The Method of Distributed Volumetric Sources for Calculating the Transient and Pseudosteady-State Productivity of Complex Well-Fracture Configurations

Abstract

The method of Distributed Volumetric Sources (DVS) is developed to solve problems of transient and pseudo steady state fluid flow. The basic building block of the method comprises calculation of the analytical response of a rectilinear reservoir with closed outer boundaries to an instantaneous volumetric source, also shaped as a rectilinear body. The solution also provides the well-testing derivative of the response to a continuous source in analytical form. This can be integrated over time to provide the pressure response to a continuous source. For production engineering applications, we cast the results into a transient/pseudo-steady productivity index form. The new method is validated through comparison to results of some of the well known well-testing solutions for simple configurations such as vertical wells with full and partial penetration, horizontal wells with unform flux and infinite conductivity, and fractured wells with uniform flux, finite or infinte conductivity. The results show a very good agreement with the existing models. The main advantage of the new solution is its applicability over the more complex fracture/well configurations, some of which is studied in the paper. The new method has shown to provide a fast, robust, and reliable way to pressure transient analysis, and well performance prediction whenever complex well/fracture configuration is considered.

Volumetric Source Model to Predict Productivity of Fractured Horizontal Well in Naturally Fractured Reservoirs

“…While Ogunsanya et al [15,16] pointed out that source functions have computational problems and the no volume assumption may not be adequate in some specific situations, then revisited the concept of volumetric source and presented a new "solid bar source" model. Amini et al [17][18][19][20] developed distributed volumetric source (DVS) model of homogeneous reservoirs, and validate the applications in vertical well, horizontal well and fractured vertical fractured well with well-known existing solutions. He also demonstrated the application of DVS model in fractured horizontal wells and emphasized advantages of the method of volumetric source.…”

A new computation model of fractured horizontal well coupling with reservoir

“…There are 4n f +4M ·n f unknown variables and 4n f +4M ·n f equations in the model (consisting of Equations (10), (11), (12), (13), (14), (15), (16), (18), (19), (20) or (21)). These equations are in a closed system, so we can solve this problem.…”

“…It also considered some complicate factors, such as the fluid frictional loss, the change of momentum and the inflow from the sidewall of wellbore. Valko and Amini [15] developed a method with distributed volume sources to simulate fractured horizontal wells in a box-shaped reservoir and a source term was added to the diffusivity equation to calculate the pressure distribution and the production rate from a fracture is computed. Guo and Yu [16] formulated a simple analytical model which described the productivity of multi-fractured horizontal well better.…”

Comprehensive Model for Flow Behavior of High-Performance Fracture Completions

“…Based on the Distributed Volumetric Sources (DVS) method (Valkó and Amini, 2007), a semi-analytical model enables both the fracture and the GP region as possible contributors to the total production. Appendix B shows this model as well as a general formulation of the DVS method.…”