Numerical investigation of dual-porosity model with transient transfer function based on discrete-fracture model

Based on the characteristics of fractures in naturally fractured reservoir and a discrete-fracture model, a fracture network numerical well test model is developed. Bottom hole pressure response curves and the pressure field are obtained by solving the model equations with the finite-element method. By analyzing bottom hole pressure curves and the fluid flow in the pressure field, seven flow stages can be recognized on the curves. An upscaling method is developed to compare with the dual-porosity model （DPM）. The comparisons results show that the DPM overestimates the inter-porosity coefficient ）, and the storage factor w. The analysis results show that fracture conductivity plays a leading role in the fluid flow. Matrix permeability influences the beginning time of flow from the matrix to fractures. Fractures density is another important parameter controlling the flow. The fracture linear flow is hidden under the large fracture density. The pressure propagation is slower in the direction of larger fracture density.

Coupled thermo-hydro-mechanical-migratory model for dual-porosity medium and numerical analysis

A coupled thermo-hydro-mechanical-migratory model of dual-porosity medium for saturated-unsaturated ubiquitous-joint rockmass was established,in which the stress field and the temperature field were single,but the seepage field and the concentration field were double,and the influences of sets,spaces,angles,continuity ratios,stiffnesses of fractures on the constitutive relationship of the medium were considered.Also,the relative two-dimensional program of finite element method was developed.Taking a hypothetical nuclear waste repository as a calculation example,the case in which the rockmass was unsaturated dual-porosity medium and radioactive nuclide leak was simulated numerically,and the temperatures,negative pore pressures,saturations,flow velocities,nuclide concentrations and principal stresses in the rockmass were investigated.The results show that the negative pore pressures and nuclide concentrations in the porosity and fracture present different changes and distributions.Even though the saturation degree in porosity is only about 1/10 that in fracture,the flow velocity of underground water in fracture is about three times that in porosity because the permeability coefficient of fracture is almost four orders higher than that of porosity.The value of nuclide concentration in fracture is close to that in porosity.

FEM analyses for influences of stress-chemical solution on THM coupling in dual-porosity rock mass

The models of stress corrosion, pressure solution and flee-face dissolution/precipitation were introduced. Taking a hypothetical nuclear waste repository in an unsaturated dual-porosity rock mass as the calculation objective, four cases were designed 1） the fracture aperture is a function of stress corrosion, pressure solution and free-face dissolution/precipitation; 2） the fracture aperture changes with stress corrosion and pressure solution; 3） the fracture aperture changes with pressure solution and free-face dissolution/precipitation; 4） the fracture aperture is only a function of pressure solution, and the matrix porosity is also a function of stress in these four cases. Then, the corresponding two-dimensional FEM analyses for the coupled thermo-hydro-mechanical processes were carried out. The results show that the effects of stress corrosion are more prominent than those of pressure solution and free-face dissolution/precipitation, and the fracture aperture and relevant permeability caused by the stress corrosion arc only about 1/5 and 1/1000 of the corresponding values created by the pressure solution and free-face dissolution/precipitation, respectively Under the action of temperature field from released heat, the negative pore and fracture pressures in the computation domain rise continuously, and are inversely proportional to the sealing of fracture aperture. The vector fields of flow velocity of fracture water in the cases with and without considering stress corrosion are obviously different. The differences between the magnitudes and distributions of stresses within the rock mass are very small in all cases.

Dual-Porosity Apparent Permeability Models of Unconventional Gas Migration Based on Biot’s Porous Media

Stress-dependent permeability models are developed for the organic pores and inorganic cleats/fractures in unconventional gas reservoirs,which are modeled as Biot’s porous media of dual-porosity.Further considering multiple flow mechanisms such as dynamic effects of gas flow and surface diffusion,apparent permeability models are obtained to investigate the characteristics of unconventional gas migration.Compared to the gas transfer in single-porosity reservoirs,the gas migration ability of cleats in dual-porosity stratums rarely changes while that of organic pores is greatly improved because cleats sustain major geomechanical shrinkage deformation when the pore pressure drops.Further,the mass flux of reservoirs is dominated by the mass flux of cleats,which has a lower peak value,but a much longer production term than those in single-porosity reservoirs due to the interaction between organic pores and cleats.Parametric analysis is conducted to identify key factors significantly impacting mass flux in unconventional reservoirs.Reasons for the mass flux variation are also explored in terms of gas migration ability and pore pressure distribution.

