Optimal Exploitation of Petroleum Resources Using the Average Reservoir Data for the Walton Canyon Reservoir in Summit County, Utah

The main concern of this study is to obtain an optimal time path of crude oil and natural gas production by controlling the pressure at the bottom of any producing well in Walton Canyon Reservoir. To achieve this goal, the following objectives were obtained: (a) an estimation of the reservoir properties at different levels of the reservoir pressure; (b) an estimation of an optimal time path of joint production using the estimated reservoir properties and the expected prices and costs in the absence and presence of severance, state, and federal income taxes, and depletion of allowances; and (c) an analysis of the changes in the rates of extraction, firms\u27 profits, revenues to local, state, and federal governments, and welfare losses as a result of changes in tax policies. To conduct this study, an optimization model is used to maximize the present value of net revenues of firms producing oil and gas in the reservoir, subject to the available stock of oil in the ground. Cost per unit of time is discussed at three stages of production (naturally flowing, pumping, and secondary recovery or pressure maintenance). Using the assumption that all producing wells in the reservoir are at the pumping stage of production, the conclusion is made that only the operating cost is related to the bottom well-hole flowing pressure. Since the goal is to control the rates of joint production by controlling the bottom well-hole flowing pressure, the operating cost of the whole reservoir is minimized through separable programming. The non-linear cost equation is solved for the values of the bottom well-hole flowing pressure under a competitive condition in the absence of externalities. In order to estimate the optimal rates of oil and gas production, the expected prices are computed using the actual domestic prices of oil, gas, and electricity. The optimal rates of oil and gas production are obtained through dynamic programming which is applied to the optimization model using a 15 percent discount rate. However, discount rates of 10 percent and 20 percent also are used to determine the influences on the optimal production plan, allowing the production period for twenty years. The empirical results indicate that the production of oil and gas from this reservoir will be profitable in the future, using a 15 percent discount rate, prior to imposition of any taxes. The whole recoverable stock of oil by pump will be extracted within three years beginning with a higher production rate in 1998 and ending with a lower production rate in the year 2000. A 10 percent discount rate influenced the net revenue of the whole reservoir but did not change the production plan. However, the optimization model and, in particular, the production plan are affected by the 20 percent discount rate. In other words, the joint production is profitable in the early years, using a 20 percent discount rate, beginning with a higher production rate in 1982 and ending with a lower production rate in 1985. The important conclusion is that imposing various taxes and depletion allowances, while using a 15 percent discount rate, did not change the optimal time path of production from that time path, which was obtained in the absence of taxation using the same discount rate. The presence of taxation, however, affected revenues and, thereby, resulted in welfare changes in the producing firms and local, state, and federal governments