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^
TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractOne of the common applications of horizontal wells is the development of thin oil columns underlain by bottom water and/or overlain by a gas cap. Vertical wells are not suited in this situation due to the rapid coning of water or gas at reasonable production rates. Horizontal wells correctly positioned in the oil column, however, can produce at high flow rates with very little drawdown. The small drawdown significantly delays the breakthrough of water or gas at flow rates much higher than the flow rates possible from a vertical well.
In water drive gas reservoirs, wells can be completed with a long perforated interval and produced at high rates to minimize abandonment pressure and maximize recovery. Alternatively, the perforations can be limited to the top of the productive interval and the well produced at a low rate in an effort to prevent coning which results in high abandonment pressures if the strength of the aquifer is adequate to support reservoir pressure. This study uses a reservoir simulation coning model to evaluate these two conflicting completion and production practices. The impact of completion interval, gas production rate, and reservoir permeability were evaluated. Ultimate gas recovery was found to be largely insensitive to variations in perforated interval and production rate in high permeability systems. Ultimate water production, however, was found to increase at high gas rates and lengthened perforated intervals. In lower permeability systems, ultimate gas recovery was found to increase significantly as production rates were increased, while ultimate water production was actually observed to fall. Sensitivity analysis of vertical to horizontal permeability ratio, fluid density contrast, relative permeability, and formation dip did not alter these conclusions. The conclusion that elevated production rates can be expected to have no detrimental impact on ultimate gas recovery suggests that gas rates should be maximized in low water disposal cost situations. This finding favors the completion of an interval sufficiently long to maximize production rate and thereby insure that gas recovery and present value of gas reserves are maximized. In high water disposal cost situations, however, it should be recognized that this strategy might result in elevated water production in high permeability systems. Introduction Many natural gas reservoirs have some level of pressure support from aquifer encroachment. In gas reservoirs with active water encroachment, it is well known that lowering reservoir pressure with fluid withdrawal rates in excess of aquifer encroachment rates can significantly increase ultimate recovery. In a reservoir produced with a single well, the well would most certainly not be at the very crest of the structure. If the reservoir pressure could be lowered by high withdrawal rates, it would be possible to actually drain up-dip gas that would otherwise be unrecoverable. In a multi-well reservoir situation, drainage and competitive situations could make the decisions on how a well of this type should be completed and produced of paramount importance. In either situation, the possibility of "out-running" the aquifer can significantly add to the ultimate recovery from the reservoir. Unfortunately, the decision to produce a water-drive gas reservoir at high production rates is not as clear-cut as it might seem from the perspective of reservoir engineering. Logic and experience indicate that this type of well will ultimately cease production as the result of excessive water production. It is well known that coning of water will occur if the well is produced at high rates. Clearly, water will be produced sooner as the perforated interval is extended toward the gas-water contact. From this point of view, the prudent course of action would be to delay the occurrence of water in the well stream by perforating the very top of the interval and producing at a restricted rate. Selection of optimum completion and production practices for water-drive gas reservoirs requires an understanding of water coning behavior and the implications of water production on well and reservoir performance. Coning behavior during the production of oil and gas has been extensively investigated. The vast majority of the literature on this subject reports the behavior of water or gas coning into an oil completion. Investigations of coning in gas-water systems are much less numerous in the literature. Kabir 1 reported the most extensive evaluation of water coning in a gas-water system in 1983. Kabir used a radial reservoir simulation model with 10 blocks logarithmically distributed in the radial direction and 14 layers in the vertical direction. This model was extremely course by modern standards. Also, reservoir simulation technology had not yet been developed to allow the inclusion of wellbore friction and loading models.
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