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.

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.

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.

Time-sensitivity of the Kaiser effect of acoustic emission in limestone and its application to measurements of in-situ stress

Measuring in-situ stress by using the Kaiser effect in rocks has such advantages as timeefficiency, low cost and little limitation, but the precision of the method is dependent on rock properties and delay time of the measurement. In this paper, experiments on the Kaiser effect in limestones were performed, and it was found that the limestones had good ability to retain a memory of their recent stress history and high time-sensitivity. The longer the experiment was delayed from the extraction of the stone, the larger the Felicity ratio was. As the Felicity ratio approached l, significant Kaiser effect was observed. In-situ stress should be determined by the limestone measurements when the delay time was 40-120 days. Finally, the in-situ stress in a limestone formation could be successfully measured in practice.

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.

Anisotropic coal permeability and its stress sensitivity

This paper focuses on anisotropy of coal permeability and its stress sensitivity.Coal blocks were taken from Xinjing Coal Mine in Yangquan Coal District.Coal cores were then drilled along the strike,dip,and vertical directions.Coal permeabilities were measured with respect to stress by using a self-developed coal permeability measurement system.The used samples exhibited significant permeability anisotropy.The permeability along the strike direction was greatest among the three directions,the permeability along the vertical direction was the smallest,and the permeability along the dip direction was between the other two directions.The sensitivity of coal permeability to stress was transversely isotropic.The stress sensitivity coefficient was greater along the horizontal directions than along the vertical directions.Coal permeability exhibited anisotropic stress sensitivity due to anisotropy in Young’s modulus and porosity.The results obtained in this study are useful for optimizing the arrangement of pre-drainage boreholes.

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 tight reservoirs during pressure loading and unloading process

Laboratory experiments were conducted on laboratory-made tight cores to investigate the stress-dependent permeability hysteresis of tight reservoirs during pressure loading and unloading process. Based on experiment results, and Hertz contact deformation principle, considering arrangement and deformation of rock particles, a quantitative stress dependent permeability hysteresis theoretical model for tight reservoirs was established to provide quantitative analysis for permeability loss. The model was validated by comparing model calculated results and experimental results. The research results show that during the early pressure-loading period, structural deformation and primary deformation worked together, rock permeability reduced dramatically with increasing effective stress. When the effective stress reached a certain value, the structural deformation became stable while the primary deformation continued; the permeability variation tended to be smooth and steady. In the pressure unloading process, the primary deformation recovered with the decreasing effective stress, while the structural deformation could not. The permeability thus could not fully recover, and the stress-dependent hysteresis was obvious.

An analytical solution of equivalent elastic modulus considering confining stress and its variables sensitivity analysis for fractured rock masses

The equivalent elastic modulus is a parameter for controlling the deformation behavior of fractured rock masses in the equivalent continuum approach.The confining stress,whose effect on the equivalent elastic modulus is of great importance,is the fundamental stress environment of natural rock masses.This paper employs an analytical approach to obtain the equivalent elastic modulus of fractured rock masses containing random discrete fractures(RDFs)or regular fracture sets(RFSs)while considering the confining stress.The proposed analytical solution considers not only the elastic properties of the intact rocks and fractures,but also the geometrical structure of the fractures and the confining stress.The performance of the analytical solution is verified by comparing it with the results of numerical tests obtained using the three-dimensional distinct element code(3DEC),leading to a reasonably good agreement.The analytical solution quantitatively demonstrates that the equivalent elastic modulus increases substantially with an increase in confining stress,i.e.it is characterized by stress-dependency.Further,a sensitivity analysis of the variables in the analytical solution is conducted using a global sensitivity analysis approach,i.e.the extended Fourier amplitude sensitivity test(EFAST).The variations in the sensitivity indices for different ranges and distribution types of the variables are investigated.The results provide an in-depth understanding of the influence of the variables on the equivalent elastic modulus from different perspectives.

Stress Relaxation and Sensitivity Weight for Bi-Directional Evolutionary Structural Optimization to Improve the Computational Efficiency and Stabilization on Stress-Based Topology Optimization

Stress-based topology optimization is one of the most concerns of structural optimization and receives much attention in a wide range of engineering designs.To solve the inherent issues of stress-based topology optimization,many schemes are added to the conventional bi-directional evolutionary structural optimization(BESO)method in the previous studies.However,these schemes degrade the generality of BESO and increase the computational cost.This study proposes an improved topology optimization method for the continuum structures considering stress minimization in the framework of the conventional BESO method.A global stress measure constructed by p-norm function is treated as the objective function.To stabilize the optimization process,both qp-relaxation and sensitivity weight scheme are introduced.Design variables are updated by the conventional BESO method.Several 2D and 3D examples are used to demonstrate the validity of the proposed method.The results show that the optimization process can be stabilized by qp-relaxation.The value of q and p are crucial to reasonable solutions.The proposed sensitivity weight scheme further stabilizes the optimization process and evenly distributes the stress field.The computational efficiency of the proposed method is higher than the previous methods because it keeps the generality of BESO and does not need additional schemes.

Sensitivity analysis of pull-in voltage for RF MEMS switch based on modified couple stress theory

An approximate analytical model for calculating the pull-in voltage of a stepped cantilever-type radio frequency （RF） micro electro-mechanical system （MEMS） switch is developed based on the Euler-Bernoulli beam and a modified couple stress theory, and is validated by comparison with the finite element results. The sensitivity functions of the pull-in voltage to the designed parameters are derived based on the proposed model. The sensitivity investigation shows that the pull-in voltage sensitivities increase/decrease nonlinearly with the increases in the designed parameters. For the stepped cantilever beam, there exists a nonzero optimal dimensionless length ratio, where the pull-in voltage is insensitive. The optimal value of the dimensionless length ratio only depends on the dimensionless width ratio, and can be obtained by solving a nonlinear equation. The determination of the designed parameters is discussed, and some recommendations are made for the RF MEMS switch optimization.

