Modification of the Transient Linear Flow Distance of Investigation Calculation for Use in Hydraulic Fracture Property Determination

Abstract

Abstract Long-term transient linear flow of hydraulically-fractured vertical and horizontal wells completed in tight/shale gas wells has historically been analyzed using the square-root of time plot. Pseudovariables are typically used for compressible fluids to account for pressure-dependence of fluid properties. Recently, a corrected pseudotime has been introduced for this purpose, where the average pressure in the distance of investigation (DOI) is calculated using an appropriate material balance equation. Therefore, the distance of investigation calculation is critically important in the determination of the linear flow parameter (product of fracture half-length and square-root of permeability, xf√k) as well as in the calculation of contacted fluid-in-place. Until now, the DOI for transient linear flow has been determined empirically, and may not be accurate for all combinations of fluid properties and operating conditions. In this work, we have developed analytically-based equations for transient linear flow DOI for different operating conditions. Two different approaches were used: the impulse respond concept, and transient/boundary-dominated flow intersection method. The performance of these approaches was tested by analyzing synthetic production data from a series of fine-grid numerical simulations. These simulation runs were set up to obtain accurate estimates of the linear flow parameter for different operating conditions. The calculated linear flow parameters determined by using our new DOI formulations and the input values in the numerical simulation are in good agreement. Of the two new DOI calculation methods provided, the unit impulse method provides more accurate results. Linear flow analysis based on the DOI calculations presented in this work is significantly improved over previous formulations.