## Section-Based Approach Optimizes Unconventional-Reservoir-Fracture Spacing

Fig. 1—Plot illustrating the h-refinement process for five meshes.

In this paper, the authors consider the development plan of shale gas or tight oil with multiple multistage fractured laterals in a large square drainage area that they call a “section” (usually 640 acres in the US). A section-based optimization of the fracture array is proposed to provide some general statements regarding spacing of wells and fractures. The approach is dependent on a reliable and efficient productivity-index (PI) calculation for the boundary-dominated state (BDS). The information derived from the section-based optimization method and the efficient and reliable algorithm for PI calculation should help the design of multistage fracturing in shale-gas or ultralow-permeability oil formations.

## Introduction

During the last decade, multiple studies have been conducted on various aspects of fracture design. Most of these use a numerical simulation that requires a large number of inputs, which, at the early stages of development, may be inaccessible or burdened by substantial uncertainty. Many of these works use quite sophisticated nonlinear search algorithms. In this work, however, only that part of the problem that can be addressed in rather general terms is considered. Therefore, simplifying assumptions are made to a point at which numerical results can be delivered. The results will provide some insight and useful bounds on achievable productivity. The methodology is dependent on an accurate numerical solution of a well-defined eigenvalue problem and, as such, can provide reference values for various research fields relying heavily on the diffusivity equation.

In the complete paper, a method that combines the finite-element method (FEM) with Richardson extrapolation is introduced to calculate the single-fracture PI both for constant-pressure and constant-rate wellbore conditions. Then, with the reliable PI for a single fracture, a convenient section-based optimization is conducted involving only two integer decision variables: the number of columns and the number of rows of the fracture array. Because the constant-pressure wellbore condition is more realistic, the overall PI of the section in the BDS flow regime is considered as the objective function. Two parameters are suggested as the main decisive factors: the dimensionless total fracture length and the feasible range of fracture half-length. In the present approach, the actual optimization takes a simple form of enumeration of a limited number of discrete cases; therefore, advanced nonlinear search algorithms are not involved. Those algorithms become irreplaceable when petrophysical and economic details are incorporated and the structure of the objective function loses its transparent nature, but such situations are beyond the focus of the present work.

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 186107, “Optimization of Spacing and Penetration Ratio for Infinite-Conductivity Fractures in Unconventional Reservoirs: A Section-Based Approach,” by S. Liu, SPE, and P.P. Valkó, SPE, Texas A&M University. The paper has been peer reviewed and published in the December 2017 SPE Journal.
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Section-Based Approach Optimizes Unconventional-Reservoir-Fracture Spacing

01 October 2018

Volume: 70 | Issue: 10

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