Deformation Analysis in Reservoir Space (DARS): A Simple Formalism for Prediction of Reservoir Deformation With Depletion

Abstract

Abstract We introduce a formalism, Deformation Analysis in Reservoir Space (DARS), to quantitatively predict the degree of compaction and potential for induced faulting in a depleting reservoir. Compaction occurs when the stress state exceeds the end cap (or critical state) of a formation at any given porosity. For reservoirs in which the vertical stress is larger than the two horizontal stresses, there is also a potential to induce normal faulting in a depleting reservoir when the change of minimum horizontal stress, ?Sh, exceeds a critical fraction of ?Pp (the change in formation pressure due to depletion). The stress path defines the change in horizontal stress with depletion (A=?Sh/?Pp). Utilizing relatively simple laboratory experiments, we transform the end caps from laboratory space into reservoir space (DARS) such that production data can be evaluated directly to study the evolution of the deforming reservoir due to production. Field X in the Gulf of Mexico is examined in the context of the DARS analysis. The analysis shows that the initial state of the reservoir was such that normal faults present in the field were active. However, production-induced normal faulting is not likely to occur. Deformation is dominated by compaction. Our analysis estimates that porosity of the formation was reduced from about 23% to 21%, while the permeability was reduced from about 230md to 50–140md. Introduction The deformation mechanisms operative in a depleting reservoir are important to understand for a variety of reasons. While it is well known that depletion can induce marked reductions in porosity (leading to compaction and possibly subsidence), it is desirable to predict the degree of compaction that might accompany depletion, the possible degree of permeability loss and, in some fields, the possibility that production-induced faulting might occur. In this study we describe a formalism by which it is possible to integrate relatively simple laboratory rock deformation data with the physical state of a reservoir to predict its evolution through time. We refer to this as Deformation Analysis in Reservoir Space (DARS) because it attempts to quantitatively "map", through time, the nature of the deformation fields inferred from laboratory experiments into the parametric space that defines the mechanical state of a reservoir (that is, the in-situ principal stresses and pore pressure). In the sections below we first provide the theoretical framework for this analysis and then consider a case study in which both laboratory and field data are available that allow us to evaluate the quantitative effects of depletion. One important component of this analysis is the change in horizontal stress, ?Sh, that accompanies a given amount of depletion, ?PP, termed the stress path, A. Poroelastic theory is often used for predicting the changes in magnitude of stresses with depletion. For an isotropic, porous and elastic reservoir that is laterally extensive with respect to its thickness (20:1), the following is applicable1.Equation 1 where ? is Poisson's ratio and a is the Biot coefficient, a=1-Kb/Kg, where Kb is the bulk modulus of the bulk rock and Kg is the bulk modulus of the mineral grains. Figure 1 demonstrates how the Biot coefficient, a, and Poisson's ratio, ?, affect the stress path. In practice, however, a depleting reservoir can undergo both elastic and significant inelastic deformation during depletion. Published data on minimum horizontal stress changes with depletion are very limited, the field names on the right hand side of Figure 1 are some published values of observed stress paths. Unfortunately, some of these reported values may not be directly related to depletion (italic and marked unknown) but a combination of all stress and pore pressure measurements in the field. Without knowing the values of a or ?, it is still possible to identify if induced normal faulting will occur in these selected fields.