An Economic Analysis of Unitized and Non-Unitized Production
Authors: Lueck D. , Schenewerk P. 
Published: December 2007

Abstract
Wasteful production of oil and gas can result when access to a reservoir is held by more than a single producer. Severe economic losses arise because of over-drilling, excessive storage, improper well-spacing, and intertemporal inefficiency as well as damage to the natural drive of the field which can reduce ultimate recovery from the reservoir. Reservoir-wide unitization has long been viewed as the ideal solution to this "common pool" problem. Unitization can be accomplished through private agreements, although in many cases these contracts are difficult to secure because of bargaining costs and hold-out problems. In many cases agreements can be reached only if unitization is compelled by law. We develop a dynamic economic model of reservoir production to analyze unitized and non-unitized reservoirs. The model uses optimal control theory to generate predictions about depletion rates and total recovery under these two regimes. Reservoir simulations are used to examine some predictions of the model and show that production from unitized reservoirs is biased toward the future compared to non-unitized reservoirs and that the initial overproduction under the rule of capture can be significant.

Introduction
When access to an oil or gas reservoir is held by more than one producer. the rule of capture can lead to over-drilling, excessive storage, improper well-spacing, intertemporal inefficiency and damage to the natural drive that may reduce ultimate recovery [Amyx et. al. 1960, Craft et. al. 1991, Hardwicke 1935, McDonald 1971, Weaver 1986]. Production under the rule of capture can lead to rapid and nonoptimal dissipation of reservoir energy, especially if a firm has the advantage of structural position in water-drive reservoirs. The result can be lower total recovery of reserves (particularly oil) with the loss of reserves inequitably distributed among the producers. In addition the waste of economic resources occurs in the form of unnecessary platforms and wells. In principle, waste from this "commonpool" problem can be eliminated by assigning production rights to a single operator. Two primary methods exist to accomplish this:Prior to drilling. ownership of surface rights to the reservoir can be consolidated through purchase of land, large scale leasing, or the formation of an exploratory unit; andOnce production has indicated a common-pool, firms can join to form a reservoir-wide unit.
In this paper, we develop a dynamic economic model of reservoir production to analyze unitized and non-unitized reservoirs. This model uses optimal control theory to generate predictions about the depletion rates and total recovery under these two regime. The general hypothesis is: Unitized production and sole ownership will generate greater field output and an optimal time-path of depletion when compared to non-unitized reservoirs. When considering the causes of reservoir ownership the theory will focus on explanations for the formation of units and the consolidation of surface ownership or production rights. The general hypothesis is: Larger surface tracts, better reservoir knowledge, and a smaller number of producers will increase the probability of unit agreements and pre-production consolidation of reservoir rights. We then use simulations of reservoirs with similar geological-engineering characteristics under unitized and non-unitized production to examine the predictions of our model. These simulations show that reservoir exploitation under unitization is consistent with an economic model that maximizes the present value of reservoir production. Finally, we examine some of the determinants of unitization contracts.

THE LAW AND ECONOMICS OF PETROLEUM CONSERVATION
Typically, an oil reservoir may exist in a variety of states, with or without a gas cap and with or without an aquifer. The energy which drives the oil to the producing well is provided by the expansion of gas and displacement by water when an active aquifer is present. As oil is produced from a well the reservoir pressure is decreased and the neighboring area is drained. The extent of this drainage depends upon subsurface pressures, oil viscosity, and the permeability and porosity of the reservoir rock.
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