Water retention behavior and shear strength of artificially cemented granite residual soil subjected to free drying

Artificially cemented soils have been widely used as filling materials in highway and railway construction.The shear strength evolution of filling materials upon moist variation can determine the stability of subgrade and embankments.This study conducted water retention tests,MIP tests,and multi-stage triaxial shear tests on cement-treated granite residual soil(GRS)to determine its water retention curve(WRC)upon free drying,pore structure,and peak shear strength qf,respectively.The water retention behavior and shear strength evolution upon free drying were modeled based on the dual-porosity structure of cement-treated GRS and the effective stress principle,respectively.Results show that the drying-WRC is bimodal and higher cement dosage yields a more severe decrease in the water retention capacity within a specific suction range.For a given confining pressure,the peak shear strength qf increased with increasing cement dosage or suction value s.The peak shear strength qf also solely depends on the suction value in the peak stress state.In addition,the cement-treated GRS has a bimodal pore size distribution curve,and its macro-and micro-void ratios remain almost unchanged after free drying.The bimodal drying-WRC of the cement-treated GRS can be modeled by differentiating the water retention mechanisms in macro-and micro-pores.Moreover,using the macro-pore degree of saturation as the effective stress parameterχ=S_(rM),the q_(f)–p′_(f)relationship(where p′_(f)is the effective mean pressure at failure)under various suction and stress conditions can be unified,and the q_(f)–s relationships at various net confining pressuresσ_(3),net can be well reproduced.These findings can help design subgrade and embankments constructed by artificially cemented GRS and assess their safe operation upon climate change.

Fracture characterization of Asmari Formation carbonate reservoirs in G Oilfield, Zagros Basin, Middle East

The Asmari Formation in the G oilfield on the Iran-Iraq border is a fractured-porous multi-lithology mixed reservoir, for which fracture is an important factor affecting oil productivity and water cut. The characterization and modeling of fractures in the carbonate reservoir of G oilfield are challenging due to weak conventional well log responses of fractures and a lack of specific logs, such as image logs. This study proposes an integrated approach for characterizing and modeling fractures in the carbonate reservoir. The features, formation mechanism, influencing factors, and prediction methods of fractures in the Asmari Formation carbonate reservoirs of G oilfield were studied using core observation, thin section, image log, cross-dipole acoustic log (CDAL), geomechanics numerical simulation (GNS), and production data. According to CDAL-based fracture density interpretation, GNS-based fracture intensity prediction between wells, and DFN-based rock fracture properties modeling, the quantitative fracture characterization for G oilfield was realized. This research shows that the fractures in the Asamri Formation are mainly medium-to high-angle shear fractures. The substantial compression stress during the Miocene played a major role in the formation of the prominent fractures and determined their trend in the region, with primary trends of NNW-SSE and NNE-SSW. The fracture distribution has regularity, and the fractures in zone A dolomites are more highly developed than that in zone B limestones vertically. Horizontally, fractures intensity is mainly controlled by faults and structural location. The results of this study may benefit the optimization of well design during field development. From 2019 to 2021, three horizontal wells pilot tests were deployed in the fractures belt in zone A, and these fractures prominently increased the permeability of tight dolomite reservoirs. The initial production of the wells is four to five times the average production of other wells in the area, showing a good development effect. Meanwhile, the updated numerical simulation validates that the history match accuracy of water cut based on the dual-porosity model is significantly improved, proving the fracture evaluation and prediction results to be relatively reliable and applicable.

