The material balance (MB) equation for stresssensitive ndersaturated and saturated naturally ractured reservoirs (nfr's) has been written taking into ccount the presence of an unsteady state naturally ractured aquifer (nfa). The nfa can be of limited or nfinite size. The solution is presented in finite difference orm to achieve a quick convergence of the iteration rocess.
Historically, non-fractured aquifers have been ttached to material balance calculations of naturally ractured reservoirs. This is not realistic from a geologic oint of view as it implies that fractures are present in the il portion of the reservoir but disappear the moment the ater oil contact is reached. It is shown that the use of an nfractured aquifer in a naturally fractured reservoir can ead to erroneous oil recovery estimates. The effect of ater influx on the material balance equation is llustrated with an example.
Forecasting the performance of a nfr subject to water entrance from a nfa is a major challenge. The problem is compounded when the nfr and nfa are stress-sensitive. In this paper the nfr is stress-sensitive, but the nfa is not. The work presented in this paper is not meant to replace a detailed reservoir simulation, which is, in my opinion, the best way to solve the problem, provided that the original oil in place, size of the aquifer, reservoir characterization and quality of the pressure and production data is good. The idea is to have a tool that can provide a quick idea with respect to potential oil recoveries from stresssensitive nfr's affected by water influx from nfa's.
Various analytical aquifers have been considered in the literature, most notably those developed by Schilthius1 Hurst2 and van Everdingen and Hurst3 for edge water and Allard and Chen,4for bottom water. All of these aquifers considered matrix porosity but ignored the presence of natural fractures. Aguilera,5, developed equations to account for the presence of natural fractures in unsteady state edge aquifers. The equations were validated by successfully comparing results against those published by van Everdingen and Hurst. 3
This paper presents MB equations for predicting oil recovery of undersaturated and saturated nfr's affected by water influx from nfa's. The nfa can be of limited or infinite size. The infinite case applies, in practice, to those aquifers that are connected with the external world (for example connected with lakes and rives). The equations are written taking into account the effective compressibility of matrix and fractures. Stress-sensitive properties such as fracture porosity, fracture permeability, partitioning coefficient and exponent for shape of relative permeabilities are taken into account.
Aguilera5 presented a solution to the problem of nonstressed nfa's following the work of van Everdingen and Hurst. 3 For the case of constant pressure at the inner boundary (constant terminal pressure case) and constant pressure at the outer boundary, the dimensionless water influx is given in Laplace space by: Equation (1) (Available in full paper)