sensitivity with respect to experimental data are 2.63%and 1.91%.Compared with other models,the proposed model has higher accuracy and better predictive generalization performance.It is also found that the porosity sensitivity exponent a,which can describe permeability-porosity relationships,is 2 when only elastic deformation is considered.a decreases from 2 when structural deformation is also considered.In addition,a may be greater than 3 due to the increase in tortuosity sensitivity when tortuosity sensitivity is considered even if the rock is not fractured.

Micromechanism and mathematical model of stress sensitivity in tight reservoirs of binary granular medium

Research on reservoir rock stress sensitivity has traditionally focused on unary granular structures,neglecting the binary nature of real reservoirs,especially tight reservoirs.Understanding the stresssensitive behavior and mathematical characterization of binary granular media remains a challenging task.In this study,we conducted online-NMR experiments to investigate the permeability and porosity evolution as well as stress-sensitive control mechanisms in tight sandy conglomerate samples.The results revealed stress sensitivity coefficients between 0.042 and 0.098 and permeability damage rates ranging from 65.6%to 90.9%,with an average pore compression coefficient of 0.0168—0.0208 MPa 1.Pore-scale compression occurred in three stages:filling,compression,and compaction,with matrix pores playing a dominant role in pore compression.The stress sensitivity of binary granular media was found to be influenced by the support structure and particle properties.High stress sensitivity was associated with small fine particle size,high fines content,high uniformity coefficient of particle size,high plastic deformation,and low Young's modulus.Matrix-supported samples exhibited a high irreversible permeability damage rate(average=74.2%)and stress sensitivity coefficients(average=0.089),with pore spaces more slit-like.In contrast,grain-supported samples showed low stress sensitivity coefficients(average=0.021)at high stress stages.Based on the experiments,we developed a mathematical model for stress sensitivity in binary granular media,considering binary granular properties and nested interactions using Hertz contact deformation and Poiseuille theory.By describing the change in activity content of fines under stress,we characterized the non-stationary state of compressive deformation in the binary granular structure and classified the reservoir into three categories.The model was applied for production prediction using actual data from the Mahu reservoir in China,showing that the energy retention rates of support-dominated,fill-dominated,and matrix-controlled reservoirs should be higher than 70.1%,88%,and 90.2%,respectively.

High-Precision Flow Numerical Simulation and Productivity Evaluation of Shale Oil Considering Stress Sensitivity

Continental shale oil reservoirs,characterized by numerous bedding planes and micro-nano scale pores,feature significantly higher stress sensitivity compared to other types of reservoirs.However,research on suitable stress sensitivity characterization models is still limited.In this study,three commonly used stress sensitivity models for shale oil reservoirs were considered,and experiments on representative core samples were conducted.By fitting and comparing the data,the“exponential model”was identified as a characterization model that accurately represents stress sensitivity in continental shale oil reservoirs.To validate the accuracy of the model,a two-phase seepage mathematical model for shale oil reservoirs coupled with the exponential model was introduced.The model was discretely solved using the finite volume method,and its accuracy was verified through the commercial simulator CMG.The study evaluated the productivity of a typical horizontal well under different engineering,geological,and fracture conditions.The results indicate that considering stress sensitivity leads to a 13.57%reduction in production for the same matrix permeability.Additionally,as the fracture half-length and the number of fractures increase,and the bottomhole flowing pressure decreases,the reservoir stress sensitivity becomes higher.

Stress sensitivity of carbonate gas reservoirs and its microscopic mechanism

In order to evaluate the stress sensitivity of carbonate reservoirs,a series of rock stress sensitivity tests were carried out under in-situ formation temperature and stress condition.Based on the calibration of capillary pressure curve,the variable fractal dimension was introduced to establish the conversion formula between relaxation time and pore size.By using the nuclear magnetic resonance(NMR)method,the pore volume loss caused by stress sensitivity within different scales of pore throat was quantitatively analyzed,and the microscopic mechanism of stress sensitivity of carbonate gas reservoirs was clarified.The results show that fractures can significantly affect the stress sensitivity of carbonate reservoirs.With the increase of initial permeability,the stress sensitivity coefficient decreases and then increases for porous reservoirs,but increases monotonously for fractured-porous reservoirs.The pore volume loss caused by stress sensitivity mainly occurs for mesopores(0.02–0.50μm),contributing more than 50%of the total volume loss.Single high-angle fracture contributes 9.6%of the stress sensitivity and 15.7%of the irreversible damage.The microscopic mechanism of the stress sensitivity of carbonate gas reservoirs can be concluded as fracture closure,elastic contraction of pores and plastic deformation of rock skeleton.

