Multiscale matrix-fracture transfer functions for naturally fractured reservoirs using an analytical, infinite conductivity, discrete fracture model

Abstract

Fracture matrix transfer functions have long been recognized as tools in modelling naturally fractured reservoirs. If a significant degree of fracturing is present, models involving single matrix blocks and matrix block distributions become relevant. However, this captures only the largest fracture sets and treats the matrix blocks as homogeneous, though possibly anisotropic. Herein, we produce the steady and transient baseline solutions for depletion for such models. Multiscale models pass below grid scale information to the larger scale system with some numerical cost. Instead, for below block scale information, we take the analytic solution to the Diffusivity Equation for transient inflow performance of wells of arbitrary trajectory, originally developed for Neumann boundary conditions, and recast it for Dirichlet boundaries with possible internal fractures of variable density, length, and orientation. As such, it represents the analytical solution for a heterogeneous matrix block surrounded by a constant pressure sink, we take to be the primary fracture system. Instead of using a constant rate internal boundary condition on a fracture surrounded by matrix, we segment the fracture and, through imposed material balance, force the internal complex fracture feature to be a constant pressure element with net zero flux. In doing so, we create a representative matrix block with infinite conductivity subscale fractures that impact the overall drainage into the surrounding fracture system. We vary the internal fracture structure and delineate sensitivity to fracture spacing and extent of fracturing. We generate the complete transient solution, enabling new well test interpretation for such systems in characterization of block size distributions or extent of below block-scale fracturing. The initial model for fully-penetrating fractures can be extended to 3D, generalized floating fractures of arbitrary inclination, and internal complex fracture networks.

Analytic representative element rate decline models for naturally fractured reservoir depletion

“…Hazlett and Younis 22 presented a transient baseline solution for depletion of single matrix blocks and effective steady state transport properties for matrix blocks with embedded fractures. Following that work, the solution to the Green’s function for depletion from a matrix block in a formation of thickness h with area 4 ab and directional permeabilities k x and k y into a surrounding constant pressure fracture system is …”

Hydraulic Fracturing and Enhanced Recovery in Shale Reservoirs: Theoretical Analysis to Engineering Applications

“…A set of field data (including both geological and engineering parameters) is prepared and used as input in Comsol Multiphysics to investigate the impacts of kerogen pore volume, kerogen permeability, inorganic matrix permeability, fracture permeability, effective stress, and Langmuir parameters on shale gas reservoir production performance. − Most simulation approaches first establish a base case model, which is an extract from the field-scale model, upon which sensitivity analysis is performed after verifying model accuracy with the field data or analytical data. − ,− For example, Zhang et al used only the gray portion (a quarter of the entire domain) of the production area to simulate and analyze, because of the symmetry of the production area, as shown in Figure a. Tian et al extended the base case model to a field-scale model by 10 times to quantitatively classify the domain contribution, as shown in Figure b.…”

“…The porous medium of shale reservoirs is complex because it harbors both the matrix and fracture networks containing phases like gas, oil, and water . The partially connected pores in the porous structure of shales are the important storage and flow zones. , Generally, the pore structure of shale reservoirs consists of the kerogen, inorganic matrix, natural fracture, and hydraulic fracture. − It is important to investigate the general structure of shale reservoirs on the basis of their geological, mineralogical, and chemical compositions because such factors affect the structure of the pore network, as well as the flow behavior of the gas from one domain to another domain. The structural properties of shale reservoirs include porosity, pore size distribution, specific surface area, tortuosity, and microstructure reconstruction. − Among these parameters, porosity is the most influential since it has a relationship with the pore morphology and the amount of space available for storage, which ultimately influences the transport of gas .…”

“…Shale reservoirs are composed of different scales that range from the nanoscale (10 –9 m) to the microscale (10 –6 m), mesoscale (10 –3 m), and macroscale (1 m). , The multiple domains form a complex flow zone that is composed of the kerogen, inorganic matrix, natural fracture, and hydraulic fracture. − Various studies with many domains have been developed to describe the storage and flow behavior of a single phase (gas) in the subsurface of shale. Figure a shows the shape factor for a slab (1D flow) where the matrix blocks were surrounded by fractures at different schemes and constant pressure under the condition of pseudosteady state .…”

“…In Figure d, a base case model is extracted from the field model to analyze individual gas production . Upon building the base case model, the next step is model verification, which in most cases is done on the basis of the field data, analytical solutions, or experimental data. − …”