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.

Experimental and theoretical study on the dynamic effective stress of loaded gassy coal during gas release

In the process of mining coalbed methane(CBM),an unsteady state often arises due to the rapid extraction,release and pressure relief of CBM.In this case,the effective stress of coal changes dynamically,affecting the stability of the gassy coal seam.In this paper,gas release tests of gassy coal under conventional triaxial compression were performed,and the dynamic effective stress(DES)during gas release was obtained indirectly based on a constitutive equation and deformation of coal.The results show that the maximum increases in DES caused by the release of free gas and adsorbed gas under the stress of 1.1 MPa were 0.811 and 5.418 MPa,respectively,which seriously affected the stress state of the coal.During the gas release,the free gas pressure and the adsorbed gas volume were the parameters that directly affected the DES and showed a positive linear relationship with the DES with an intercept of zero.The DES of the coal sample increased exponentially with time,which was determined by the contents of free and adsorbed gas.Based on the experimental results and theoretical analysis,an effective stress model was obtained for loaded gassy coal during gas release.The results of verification indicated accuracy greater than 99%.

Effects of effective stress and temperature on permeability of sandstone from CO2-plume geothermal reservoir

Rock is generally complex and heterogeneous,therefore the heterogeneity effects of effective stress and temperature on permeability should be taken into account.In this study,two-part Hooke’s model（TPHM） is introduced to understand the influences of effective stress and temperature on permeability of soft and hard parts（two parts） of rock based on coupling thermo-hydro-mechanical tests.Under a fixed temperature level（25 ℃.35 ℃.50 ℃.65 ℃.80 ℃.90 ℃ and 95 ℃）.the tests were carried out in a conventional triaxial system whereas the confining pressure was remained at 50 MPa.and the pore pressure was increased to the specified levels step by step.i.e.8 MPa,18 MPa.28 MPa.38 MPa.41 MPa,44 MPa.46 MPa and 48 MPa.The temperature-dependent relationships for two parts permeabilities are proposed on the basis of the initial test results.We point out that temperature of 65 ℃-90 ℃ is the threshold for the development of CO2-plume geothermal（CPC） reservoir sandstone cracking under low effective stress（2-9 MPa） based on the relationship between temperature and soft part permeability.Furthermore,we discuss the effect of temperature on the two parts in the rock.The results indicate that as the temperature increases from 25 ℃ to 65 ℃.the flow channel in the hard part has a stronger response to temperature than that in the soft part at a fixed effective stress level,which is opposite to the situation of effective stress.Considering that natural rock is generally heterogeneous with non-uniform pore structure,we suggest a physical interpretation of the phenomenon that before the thermal cracking threshold the two parts have different responses to temperature.

THEORETICAL MODEL OF EFFECTIVE STRESS COEFFICIENT FOR ROCK/SOIL-LIKE POROUS MATERIALS

Physical mechanisms and influencing factors on the effective stress coefficient for rock/soil-like porous materials are investigated, based on which equivalent connectivity index is proposed. The equivalent connectivity index, relying on the meso-scale structure of porous material and the property of liquid, denotes the connectivity of pores in Representative Element Area （REA）. If the conductivity of the porous material is anisotropic, the equivalent connectivity index is a second order tensor. Based on the basic theories of continuous mechanics and tensor analysis, relationship between area porosity and volumetric porosity of porous materials is deduced. Then a generalized expression, describing the relation between effective stress coefficient tensor and equivalent connectivity tensor of pores, is proposed, and the expression can be applied to isotropic media and also to anisotropic materials. Furthermore, evolution of porosity and equivalent connectivity index of the pore are studied in the strain space, and the method to determine the corresponding functions in expressions above is proposed using genetic algorithm and genetic programming. Two applications show that the results obtained by the method in this paper perfectly agree with the test data. This paper provides an important theoretical support to the coupled hydro-mechanical research.