Effect of stress sensitivity on displacement efficiency in CO_2 flooding for fractured low permeability reservoirs

Carbon dioxide flooding is an effective means of enhanced oil recovery for low permeability reservoirs. If fractures are present in the reservoir, CO2 may flow along the fractures, resulting in low gas displacement efficiency. Reservoir pore pressure will fluctuate to some extent during a CO2 flood, causing a change in effective confining pressure. The result is rock deformation and a reduction in permeability with the reduction in fracture permeability, causing increased flow resistance in the fracture space. Simultaneously, gas cross flowing along the fractures is partially restrained. In this work, the effect of stress changes on permeability was studied through a series of flow experiments. The change in the flowrate distribution in a matrix block and contained fracture with an increase in effective pressure were analyzed. The results lead to an implicit comparison which shows that permeability of fractured core decreases sharply with an increase in effective confining pressure. The fracture flowrate ratio declines and the matrix flowrate ratio increases. Fracture flow will partially divert to the matrix block with the increase in effective confining pressure, improving gas displacement efficiency.

Stress sensitivity of formation during multi-cycle gas injection and production in an underground gas storage rebuilt from gas reservoirs

Permeability sensitivity to stress experiments were conducted on standard core samples taken from Wen 23 Gas Storage at multi-cycle injection and production conditions of the gas storage to study the change pattern of stress sensitivity of permeability.A method for calculating permeability under overburden pressure in the multi-cycle injection and production process was proposed,and the effect of stress sensitivity of reservoir permeability on gas well injectivity and productivity in UGS was analyzed.Retention rate of permeability decreased sharply first and then slowly with the increase of the UGS cycles.The stress sensitivity index of permeability decreased with the increase of cycle number of net stress variations in the increase process of net stress.The stress sensitivity index of permeability hardly changed with the increase of cycle number of net stress variations in the decrease process of net stress.With the increase of cycle number of net stress variation,the stress sensitivity index of permeability in the increase process of net stress approached that in the decrease process of net stress.The lower the reservoir permeability,the greater the irreversible permeability loss rate,the stronger the cyclic stress sensitivity,and the higher the stress sensitivity index of the reservoir,the stronger the reservoir stress sensitivity.The gas zones with permeability lower than 0.3’10-3 mm2 are not suitable as gas storage regions.Stress sensitivity of reservoir permeability has strong impact on gas well injectivity and productivity and mainly in the first few cycles.

A Reasonable Approach for the Development of Shale Gas Wells with Consideration of the Stress Sensitivity

High-pressure deep shale gas reservoirs are usually highly stress-sensitive.When the reasonable production mode of shale gas well is built,the impact of strong stress sensitivity should be fully considered.First,this study calculated the relationship between permeability and formation pressure under different elastic modulus based on the shale lithology of Long Ma Xi formation in Sichuan Basin by testing and analysing the mechanical parameters of the rock.According to numerical simulation result,when the elastic modulus exceeds 14.0 GPa,the stress sensitivity of the matrix will slight affect the cumulative gas production of shale gas.Second,the changing relation between fracture conductivity and permeability with fracture pressure and the time of pressure acts were experimentally studied.The numerical simulation result suggested that the 30-year cumulative gas production considering the stress sensitivity was reduced by 13.5%compared with the 30-year cumulative gas production without considering the stress sensitivity.Finally,the production of different production modes under different stress sensitive characteristics was predicted using numerical simulation method.When the matrix and fractures are fixed with a same stress-sensitive curve,the initial production allocation will not significantly impact the cumulative gas production.When the fractured fractures are subjected to a varying stress sensitive curve,the lower production allocation will result in higher post-production and cumulative gas production.

