Denis Biryukov

Transient Pressure Behavior of Reservoirs with Discrete Conductive Faults and Fractures

Fractures and faults are common features of many well-known reservoirs. They create traps, serve as conduits to oil and gas migration, and can behave as barriers or baffles to fluid flow. Naturally fractured reservoirs consist of fractures in igneous, metamorphic, sedimentary rocks (matrix), and formations. In most sedimentary formations both fractures and matrix contribute to flow and storage, but in igneous and metamorphic rocks only fractures contribute to flow and storage, and the matrix has almost zero permeability and porosity. In this study, we present a mesh-free semianalytical solution for pressure transient behavior in a 2D infinite reservoir containing a network of discrete and/or connected finite- and infinite-conductivity fractures. The proposed solution methodology is based on an analytical-element method and thus can be easily extended to incorporate other reservoir features such as sealing or leaky faults, domains with altered petrophysical properties (for example, fluid permeability or reservoir porosity), and complicated reservoir boundaries. It is shown that the pressure behavior of discretely fractured reservoirs is considerably different from the well-known Warren and Root dual-porosity reservoir model behavior. The pressure behavior of discretely fractured reservoirs shows many different flow regimes depending on fracture distribution, its intensity and conductivity. In some cases, they also exhibit a dual-porosity reservoir model behavior.

Pressure Transient Behavior of Horizontal Wells Intersecting Multiple Hydraulic Fractures in Naturally Fractured Reservoirs

In this study, we present a mesh-free semi-analytical technique for modeling pressure transient behavior of continuously and discretely hydraulically and naturally fractured reservoirs for a single-phase fluid. In our model, we consider a 3D reservoir, where each fracture is explicitly modeled without any upscaling or homogenization as required for dual-porosity media. Fractures can have finite or infinite conductivities, and the formation (matrix) is assumed to have a finite permeability. Our approach is based on the boundary element method. The method has advantages such as the absence of grids and reduced dimensionality. It provides continuous rather than discrete solutions. The uniform-pressure boundary condition over the wellbore is used in our mathematical model. This is the true physical boundary condition for any type of well, whether fractured or not, provided that the friction pressure drop in the wellbore is small and the fluid is Newtonian. The method is sufficiently general to be applied to many different well geometries and reservoir geological settings, where the spatial domain may include arbitrary fracture and/or fault distribution, a number of horizontal wells with and without hydraulic fractures, and different types of outer boundaries. The model also applies to multistage hydraulically fractured horizontal wells in homogenous reservoirs. More specifically, it is applied to investigate the pressure transient behavior of horizontal wells in continuously and discretely naturally fractured reservoirs, including multistage hydraulically fractured horizontal wells. A number of solutions have been published in the literature for horizontal wells in naturally fractured reservoirs using the conventional dual-porosity models that are not applicable to many of these reservoirs that contain horizontal wells with multiple fractures. Most published solutions for fractured horizontal wells in homogenous and naturally fractured reservoirs ignore the presence of the wellbore and the contribution to flow from the formation directly into the unfractured horizontal sections of the wellbore. Therefore, some of the flow regimes from these solutions are incorrect or do not exist, such as fracture-radial flow regime. In our solutions, all or some of multistage hydraulic fractures may intersect the natural fractures, which is very important for shale gas and oil reservoir production. The number and type of fractures (hydraulic or natural) intersecting the wellbore and with each other are not limited in both homogeneous and naturally fractured reservoirs. Our solutions are compared with a number of existing solutions published in the literature. Example diagnostic derivative plots are presented for a variety of horizontal wells with multiple fractures in homogenous and naturally fractured reservoirs.

Pressure Transient Solutions for Vertically Slotted-Partially Penetrated Vertical Wells in Porous Media

In this paper, we present semi-analytical pressure transient solutions for vertically slotted-limited entry or partially penetrated vertical wells. These solutions are needed for interpretation of the pressure transient tests conducted with the Wireline Formation Testing vertically slotted-packer configuration, and in wells with vertically slotted-liner completions. These slots have limited size openings and are vertically placed on a non-permeable cylindrical wellbore in a porous medium. The fluid from the formation is produced through these slots into the wellbore. Pressure transient solutions are not readily available for the uniform pressure boundary condition on the surface of the slots because such a condition creates a mixed boundary value problem, which is difficult to solve. Here we present exact pressure transient solutions obtained under the assumption that the pressure on the slot surface is uniform but a priori unknown, and the rest of the wellbore surface is non-permeable (no-flow condition). Furthermore, we generalize our solution for the case of multiple slots (open sections) on the wellbore for both well testing and Wireline formation tester packer modules. Our solutions are compared with the existing solutions. A new formula for obtaining the drawdown horizontal mobility is presented for anisotropic media.