EFFECTIVE STRESS LAWS FOR MULTI_POROSITY MEDIA

In this paper, the effective stress for multi-porosity elasticity model is presented by means of stress analysis for double porosity media elements. It is found that the effective stress law is not unique, it depends on the hypothesis of constitutive equations for multi-porosity media. Diversified effective stress laws for multi-porosity are developed.

Effective stress analysis method of seismic response for high tailings dam

Based on the analysis method for tailings dam in upstream raising method presently used in metallurgy and nonferrous metals tailings depository in the world, an effective stress analysis method of seismic response for high tailings dam was developed according to the results of engineering geological exploration, static and dynamic test and stability analysis on Baizhishan tailing dam 113.5 m high. The law of generation, diffusion and dissipation of seismic pore water pressure during and after earthquake was investigated, and the results of tailings dam’s acceleration, seismic dynamic stress and pore water pressure were obtained. The results show that the seismic stability and liquefaction resistance of high tailings dam are strengthened remarkably, and the scope and depth of liquefaction area at the top of dam are reduced greatly. The interior stress is compressive stress, the stress level of every element is less than 1.0 and the safety coefficient of every element is greater than 1.0. The safety coefficient against liquefaction of every element of tailing dam is greater than 1.5 according to the effective stress analysis of seismic response by finite element method. The calculated results prove that liquefaction is the main reason of seismic failure of high tailing dams, and the effect of seismic inertia forces on high tailing dams’ stability during earthquake is secondary reason.

Effective stress in soils under different saturation conditions

BISHOP’s effective stress or two state stress variables are unsatisfactory for unsaturated soils where one of fluid phases is discontinuous, so new expressions of effective stress should be founded. The approach for derivation was according to the principle of equilibrium of forces (i.e., the stress-sharing principle), and it was firstly validated by demonstrating TERZAGHI’s principle of effective stress. And then, the derivations were subdivided into four parts according to different pore air states: 1) air bubbles were spherical and suspended in pore water; 2) air bubbles were bound on soil skeleton; 3) air bubbles held almost the single section of pore; 4) air phase was continuous. The different formulae of effective stress were presented. Conclusions are drawn as follows: 1) For nearly-saturated soils, the "real" effective stress would be a little smaller than TERZAGHI’s effective stress; 2) For soils in which air phase is discontinuous in the form of bubbles, a new concept of pore air elastic pressure is put forward, and the total stress can be constituted by effective stress, pore water pressure and pore air elastic pressure; 3) For soils in which air phase is continuous, effective stress is equal to the value of the total stress plus suction; 4) Suction can be divided into two parts: one is the effect caused by additional pressure, and the other is the contract action by the "skin".

Examination of effective stress in clay rock

This paper examines the effective stress in indurated clay rock theoretically and experimentally.A stress concept is derived from the analysis of the microstructure and of the pore water in the highly-indurated Callovo-Oxfordian and Opalinus clay rocks,and subsequently validated by various experiments performed on these claystones.The concept suggests that the interparticle or effective stress in a dense clay ewater system is transferred through both the adsorbed interparticle pore water in narrow pores and the solidesolid contact between non-clay mineral grains.The experiments show that the adsorbed pore water in the claystones is capable of bearing deviatoric effective stresses up to the failure strength.The applied stresses are for the most part or even totally transferred by the bound pore water,i.e.the swelling pressure in the interparticle bound pore water is almost equivalent to the effective stress.This stress concept provides a reasonable view to the nature of the effective stress in argillaceous rock and forms the fundamental basis for studies of the hydro-mechanical properties and processes in clay formations.