Stress sensitivity of coal samples in terms of anisotropy

The permeability and porosity of coal seams are anisotropic, and the variation of confining stress may induce deformation in coal samples. In order to study these characteristics, experiments and model analyses were conducted to understand the behaviors of anisotropic stress sensitivity of lean coal samples. The results showed as the closure of cleats and the generation of micro-cracks, the strong stress sensitivity of coal samples and the discrete changes in porosity were caused by confining pressure changes. In the compression period, the anisotropy trend first increased, and then decreased. In the direction perpendicular to the bedding plane, the permeability decrease rate and the irreversible damage rate were the highest. In the direction parallel to the cleats, permeability recovery rate was higher and the irreversible damage rate was lower along butt cleats. Compared to the cube root of permeability to porosity, a 1/6 power relationship was proved to be closer to the experiment results, the new relationship had the highest fit level in the face cleat direction, and the lowest fit level in the vertical direction

Stress sensitivity analysis for a wide-chord fan blade using an adjoint method

High-performance compressor design is best achieved with a good trade-off between aerodynamic and structural considerations,which requires efficient and accurate multidisciplinary design and optimization tools.As advanced compressors are defined with a large design space,their optimization is most efficiently achieved using a gradient-based approach,where the gradient can be computed using an adjoint method,at a cost nearly independent of the dimension of the design space.While the adjoint method has been widely used for aerodynamic shape optimization,its use for structural shape optimizations of compressor blades has not been as well studied.This paper discussed a discrete adjoint solver for structural sensitivity analysis developed within the opensource Computational Structural Mechanics(CSM)software CalculiX,and proposed an efficient stress sensitivity analysis method based on the Finite Element Method(FEM)using adjoint.The proposed method is applied to compute the stress sensitivity of a wide-chord fan blade in a highbypass-ratio engine.The accuracy of the adjoint-based stress sensitivity is verified against central finite differences.In terms of computational efficiency,the adjoint approach is about 4.5 times more efficient than the conventional approach using finite differences.This works marks an important step towards fluid-structural coupled adjoint optimization of wide-chord fan blades.

A semi-analytical model for coupled flow in stress-sensitive multi-scale shale reservoirs with fractal characteristics

A large number of nanopores and complex fracture structures in shale reservoirs results in multi-scale flow of oil. With the development of shale oil reservoirs, the permeability of multi-scale media undergoes changes due to stress sensitivity, which plays a crucial role in controlling pressure propagation and oil flow. This paper proposes a multi-scale coupled flow mathematical model of matrix nanopores, induced fractures, and hydraulic fractures. In this model, the micro-scale effects of shale oil flow in fractal nanopores, fractal induced fracture network, and stress sensitivity of multi-scale media are considered. We solved the model iteratively using Pedrosa transform, semi-analytic Segmented Bessel function, Laplace transform. The results of this model exhibit good agreement with the numerical solution and field production data, confirming the high accuracy of the model. As well, the influence of stress sensitivity on permeability, pressure and production is analyzed. It is shown that the permeability and production decrease significantly when induced fractures are weakly supported. Closed induced fractures can inhibit interporosity flow in the stimulated reservoir volume (SRV). It has been shown in sensitivity analysis that hydraulic fractures are beneficial to early production, and induced fractures in SRV are beneficial to middle production. The model can characterize multi-scale flow characteristics of shale oil, providing theoretical guidance for rapid productivity evaluation.