3D thermo-hydro-mechanical-migratory coupling model and FEM analyses for dual-porosity medium

One kind of 3D coupled thermo-hydro-mechanical-migratory model for saturated-unsaturated dual-porosity medium was established,in which the stress field and the temperature field are single,but the seepage field and the concentration field are double,and the influences of sets,spaces,angles,continuity ratios,stiffness of fractures on the constitutive relationship of the medium can be considered.The relative three-dimensional program of finite element method was also developed.By comparing with the existing computation example,reliability of the model and the program were verified.Taking a hypothetical nuclear waste repository as a calculation example,the radioactive nuclide leak was simulated numerically with both the rock mass and the buffer being unsaturated media,and the temperatures,negative pore pressures,flow velocities,nuclide concentrations and normal stresses in the rock mass were investigated.The results showed that the temperatures,negative pore pressures and nuclide concentrations in the buffer all present nonlinear changes and distributions that even though the saturation degree in porosity is only about 1/9 of that in fracture,the flow velocity of underground water in fracture is about 6 times of that in porosity because the permeability coefficient of fracture is almost four orders higher than that of porosity,and that the regions of stress concentration occur at the vicinity of two sides of the boundary between buffer and disposal pit wall.

Impact of stress on solute transport in a fracture network: A comparison study

This paper compares numerical modeling of the effect of stress on solute transport （advection and matrix diffusion） in fractured rocks in which fracture apertures are correlated with fracture lengths. It is mainly motivated by the performance and safety assessments of underground radioactive waste repositories. Five research teams used different approaches to model stress/deformation, flow and transport pro- cesses, based on either discrete fracture network or equivalent continuum models. The simulation results derived by various teams generally demonstrated that rock stresses could significantly influence solute transport processes through stress-induced changes in fracture apertures and associated changes in per- meability. Reasonably good agreement was achieved regarding advection and matrix diffusion given the same fracture network, while some observed discrepancies could be explained by different mechanical or transport modeling approaches.

FEM analyses for influences of stress corrosion and pressure solution on THM coupling in dual-porosity rock mass

With the models of stress corrosion and pressure solution, by Yasuhara et al., two computation conditions were designed for a hypothetical nuclear waste repository in an unsaturated dual-porosity rock mass: (i) the fracture apertures are changed with the stress corrosion and pressure solution (the porosity of rock matrix is also a function of stress); (ii) the fracture apertures and the porosity of rock matrix are constants. Then the corresponding two-dimensional FEM analyses for the coupled thermohydro-mechanical processes were carried out, and the states of temperatures, rates and magnitudes of aperture closure, pore pressures, flow velocities and stresses in the rock mass were investigated. The results show the followings: The aperture closure rates caused by stress corrosion are almost six orders higher than those caused by pressure solution, and the two kinds of closure rates climb up, then decline, furthermore tend towards stability; the fracture apertures decrease from the original value and tend towards the residual value, and the contact-area ratios of asperities increase also from the original value and tend towards the nominal value; when the effects of stress corrosion and pressure solution are considered, the negative fracture pressures in near field rise very highly; the differences between the magnitudes and distributions of stresses within the rock mass in two calculation cases are very small.

A NEW WELL TEST MODEL FOR STRESS-SENSITIVE AND RADIALLY HETEROGENEOUS DUAL-POROSITY RESERVOIRS WITH NON-UNIFORM THICKNESSES

This article presents a new well test model for stress-sensitive composite dual-porosity reservoirs based on the concept of permeability modulus, where the rock and fluid properties as well as the formation thickness vary in the radial direction. An analytical solution in the Laplace space for the pressure-transient behavior for a line-source, constant-rate well of this type of reservoir is obtained with the Laplace transformation and the perturbation technique. The pressure and its derivative in the reservoir and the effects of relevant parameters on the pressure-transient response are obtained. The model as well as the corresponding type curves may be used in predicting the production performance or analyzing the production data for this type of reservoir.

