Optimum Fracture Design under Transient and Pseudosteady Conditions Using Constant Fracture Volume Concept

Abstract

ABSTRACT The Unified Fracture Design (UFD) or constant proppant volume technique introduced by Valko and Economides1,2 was originally developed for pseudo-steady state flow conditions and oil industry has been applying this technique even for low permeability reservoirs where the transient conditions last considerable time. There is nothing in the literature that shows that optimum fracture design using constant-proppant volume concept for pseudo-steady state flow is the same or different than the optimum one for transient flow conditions. This paper will present an extension of UFD technique (fixed proppant volume technique) to cover not only pseudosteady conditions but also transient flow regime. Results have shown that each "dimensionless time snap shot" presents a similar JD type curve3 with different optimum design curve. Therefore, the optimum fracture design is time dependant until pseudo-steady state condition is reached. Additionally, this paper presents a equivalent pseudo-steady state equation to calculate the dimensionless productivity index (JD) of finite-conductivity fractured wells producing at either transient or pseudo-steady state conditions. The pseudosteady state equation uses the definition of equivalent wellbore radius presented by Rueda3, to take into account the finite conductivity, fracture penetration and time dependency of the solution. Following pseudo-steady state equation concept, new correlations (from 1500 numerical simulation runs) to calculate shape factors and f-functions for a fractured well were developed, where the f-function is an extension of the original Cinco-Ley's function for transient and pseudo-steady state flow period. These correlations are functions of dimensionless fracture conductivity (CFD), fracture penetration ratio (Ix), and dimensionless time (tDA). This pseudo-steady state equivalent equation can be used to generate a series of new JD type curves of a finite-conductivity fractured well for different dimensionless times tDA. Having this equation, a new approach to get the optimum fracture geometry for a specific proppant number (Nprop) for a "fixed period of time" was also developed and presented in this paper.