Impact of effective stress on permeability for carbonate fractured-vuggy rocks

To gain insight into the flow mechanisms and stress sensitivity for fractured-vuggy reservoirs,several core models with different structural characteristics were designed and fabricated to investigate the impact of effective stress on permeability for carbonate fractured-vuggy rocks(CFVR).It shows that the permeability performance curves under different pore and confining pressures(i.e.altered stress conditions)for the fractured core models and the vuggy core models have similar change patterns.The ranges of permeability variation are significantly wider at high pore pressures,indicating that permeability reduction is the most significant during the early stage of development for fractured-vuggy reservoirs.Since each obtained effective stress coefficient for permeability(ESCP)varies with the changes in confining pressure and pore pressure,the effective stresses for permeability of four representative CFVR show obvious nonlinear characteristics,and the variation ranges of ESCP are all between 0 and 1.Meanwhile,a comprehensive ESCP mathematical model considering triple media,including matrix pores,fractures,and dissolved vugs,was proposed.It is proved theoretically that the ESCP of CFVR generally varies between 0 and 1.Additionally,the regression results showed that the power model ranked highest among the four empirical models mainly applied in stress sensitivity characterization,followed by the logarithmic model,exponential model,and binomial model.The concept of“permeability decline rate”was introduced to better evaluate the stress sensitivity performance for CFVR,in which the one-fracture rock is the strongest,followed by the fracture-vug rock and two-horizontalfracture rock;the through-hole rock is the weakest.In general,this study provides a theoretical basis to guide the design of development and adjustment programs for carbonate fractured-vuggy reservoirs.

Stress sensitivity of coal reservoir and its impact on coalbed methane production in the southern Qinshui Basin, north China

Stress sensitivity has significant negative effects on the permeability and production of coalbed methane(CBM)reservoirs.To effectively minimize these negative effects,the degree of stress sensitivity during the CBM production process should be carefully studied.In this work,the curvature of the stress-sensitivity curve was adopted to explore the degree of stress sensitivity,dividing the stress-sensitivity curve and the drainage process into five stress stages:sharp decrease,rapid decrease,low-speed decrease,slower decrease and harmless with four critical stress points—transition,sensitivity,relief and harmless.The actual stages were determined by the initial permeability,stress-sensitivity coefficient and difference between the reservoir pressure and desorption pressure.The four critical stress points did not completely exist in the stress-sensitivity curve.With an increase in the initial permeability of coal,the number of existing critical stresses increases,leading to different gas-water drainage strategies for CBM wells.For reservoirs with a certain stress-sensitivity coefficient,the permeability at the sensitive stress point was successively greater than that at the transition,relief and the harmless stresses.When the stress-sensitivity coefficient is different,the stage is different at the beginning of drainage,and with an increase in the stress-sensitivity coefficient,the decrease rate of the permeability increases.Therefore,the stress-sensitivity coefficient determines the ability to maintain stable CBM production.For well-fractured CBM reservoirs,with a high stress-sensitivity coefficient,permeability damage mainly occurs when the reservoir pressure is less than the relief stress;therefore,the depressurization rate should be slow.For CBM reservoirs with fewer natural fractures,the reverse applies,and the depressurization rate can be much faster.The higher the difference between the reservoir and desorption pressures,the higher the effective stress and permeability damage after desorption,resulting in a much longer drainage time and many difficulties for the desorption of coalbed methane.The findings of this study can help better understand and minimize the negative effects of stress sensitivity during the CBM production process.

An Arabidopsis mutant atcsr-2 exhibits high cadmium stress sensitivity involved in the restriction of H_2S emission

The gene AtCSR encodes peptidyl-prolyl cis/trans isomerases (PPIases) that accelerate energetically unfavorable cis/trans isomerization of the peptide bond preceding proline production.In our studies,we found that AtCSR was associated with cadmium (Cd)-sensitive response in Arabidopsis.Our results show that AtCSR expression was triggered by Cd-stress in wild type Arabidopsis.The expression of some genes responsible for Cd2+ transportation into vacuoles was induced,and the expression of the iron-regulated transporter 1 (IRT1) related to Cd2+ absorption from the environment was not induced in wild type with Cd2+ treatment.The expression of Cd-transportation related genes was not in response to Cd-stress,whereas IRT expression increased dramatically in atcsr-2 with Cd2+ treatment.The expression of glutathione 1 (GSH1) was consistent with GSH being much lower in atcsr-2 in comparison with the wild type with Cd2+ treatment.Additionally,malondialdehyde (MDA),hydrogen peroxide,and Cd2+ contents,and activities of some antioxidative enzymes,differed between the wild type and atcsr-2.Hydrogen sulfide (H2S) has been confirmed as the third gas-transmitter over recent years.The findings revealed that the expression pattern of H2 S-releasing related genes and that of Cd-induced chelation and transportation genes matched well in the wild type and atcsr-2,and H2S could regulate the expression of the Cd-induced genes and alleviate Cd-triggered toxicity.Finally,one possible suggestion was given:down-regulation of atcsr-2,depending on H2S gas-transmitter not only weakened Cd2+ chelation,but also reduced Cd2+ transportation into vacuoles,as well as enhancing the Cd2+ assimilation,thus rendering atcsr-2 mutant sensitive to Cd-stress.

