This paper presents an approach that integrates pressure transient and multi-component seismic data to determine the characteristics of single- and double-porosity reservoirs. It is shown that a functional dependence exists between the well-test-determined storage capacity ratio and the seismic estimate of the normal fracture compliance. This functional dependence provides a means to obtain an estimate of the normal fracture compliance from well-test data or an estimate of the storage capacity ratio from seismic data. Obtaining estimates of these parameters by independent means helps reduce the non-uniqueness problem encountered in the interpretation of well-test or seismic data by reducing the number of parameters to be determined. In addition, it is shown that assuming a fracture model, the fracture density may be predicted from the storage capacity ratio. The application of the approach developed in this work is demonstrated by the analysis of the pressure buildup data from the Weyburn Field.
Introduction
Pressure-transient analysis is the generic name given to the interpretation of pressure and flow-rate data measured at the well location. If Darcy's law is valid and the rock behaves elastically, the diffusion equation describes fluid flow through the reservoir making it possible to obtain estimates of average permeability, average pressure, and storage capacity from the pressure-transient analysis of the well test data.1 In fractured reservoirs represented by the double-porosity models,2–5 it is possible to estimate the ratio of the storage capacity of the fractures to the total storage capacity of the rock (storage capacity ratio, ?.
The condition of elasticity inherent in the diffusion equation links the storage capacity to the pore space compressibility, which, in turn, may be related to the bulk modulus of the rock.6 Since in fractured rocks, the bulk modulus is a function of the normal fracture compliance, in this study, we were able to derive a relation between the estimates of the storage capacity, ?, and normal fracture compliance, ZNf. Using Zimmerman's6 rock compressibility relations and the linear slip theory introduced by Schoenberg and Douma7 and Schoenberg and Sayers,8 we show that the storage capacity ratio determined by engineers may be related to the normal compliance of the fracture system estimated by geophysicists. If it is assumed that the fractures behave elastically as penny shaped cracks, then, the storage capacity ratio is a function of the fracture density and fracture porosity.
Bakulin et al.9 have shown that the normal fracture compliance may be estimated from multi-component seismic data, for the case of a single fracture set and two orthogonal fracture sets. Therefore, the relation we derive in this study allows a quantitative comparison between independent pressure-transient and seismic experiments. Furthermore, normal fracture compliance values derived from seismic data may be used to predict the storage capacity ratio where no wells are available.
The development and the results presented in this paper demonstrate an example of integrating pressure-transient and seismic data to enhance the description of reservoir characteristics. Below, we first introduce the general concepts used in our development and present the functional dependence between the storage capacity ratio and the normal fracture compliance. We, then, present practical relations to obtain estimates of normal fracture compliance (ZNf) from pressure-transient analysis or estimates of storage capacity ratio (?) from seismic data analysis. Finally, an example application of the concepts and the results developed in this work is presented by considering the analysis of pressure-transient data from the fractured Mississippian carbonate reservoir at Weyburn field, Saskatchewan, Canada.
