Reflection of plane seismic waves at the surface of double-porosity dual-permeability materials

The present work deals with the reflection of plane seismic waves at the stress-free plane surface of double-porosity dualpermeability material. The incidence of two main waves（i.e., P1 and SV） is considered. As a result of the incident waves,four reflected（three longitudinal and one shear） waves are found in the medium. The expressions of reflection coefficients for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy for fully closed as well as perfectly open pores. Effect of incident direction on the partition of the incident energy is analyzed with the change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure. It has been confirmed from the numerical interpretation that during the reflection process, conservation of incident energy is obtained at each angle of incidence.

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.

Reflection and refraction of plane waves at the boundary of an elastic solid and double-porosity dual-permeability materials

Phenomena of reflection and refraction of plane harmonic waves at a plane interface between an elastic solid and doubleporosity dual-permeability material are investigated. The elastic solid behaves non-dissipatively, while double-porosity dual-permeability materials behave dissipatively to wave propagation due to the presence of viscosity in pore fluids. All the waves(i.e., incident and reflected) in an elastic medium are considered as homogeneous(i.e., having the same directions of propagation and attenuation), while all the refracted waves in double-porosity dual-permeability materials are inhomogeneous(i.e., having different directions of propagation and attenuation). The coefficients of reflection and refraction for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected and refracted waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy among various reflected and refracted waves. The effect of incident direction on the partition of the incident energy is analyzed with a change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure.It has been confirmed from numerical interpretation that during the reflection/refraction process, conservation of incident energy is obtained at each angle of incidence.

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.

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.

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.

A STUDY ON TRANSIENT FLUID FLOW OF HORIZONTAL WELLS IN DUAL-PERMEABILITY MEDIA

To adopt horizontal wells in dual media reservoirs, a good understanding of the related fluid flows is necessary. Most of the recent studies focus on dual porosity media instead of dual permeability media. In this article, through both integral transformation and sink-source superposition, a new Laplace-domain solution is obtained for the slightly-compressible fluid flow in the 3-D dual-permeability media in which the horizontal well is operating in a constant rate of production. Major asymptotic characteristics of diagnosis curves of dimensionless downhole pressure are analyzed by the limited analysis. Effects of parameters of dual-permeability media including mobility ratio k, storativity ratio ω and inter-porosity flow parameter k on the downhote pressure are studied by using the Laplace numerical inversion. The new solution obtained in this article includes and improves the previous results and then can be used as a basis for either pressure transient analysis or formation behavior evaluation for the typical reservoir with horizontal wells.

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.

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.