Influence of two-step aging on structure and stress corrosion sensitivity of friction stir welded 7050-T7451 aluminum alloys

3 mm thick 7050-T7451 aluminum alloy joint was obtained by friction stir welding, and the two-step aging treatment was performed at 121 ℃ × 5 h + 163 ℃× 27 h after welding. Microstructure, hardness profiles and stress corrosion sensitivity of the joint were measured and studied. The results indicate that through the two-step aging, the grain size is coarsened, the age-hardening precipitates and PFZ become wider at the same time, which results in the discontinuous grain boundary;the microhardness of the FSW joints decreased, but the heat-affected zone significantly narrowed, which increased the uniformity of the microhardness of the FSW joints;and the two-stage aging effectively reduced the stress corrosion sensitivity of the FSW joints. The joints with aging treatment were not broken after 60 days,however all the joints without aging treatment were broken within 1 day.

Evaluation of Well Spacing for Primary Development of Fractured Horizontal Wells in Tight Sandstone Gas Reservoirs

Methods for horizontal well spacing calculation in tight gas reservoirs are still adversely affected by the complexity of related control factors,such as strong reservoir heterogeneity and seepage mechanisms.In this study,the stress sensitivity and threshold pressure gradient of various types of reservoirs are quantitatively evaluated through reservoir seepage experiments.On the basis of these experiments,a numerical simulation model(based on the special seepage mechanism)and an inverse dynamic reserve algorithm(with different equivalent drainage areas)were developed.The well spacing ranges of Classes I,II,and III wells in the Q gas field are determined to be 802–1,000,600–662,and 285–400 m,respectively,with their average ranges as 901,631,and 342.5 m,respectively.By considering both the pairs of parallel well groups and series well groups as examples,the reliability of the calculation results is verified.It is shown that the combination of the two models can reduce errors and provide accurate results.

Rate transient analysis methods for water-producing gas wells in tight reservoirs with mobile water

Tight gas reservoirs with mobile water exhibit multi-phase flow and high stress sensitivity.Accurately analyzing the reservoir and well parameters using conventional single-phase rate transient analysis methods proves challenging.This study introduces novel rate transient analysis methods incorporating evaluation processes based on the conventional flowing material balance method and the Blasingame type-curve method to examine fractured gas wells producing water.By positing a gas-water two-phase equivalent homogenous phase that considers characteristics of mobile water,gas,and high stress sensitivity,the conventional single-phase rate transient analysis methods can be applied by integrating the phase's characteristics and defining the phase's normalized parameters and material balance pseudotime.The rate transient analysis methods based on the equivalent homogenous phase can be used to quantitatively assess the parameters of wells and gas reservoirs,such as original gas-in-place,fracture half-length,reservoir permeability,and well drainage radius.This facilitates the analysis of production dynamics of fractured wells and well-controlled areas,subsequently aiding in locating residual gas and guiding the configuration of well patterns.The specific evaluation processes are detailed.Additionally,a numerical simulation mechanism model was constructed to verify the reliability of the developed methods.The methods introduced have been successfully implemented in field water-producing gas wells within tight gas reservoirs containing mobile water.