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.

Ginger oil-loaded transdermal adhesive patch treats post-traumatic stress disorder

Objective:To find a viable alternative to reduce the number of doses required for the patients with post-traumatic stress disorder(PTSD),and to improve efficacy and patient compliance.Methods: In this study,we used ginger oil,a phytochemical with potential therapeutic properties,to prepare ginger oil patches.High-performance liquid chromatography(HPLC)was used to quantify the main active component of ginger oil,6-gingerol.Transdermal absorption experiments were conducted to optimize the various pressure-sensitive adhesives and permeation enhancers,including their type and concentration.Subsequently,the ginger oil patches were optimized and subjected to content determination and property evaluations.A PTSD mouse model was established using the foot-shock method.The therapeutic effect of ginger oil patches on PTSD was assessed through pathological sections,behavioral tests,and the evaluation of biomarkers such as tumor necrosis factor-α(TNF-α),interleukin-6(IL-6),brain-derived neurotrophic factor(BDNF),and melatonin(MT).Results: The results demonstrated that ginger oil patches exerted therapeutic effects against PTSD by inhibiting inflammatory responses and modulating MT and BDNF levels.Pharmacokinetic experiments revealed that ginger oil patches maintained a stable blood drug concentration for at least one day,addressing the rapid metabolism drawback of 6-gingerol and enhancing its therapeutic efficacy.Conclusions: Ginger oil can be prepared as a transdermal drug patch that meets these requirements,and the bioavailability of the prepared patch is better than that of oral administration.It can improve PTSD with good patient compliance and ease of administration.Therefore,it is a promising therapeutic formulation for the treatment of PTSD.

Stress Sensitivity and Signs of Anxiety or Depression among First Year Clinical Dental and Medical Students

Background: Negative stress symptoms are reported in the literature among clinical dental and medical students and can include signs of anxiety or depression. However, very little has been researched about existing psychological preconditions of these students that could make them more vulnerable to negative stress symptoms. Objective: The aims were to explore first year clinical dental and medical students’ experiences of stress intensity, stress sensitivity and signs of anxiety or depression. Gender was also explored as a possible predictor of these psychosocial phenomena. Methods: First year clinical students at Aarhus University dental (n = 49) and medical schools (n = 59) were recruited to fill out a 45-item questionnaire that comprised demographics and three scales: Cohens Perceived Personal Stress (PPS-10), Stress Sensitivity Inventory (SSI) and Depression Anxiety & Stress Scale (DASS-21). Groups and genders were compared by frequency and using association statistics, bivariate odds ratios, nominal logistic regression and ANOVA. Results: Stress intensity perceptions were moderate to high for many. Dental students scored higher than medical students on all mean test scores. In general, women showed higher levels of stress than men. Dental students scored significantly higher than medical students on Depression, Anxiety and Chronic Stress with ANOVA tests. However, when gender, age and medical or dental student status were added into a logistic regression analysis in which high stress sensitivity was the main dependent variable, only high scores in perceived stress intensity and signs of depression and anxiety showed significant main effects. Conclusion: Present study confirmed the literature that reports high degrees of stress among dental and medical students. But more importantly, Stress Sensitivity Inventory appeared to be a reliable and excellent predictor of high perceived stress and signs of depression and anxiety. It can be useful to detect and prevent student psychosocial dysfunction in clinical learning environments. An important challenge for medical and dental educational institutions is to provide specific student emotional support as early as needed as well as to consider appropriate stress prevention curriculum reforms.

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

Association between Depression, Pressure Pain Sensitivity, Stress and Autonomous Nervous System Function in Stable Ischemic Heart Disease: Impact of Beta-Adrenergic Receptor Blockade

Background: Depression and ischemic heart disease (IHD) are associated with persistent stress and autonomic nervous system (ANS) dysfunction. The former can be measured by pressure pain sensitivity (PPS) of the sternum, and the latter by the PPS and systolic blood pressure (SBP) response to a tilt table test (TTT). Beta-blocker treatment reduces the efferent beta-adrenergic ANS function, and thus, the physiological stress response. Objective: To test the effect of beta-blockers on changes in depression score in patients with IHD, as well as the influence on persistent stress and ANS dysfunction. Methods: Three months of non-pharmacological intervention aiming at reducing PPS and depression score in patients with stable IHD. Beta-blocker users (N = 102) were compared with non-users (N = 75), with respect to signs of depression measured by the Major Depressive Inventory questionnaire (MDI), resting PPS, and PPS and SBP response to TTT. Results: MDI score decreased 30% in non-users (p = 0.005) compared to 4% (p > 0.1) among users (between-group p = 0.003;effect size = 0.4). Resting PPS decreased in both the groups. Among most vulnerable patients with MDI ≥ 15, reductions in MDI score and resting PPS score correlated in non-users, only (r = 0.69, p = 0.007). Reduction in resting PPS correlated with an increase in PPS and SBP response to TTT. Conclusions: Stress intervention in patients with IHD was anti-depressive in non-users, only. Similarly, the association between the reduction in depression, reduction in persistent stress, and restoration of ANS dysfunction was only seen in non-users, suggesting a central role of beta-adrenergic receptors in the association between these factors.

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.