Effective stress law for rock masses and its application in impoundment analysis based on deformation reinforcement theory

Reservoir impoundment is related to several hydraulic engineering concerns,including irreversible valley contractions,landslides and reservoir-induced earthquakes.However,these phenomena,such as valley contractions,are hardly to be explained by the conventional method.The scientific understanding of water effects during impoundment and their hazards to hydraulic structure are needed.The effective stress law for fissured rock masses is introduced in the elasto-plastic model employing the Drucker-Prager criterion and implemented in the three dimension(3D)nonlinear finite element method(FEM)program Three-dimensional FINite Element(TFINE).The slope deforms towards river-way during impoundment since the increasing pore pressure in fissures changes stress state and leads to additional plastic deformation in the rock materials.The value of Biot coefficient and the influence of water on rock materials are discussed in detail.Thus,the mechanism of slope deformation during the impoundment of Jinping-I arch dam is revealed,and the deformation is accurately measured.The application of the effective stress law provides a method to consider stress assessment,deformation evaluation and stability estimate of hydraulic structures during the impoundment process.This is a beneficial exploration and an improvement of hydraulic engineering design.

EFFECTIVE STRESS AND STRAIN IN FINITE DEFORMATION

Whether the concept of effective stress and strain in elastic-plastic theory is still valid under the condition of finite deformation was mainly discussed. The uni-axial compression experiments in plane stress and plane strain states were chosen for study. In the two kinds of stress states, the stress-strain curve described by logarithm strain and rotated Kirchhoff stress matches the experiments data better than the curves defined by other stress-strain description.

Experiment study on the law of effective stress of coal masses during methane drainage

The methane drainage can not only make coal seams deformation, but also effect its stress distribution. Based on lab experiment on methane drainage with a cubic coal sample of 500 mm×500 mm×500 mm, mutative law of coal of pore pressure （p） and effective stress （σef）i were investigated during methane drainage with the coal sample of China Lu＇an coal field No.3 coal seam. The experiment results indicate： during methane drainage pore pressure （p） follows exponential attenuation law： p=aexp（-bt）; effective stress （σef）i of coal masses follows logarithm incremental law： （σef）,=aln t＋b, （i=x, y, z）; effective stress coefficient（a） follows logarithm attenuation law： a=a-bln t; effective stress coefficient, volume stress （Θef） and pore pressure （p） follow bilinear law.

Verification of Effective Stress for Unsaturated Clay by Collapse Test

Generally, a suction control apparatus is used to examine compression properties of unsaturated clay. This is usually carried out with a pore water pressure of 0 under condition of applying pore air pressure, which is positive pore air pressure in a triaxial compression test. It is known as the Axis Translation Technique. However in this study, the suction control apparatus does not employ a method of controlling initial degree of saturation of specimen. The method for making specimen using micro wave is used to ensure a uniform distribution of water content of specimen （microwave oven method）. Consequently, both compression properties are similar to each other. Collapse tests were carried out using specimens under the microwave oven method and air dry state. As a result, it was found that the former does not result in collapse but the latter results in a significant amount of collapse. Such occurrence of collapse is dependent on the soil structure. Therefore, the equation of effective stress for unsaturated soil proposed Bishop should not neglect as an occurrence of collapse for unsaturated soils.

Evaluation of Effective Stresses and State Surfaces for Unsaturated Clayey Silt

Terzaghi had established soil mechanics as an academic scholarship due to the discovery of the principal of effective stress for saturated soils when he considered the consolidation theory of saturated clay. The reason of the existence of the effective stress is that soil particles and water are composited by incompressible solid and liquid. Although air is very compressible fluid, the principle of effective stress is also used in unsaturated soils in the resent developed numerical analyses. Schrefler＇s equation is most frequently used, but the effective stress is not verified by the experimental results. In this study, the equations for unsaturated soils proposed by Schrefler, Aitchison, Khalili and Khabbaz and Kohgo are compared with using the results of suction controlled consolidometer tests. As a result, the effective stress for unsaturated soils calculated by Schrefler＇s equation was average of them.

Analysis on effective stress formula and consolidation of gassy muddy clay

In order to found an applicable equation of consolidation for gassy muddy clay, an effective stress formula of gas-charged nearly-saturated soils was introduced. And then, a consolidation equation was derived. Subsequently, supposing soils were under tangential loading, the expressions of pore water pressure were presented. The analytic solution of pore water pressure was attempted to be validated by the measured values in a real embankment. The parameters in the expressions of pore water pressure were gotten by the method of trial. The result shows that the consolidation model is rational and the analytic solution of pore water pressure is correct. The following conclusions can be made: 1) the influence of bubbles on the compressibility of pore fluid should be considered; 2) the effective stress would be influenced by bubbles, and the consolidation would depend on the compressibility of soil skeleton: the softer the soils are, the more distinct the influence of bubbles is; for normal clay, the influence of bubbles on the effective stress may be commonly neglected.