Characterization of 3D pore nanostructure and stress-dependent permeability of organic-rich shales in northern Guizhou Depression,China

The three-dimensional(3D)pore structures and permeability of shale are critical for forecasting gas production capacity and guiding pressure differential control in practical reservoir extraction.However,few investigations have analyzed the effects of microscopic organic matter(OM)morphology and 3D pore nanostructures on the stress sensitivity,which are precisely the most unique and controlling factors of reservoir quality in shales.In this study,ultra-high nanoscale-resolution imaging experiments,i.e.focused ion beam-scanning electron microscopy(FIB-SEMs),were conducted on two organic-rich shale samples from Longmaxi and Wufeng Formations in northern Guizhou Depression,China.Pore morphology,porosity of 3D pore nanostructures,pore size distribution,and connectivity of the six selected regions of interest(including clump-shaped OMs,interstitial OMs,framboidal pyrite,and microfractures)were qualitatively and quantitatively characterized.Pulse decay permeability(PDP)measurement was used to investigate the variation patterns of stress-dependent permeability and stress sensitivity of shales under different confining pressures and pore pressures,and the results were then used to calculate the Biot coefficients for the two shale formations.The results showed that the samples have high OM porosity and 85%of the OM pores have the radius of less than 40 nm.The OM morphology and pore structure characteristics of the Longmaxi and Wufeng Formations were distinctly different.In particular,the OM in the Wufeng Formation samples developed some OM pores with radius larger than500 nm,which significantly improved the connectivity.The macroscopic permeability strongly depends on the permeability of OM pores.The stress sensitivity of permeability of Wufeng Formation was significantly lower than that of Longmaxi Formation,due to the differences in OM morphology and pore structures.The Biot coefficients of 0.729 and 0.697 were obtained for the Longmaxi and Wufeng Formations,respectively.

Effects of time lag and stress loading rate on permeability in low permeability reservoirs

In order to study the effect of time lag and stress loading rates on rock deformation,the conventional stepped stress loading mode was changed into a continuous mode to investigate the effect of effective pressure on permeability and porosity.The time lag effect of rock deformation illustrating the relationship between changes in permeability and steady time was studied.Permeability reduction ratios were measured under different stress loading rates which were achieved by different pump rate settings.The results show that permeability and porosity gradually decrease with increases in effective pressure.Permeability at high effective pressure attains stability quickly.Steady times at low effective pressure are very long.Reduction in permeability at lower stress loading rates is small,while,in contrast,it is large at high stress loading rates.

Application of Heterogeneous Composite Model with Consideration of Stress Sensitive in Low Permeability Gas Reservoir

Stress sensitivity is a key factor affecting the productivity of single wells in low permeability gas reservoirs. A well test model for heterogeneous composite gas reservoirs under the influence of stress-sensitive effects was established. Based on the theoretical model, the well test was designed by gradually increasing the pressure difference. The relationship between abnormal high pressure and reservoir stress sensitivity was analyzed. Theoretical research shows that stress sensitivity will cause permeability damage during the production process, and the pressure drop test curve shows that the physical properties of the reservoir have gradually deteriorated. The pressure recovery test curve shows that the physical properties of the reservoir are getting better. Field practice shows that stress sensitivity is related to the formation of abnormally high pressure in the formation without considering the micro-cracks in the formation. Stress-sensitive reservoirs are generally unbalanced and compacted due to overpressure, for fluid expansion/conduction overpressure in Ledong Area. For these reservoirs, there is almost no stress sensitivity. The research results have significance for guiding the design and data interpretation of stress-sensitive reservoir.

In-situ observation and modeling approach to evolution of pore-fracture structure in coal

The characterisation of the pore-fracture structure(PFS)and its evolution in coal during mining are essential for preventing gas outbursts and improving gas extraction efficiency.In this study,the evolution of the PFS in coal samples under the condition of mining stress was directly captured in situ by combination of the mechanical testing system with high-precision visualisation nuclear magnetic resonance equipment.A fractional derivative model was established to describe the relationship between stress and porosity based on experimental results of the PFS under different stress states.The results showed that with an increase in the deviatoric stress,the adsorption pore content increases rapidly initially and then increases slowly or remains unchanged;the seepage pore and fracture(SPF)content decreases initially and then increases.The SPF compressibility coefficient decreases with an increase in the deviatoric stress.The fractional derivative model can accurately describe the stress sensitivity of the SPFs at the pre-peak stage,thus providing a new approach for accurately characterising the seepage characteristics of coal reservoirs.