Improved vertical stress profiling for unconventional reservoirs

Abstract

A critical input in a hydraulic fracture stimulation design is the vertical stress profile. From it, designers can determine the variation in the minimum horizontal stress as a function of depth. The depth profile of the minimum horizontal stress (i.e., the vertical stress profile) is a major factor in controlling the geometry of a hydraulic fracture or fracture network development (e.g., Economides and Nolte, 2000). For example, an optimum stimulation design would define the pumping variables and schedule so as to limit height growth to the productive interval while promoting optimum horizontal growth. Height growth into non-productive layers above or below the pay interval reduces the horizontal length in the productive interval. In addition, gravity can concentrate the proppant in the fractures below the producing interval, diminishing fracture conductivity in the producing interval. Both mechanisms decrease production. Therefore, to design an optimal stimulation, an accurate vertical stress profile is required. This requires appropriate and accurate stress models. Petroleum geomechanics typically uses one of two general classes of analytic stress models. One model is based on linear elasticity; the other is based on failure mechanics. Linear elastic models use Hooke’s law and therefore assume the target formation is continuous and homogeneous. In these models, the formation’s elastic constants linearly relate stress with strain. Failure models, such as Mohr-Coulomb, assume a maximum in situ shear stress above which failure occurs and which is controlled by the shear strength of the formation. While these two classes of models use strikingly different assumptions, they often yield similar stress profiles (Thiercelin and Plumb, 1994). Because elastic and failure models predict similar stress profiles plus the belief that the linear elasticity is more appropriate, almost all hydraulic fracture stimulation designs use only linear elastic models. As we show below, this (overused) practice, using only linear elastic models, can be inappropriate and results in inaccurate and misunderstood results. We show this practice results in a compromised vertical stress profile when weak layers exist in the stimulated interval. Weak layers can be stressed beyond their elastic limit, causing additional, unaccounted for strain due to yielding. The increased strain results in an increase in the minimum horizontal stress, exceeding that predicted by linear elasticity. The consequence is an incorrect vertical stress profile and an inaccurate understanding of the fracture geometry from the stimulation. This paper details an improved workflow for formations that include zones or layers whose present state exceeds their linear elastic limit. For example, when weak layers are present, numerical modelling is a reasonable and possibly more accurate alternative to analytical modelling for predicting the vertical stress profile. With today’s computing power, accurate and appropriate numerical models can be built and run in minutes to hours rather than the days to weeks of past decades. Below we develop and illustrate such a workflow. Choosing and implementing the appropriate model, whether it is analytic or numerical, as shown by this work, gives a more accurate vertical stress profile. This will in turn improve completion and stimulation designs and the understanding of the stimulated fracture or fracture network geometry.