A direct method for property estimation from analysis of infinite acting production in shale/tight gas reservoirs

• An explicit method is developed for estimating fracture length.
• Implicit and iterative nature of pseudotime calculations is removed.
• Simple semi-analytic solutions are provided.
• Solutions are developed for different bottomhole conditions.
• Real field examples are practiced.

Infinite acting linear flow is a dominant flow regime in many multi-fractured horizontal wells completed in shale/tight gas reservoirs. A well-accepted methodology for analysis of this flow regime in systems without aquifer influence is the square-root of time plot. For reservoirs producing single phase oil, fracture half-length can be estimated from the slope of this plot, provided reservoir permeability is known. However, for gas reservoirs, pseudovariables are required to account for the pressure-dependence of gas properties. For example, the pseudotime function must be used to account for the strong dependence of gas viscosity and compressibility on pressure. As has been previously noted, for tight reservoirs, the pseudotime function must be evaluated at average pressure in the region of influence, which in turn is calculated from the material balance equation. Therefore, the linear flow equation should be coupled with the material balance equation so that fracture half-length can be estimated. This solution methodology is implicit and may require iterative procedures.This paper introduces an explicit solution methodology for estimating fracture half-length. As in the case of implicit solution methodology, the assumptions of no aquifer influence and infinite acting flow are considered. Because of no aquifer support, we can use material balance equation of volumetric reservoirs. We propose an appropriate correlation between viscosity–compressibility product and the material balance equation. This correlation helps to simplify pseudotime calculations and remove the implicit and iterative nature of the previous solution methodology. Accordingly, we have developed simple semi-analytic solutions that provide a methodology for direct estimation of fracture half-length. The solutions were developed for constant rate, constant pressure, and variable pressure/rate production from wells. We used numerical simulation to generate many synthetic production examples with wide ranges in reservoir properties to validate the introduced equations. We further used our approach for analysis of field cases (multi-fractured horizontal wells completed in shale reservoirs) to demonstrate its practical applicability to real data.