FEM ANALYSIS FOR INFLUENCES OF A FAULT ON COUPLED T-H-M-M PROCESS IN DUAL-POROSITY ROCK MASS

For the case in which a large geological structure like fault existing within the surrounding rock mass in the near field of a repository for high-level radioactive nuclear waste, one kind of coupled thermo-hydro-mechanical-migratory model of dual-porosity medium for saturated- unsaturated ubiquitous-joint rock mass was established. In the present model, the seepage field and the concentration field are double, but the stress field and the temperature field are single, and the influences of sets, spaces, angles, continuity ratios, stiffness of fractures on the constitutive relationship of the medium can be considered. At the same time, a two-dimensional program of finite element method was developed. Taking a hypothetical nuclear waste repository located at a rock mass being unsaturated dual-porosity medium as a calculation example, the FEM analysis for thermo-hydro-mechanical-migratory coupling were carried out under the condition of radioac- tive nuclide leaking for the cases with and without a fault, and the temperatures, pore pressures, flow velocities, nuclide concentrations and principal stresses in the rock mass were investigated. The results show that the fracture water in the fault flows is basically along the fault direction, and its flow velocity is almost three orders of magnitude higher than that of fracture water in rock mass; the nuclide concentration in the fault is also much higher than that without fault, and the nuclides move along the fault faster; moreover, the fault has obvious influences on the pore pressures and the principal stresses in the rock mass.

Dual-porosity model of rate transient analysis for horizontal well in tight gas reservoirs with consideration of threshold pressure gradient

Most researches of the threshold pressure gradient in tight gas reservoirs are experimental and mainly focus on the transient pressure response, without paying much attention to the transient rate decline. This paper establishes a dual-porosity rate transient decline model for the horizontal well with consideration of the threshold pressure gradient, which represents the non-Darcy flow in a fracture system. The solution is obtained by employing the Laplace transform and the orthogonal transform. The bi-logarithmic type curves of the dimensionless production rate and derivative are plotted by the Stehfest numerical inversion method. Seven different flow regimes are identified and the effects of the influence factors such as the threshold pressure gradient, the elastic storativity ratio, and the cross flow coefficient are discussed. The presented research could interpret the production behavior more accurately and effectively for tight gas reservoirs.

Evidence of Dual Scale Porous Mechanisms During Fluid Migration in Hardwood Species (Ⅱ) A Dual Scale Computational Model to Describe the Experimental Results

The second part of this paper is devoted to the computational modelling of transient water migration in hardwood. During re-saturation, the moisture content, measured during the process by using X-ray attenuation (see part 1 of this paper), increases quickly very close to the cavity, but requires a very long time for the remaining part of the sample to absorb the moisture in wetting. For this configuration and this material, the macroscopic approach fails. Consequently, a dual-porosity approach is proposed. The computational domain uses a 2-D axisymmetric configuration for which the axial coordinate represents the macroscopic longitudinal direction of the sample whereas the radial coordinate allows the slow migration from each active vessel towards the fibre zone to be considered. The latter is a microscopic space variable. The moisture content field evolution depicts clearly the dual scale mechanisms:a very fast longitudinal migration in the vessel followed by a slow migration from the vessel towards the fibre zone.The macroscopic moisture content field resulting from this dual scale mechanism is in quite good agreement with the experimental data.

Prediction of oil recovery in naturally fractured reservoirs subjected to reinfiltration during gravity drainage using a new scaling equation

By comparing numerical simulation results of single-porosity and dual-porosity models,the significant effect of reinfiltration to naturally fractured reservoirs was confirmed.A new governing equation was proposed for oil drainage in a matrix block under the reinfiltration process.Utilizing inspectional analysis,a dimensionless equation suitable for scaling of recovery curves for matrix blocks under reinfiltration has been obtained.By the design of experiments,test cases with different rock and fluid properties were defined to confirm the scope of the presented equation.The defined cases were simulated using a realistic numerical simulation approach.This method can estimate the oil amount getting into the matrix block through reinfiltration,help simulate the oil drainage process in naturally fractured reservoirs accurately,and predict the recovery rate of matrix block in the early to middle periods of production.Using the defined scaling equation in the dual-porosity model can improve the accuracy of the predicted recovery rate.