An analytical solution is developed in this paper to forecast the production behavior of two-dimensional closed-boundary reservoirs producing from multiple wells under constant different bottomhole pressures. Wells are represented as line sources arbitrarily located in the domain of the reservoir; damage is considered. Solution is obtained through combination of Laplace transformation and Green's functions Methods.

The production decline of the wells during the boundary dominated flow period is shown to be of a modified-exponential nature: qwDj(tD)=qwDj+(qwDj0qwDj)exp(DtD),j=1,2,..nw. When all wells produce at the same bottom-hole pressure, it is shown that qwDj=0 and production declines exponentially. It is also shown that the production decline of the reservoir is in all cases exponential: qD(tD)=qD0exp(DtD), being qD0=j=1nwqwDj0.

It is found that the decline coefficient, D, is the same for the reservoir and for each of the wells. D depends on the size and shape of the reservoir as well as on the number of wells, its location and damage. Parameters qwDj0,qwDj and qD0 besides of depending on the same parameters as D, also depend on the bottomhole pressures of the wells. As expected, production under unequal bottomhole pressures or under irregular wells-reservoir patterns, yield uneven well productions. It is also found that stimulation, or damage, of a single well modifies the entire production characteristics of the wells-reservoir system. A simple method of analysis that provides the production decline parameters qwj0,qwj,j=1,2,,nw and D, is developed.

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