Modeling of Asymmetric Vertical Growth in Elongated Hydraulic Fractures and Application to First MWX Stimulation

Abstract

ABSTRACT When a continuous sand is bounded by zones of higher, but unequal, minimum in-situ stress, a vertically asymmetric hydraulic fracture results. The modeling is much more difficult than in the symmetric case mainly because the width equation is harder to formulate and solve. In this paper we present the principal components of the modeling, which includes non-Newtonian flow, leakoff with spurt loss, and "storage" of fluid due to volume expansion. The assumption is that the fracture is highly elongated, i.e., stress contrasts between pay and bounding zones are relatively large (≳ few hundred psi). Vertical gradients of minimum in-situ stress and fluid pressure can be included in the modeling. To illustrate, the results, we present design calculations for a 30,000 gallon fracture, which was the first stimulation in the Multi-Well Experiment. The 80 ft fracture interval in the Paludal zone has at its upper edge a 520 psi stress contrast, and at its lower edge a 1195 psi contrast. Computed fracture height growth above and below the perforated interval, bottomhole pressure, and width profiles in vertical sections are displayed. Comparison is made with diagnostic measurements of fracture length, height, and bottomhole pressure.