Effective stress law for anisotropic double porous media

An effective stress law is derived analytically to describe the effect of pore (fracture pore and matrix-block pore) fluid pressure on the linearly elastic response of ani- sotropic saturated dual-porous rocks, which exhibit anisot- ropy. For general anisotropy the difference between the ef- fective stress and the applied stress is not hydrostatic simply multiplied by Biot coefficient. The effective stress law in- volves four constants for transversely isotropic response; these constants can be expressed in terms of the moduli of the single porous material, double porous material and of the solid material. These expressions are simplified considerably when the anisotropy is structural rather than intrinsic, i.e. in the case of an isotropic solid material with an anisotropic pore structure. In this case the effective stress law involves grain bulk modulus, four moduli and two compliances of the porous material for transverse isotropy. The law reduces, in the case of isotropic response, to that suggested by Li Shuiquan (2001). And reduction to the single-porosity (de- rived analytically by Carroll (1979)) is presented to demon- strate the conceptual consistency of the proposed law.

Determination of effective stress parameter of unsaturated soils:A Gaussian process regression approach

This article examines the capability of Gaussian process regression(GPR)for prediction of effective stress parameter(χ)of unsaturated soil.GPR method proceeds by parameterising a covariance function,and then infers the parameters given the data set.Input variables of GPR are net confining pressure(σ_(3)),saturated volumetric water content(θ_(s)),residual water content(θ_(r)),bubbling pressure(h_(b)),suction(s)and fitting parameter(l).A comparative study has been carried out between the developed GPR and Artificial Neural Network(ANN)models.A sensitivity analysis has been done to determine the effect of each input parameter onχ.The developed GPR gives the variance of predictedχ.The results show that the developed GPR is reliable model for prediction ofχof unsaturated soil.

Effect of Weld Parameters on Effective Notch Stress at Weld Root and Toe of Load Carrying Cruciform Joints

Cruciform joints in ships are prone to fatigue damage and the determination of type of weld plays a significant role in thefatigue design of the joint. In this paper, the effect of weld geometry on fatigue failure of load carrying cruciform joints inships is investigated using Effective Notch Stress (ENS) approach. A fictitious notch of 1 mm radius is introduced at theweld root and toe and fatigue stress is evaluated. The effect of weld leg length (l) and weld penetration depth (p) on ENS atweld root and toe are determined. The critical weld leg length (lcr) at which fatigue failure transitions from weld root toweld toe is investigated. An approximation formula for determination of the critical weld leg length considering weldpenetration depth (p) is proposed.

Effects of stress loading mode on microstructures and properties of Mg-9Gd-2Nd-0.5Zr alloy treated by creep aging

Creep aging forming(CAF) is a potential process used to manufacture large integral components of magnesium(Mg) alloys. The selected stress plays a crucial role in creep aging processes but the mechanism by which stress loading method affects creep aging of Mg alloys is still unclear. In this paper, the microstructural evolution of precipitated phases and precipitation-free zones(PFZ) at grain boundaries with different stress loading modes(unstressed, unidirectional tensile stress, and cyclic stress) at 250 ℃ were investigated along with changes in mechanical properties. The results showed that the addition of stress during aging effectively promoted the precipitation of precipitated phases, while unaffecting grain size. Unidirectional tensile stress caused directional growth of β phase([1010]), as well as rotation of weave towards the basal plane texture, resulting in namely stress orientation effect. Solute atoms diffused in the direction of tensile stress while vacancies moved perpendicular to the direction of tensile stress, resulting in PFZ at grain boundaries(157.06 nm). By contrast, cyclic stresses led to the growth of β phase in three directions([1010], [1100] and [0110]). The solute atoms and vacancies were uniformly distributed in the Mg matrix instead of directional diffusion, effectively reducing the width of PFZ(112.39 nm) at the grain boundary. These features significantly improved the mechanical properties of alloy specimens after cyclic stress creep aging when compared to unidirectional stress creep aging, with yield strength(YS), ultimate tensile strength(UTS), and elongation(EL) enhanced from 171.6 MPa, 305.5 MPa, and 4.4%to 174.8 MPa, 326.3 MPa, and 6.9%, respectively.

