Prediction of Maximum Flow Rates From Geopressured Aquifers
Authors: McMullan J.H. , Bassiouni Z.A. 
Published: December 2007

Summary
Three methods were developed to predict production history of a geopressured aquifer with surface pressure maintained at a constant, minimal value. Production of a geopressured aquifer in this manner would accelerate the recovery of the energy and thereby maximize its present value.
The first technique is centered around the exponential integral solution to the diffusivity equation. The constantly changing flow rate is approximated in a stepwise fashion using the principle of superposition. The effects of aquifer boundaries are included by the addition of image wells to create a rectangular aquifer with the well located at any position within the aquifer.
The second technique uses the semisteady-state solution to the diffusivity equation. As before, the constantly changing flow rate is approximated in a stepwise fashion. The effects of aquifer boundaries are included by assuming that the reservoir is circular with the well located at its center.
The third technique uses the terminal-pressure, limited-reservoir solution to the diffusivity equation. This technique differs from the other two in that the constantly changing bottomhole pressure (BHP) is approximated in a stepwise fashion using superposition. As in the semisteady-state solution, a circular reservoir with the well located at its center is assumed.
The three techniques were applied to two typical south Louisiana geopressured aquifers. Predicted production rates from all three techniques were essentially equal. A sensitivity analysis of the various parameters indicates that production rates are most sensitive to tubing size, formation damage, and those parameters that dictate ultimate possible water recovery, such as PV and initial pressure.

Introduction
To determine the economic feasibility of producing geopressured aquifers for energy, several investigators have utilized simplified reservoir engineering techniques to predict aquifer behavior during production. These techniques assume an arbitrary, constant flow rate, and the well is produced at this rate until the surface pressure falls to some limiting value. The rate then can be reduced and production continued until the limiting pressure is once again reached.
While these previous investigations provided valuable information, the use of a constant flow rate in determining the rate of energy production can decrease the present value of the energy by spreading the production over a long time span. In practice, the optimal flow rate from a geopressured aquifer for a given development scheme could be the maximum possible flow rate. The maximum production rate is realized if a well is produced with the minimum surface pressure possible. The resulting flow rate and BHP would decrease continuously with time, making treatment by simplified reservoir engineering techniques impossible.
The optimal development scheme would maximize the present value, requiring both a reservoir engineering study using the described techniques and an economic study. This would consider development and operating costs as well as the income from methane production. This type study would optimize the number of wells and the size of wellbores, and would consider the effects of different well spacings.
The scope of this paper is limited to the adaptation of well-known solutions to the diffusivity equation to the treatment of the case where both flow rate and BHP decrease continuously with time. A follow up paper by Quitzau and Bassiouni considers the economics of geopressured energy using one of the techniques discussed in this paper and Monte Carlo simulation.

Development of Equations
During production of a geopressured aquifer, the surface pressure at any given time is equal to the aquifer pressure near the wellbore less any pressure drop caused by formation damage (skin), and less hydrostatic and frictional losses in the tubing string:The pressure drop caused by skin damage can be found bySince gas will be coming out of solution as the pressure is reduced in the flow string, the frictional and hydrostatic pressure loss terms have to be estimated with one of the numerous two-phase flow correlations available for that purpose.
Most of these correlations are documented by Brill and Beggs. Note that these correlations were developed for flow rates and flow path sizes that are much smaller than these required for optimal exploitation of a geopressured well.
JPT
P. 503^