Hydromechanical characterization of gas transport amidst uncertainty for underground nuclear explosion detection

Given the challenge of definitively discriminating between chemical and nuclear explosions using seismic methods alone,surface detection of signature noble gas radioisotopes is considered a positive identification of underground nuclear explosions(UNEs).However,the migration of signature radionuclide gases between the nuclear cavity and surface is not well understood because complex processes are involved,including the generation of complex fracture networks,reactivation of natural fractures and faults,and thermo-hydro-mechanical-chemical(THMC)coupling of radionuclide gas transport in the subsurface.In this study,we provide an experimental investigation of hydro-mechanical(HM)coupling among gas flow,stress states,rock deformation,and rock damage using a unique multi-physics triaxial direct shear rock testing system.The testing system also features redundant gas pressure and flow rate measurements,well suited for parameter uncertainty quantification.Using porous tuff and tight granite samples that are relevant to historic UNE tests,we measured the Biot effective stress coefficient,rock matrix gas permeability,and fracture gas permeability at a range of pore pressure and stress conditions.The Biot effective stress coefficient varies from 0.69 to 1 for the tuff,whose porosity averages 35.3%±0.7%,while this coefficient varies from 0.51 to 0.78 for the tight granite(porosity<1%,perhaps an underestimate).Matrix gas permeability is strongly correlated to effective stress for the granite,but not for the porous tuff.Our experiments reveal the following key engineering implications on transport of radionuclide gases post a UNE event:(1)The porous tuff shows apparent fracture dilation or compression upon stress changes,which does not necessarily change the gas permeability;(2)The granite fracture permeability shows strong stress sensitivity and is positively related to shear displacement;and(3)Hydromechanical coupling among stress states,rock damage,and gas flow appears to be stronger in tight granite than in porous tuff.

A hybrid machine learning optimization algorithm for multivariable pore pressure prediction

Pore pressure is essential data in drilling design,and its accurate prediction is necessary to ensure drilling safety and improve drilling efficiency.Traditional methods for predicting pore pressure are limited when forming particular structures and lithology.In this paper,a machine learning algorithm and effective stress theorem are used to establish the transformation model between rock physical parameters and pore pressure.This study collects data from three wells.Well 1 had 881 data sets for model training,and Wells 2 and 3 had 538 and 464 data sets for model testing.In this paper,support vector machine(SVM),random forest(RF),extreme gradient boosting(XGB),and multilayer perceptron(MLP)are selected as the machine learning algorithms for pore pressure modeling.In addition,this paper uses the grey wolf optimization(GWO)algorithm,particle swarm optimization(PSO)algorithm,sparrow search algorithm(SSA),and bat algorithm(BA)to establish a hybrid machine learning optimization algorithm,and proposes an improved grey wolf optimization(IGWO)algorithm.The IGWO-MLP model obtained the minimum root mean square error(RMSE)by using the 5-fold cross-validation method for the training data.For the pore pressure data in Well 2 and Well 3,the coefficients of determination(R^(2))of SVM,RF,XGB,and MLP are 0.9930 and 0.9446,0.9943 and 0.9472,0.9945 and 0.9488,0.9949 and 0.9574.MLP achieves optimal performance on both training and test data,and the MLP model shows a high degree of generalization.It indicates that the IGWO-MLP is an excellent predictor of pore pressure and can be used to predict pore pressure.