Crude Oil Prorationing As An Optimization Problem
Authors: Walden Thorn 
Published: March 2010

Abstract
Criteria employed in various jurisdictions to prorate oil production from a number of reservoirs to market demand are expressed as linear and quadratic programming problems. Prorationing in practice uses rather cumbersome approximate methods.

Introduction
Crude oil prorationing to market demand has largely been confined to the North American continent. It deals with the problems which arise when three circumstances occur in combination.The rule of capture (if you produce it you own it, even if itfound its way to your well from an adjoining property).Fragmented reservoir ownership and operation.Accessible markets not sufficient to absorb output at full capacity.
This combination if unchecked can result in competitive extraction, with each operator trying to drain hydrocarbons from adjoining properties. Where some producers own refineries and some do not, the latter may be severely drained if they cannot find markets and cannot get their more fortunate competitors to share their markets. On other continents a different land tenure system prevails, the rule of capture generally does not apply, and reservoirs are typically under the control of a single operator.
If the first two conditions hold and markets are capable of absorbing output at full capacity, the problem of allocating output among pools disappears. There remains the problem of achieving efficient reservoir management while ensuring that output within a reservoir is in accordance with some criterion of fairness to the ownership interests, thereby addressing the problem of competitive extraction.
This paper expresses the full range of oil prorationing criteria that have come to the writer's attention as linear or quadratic programming problems, and should provide a basis for analogous treatment of any that may have been overlooked.

Prorationing in Alberta
The Energy Resources Conservation Board (ERCB) has administered Alberta's prorationing system since the program's province-wide introduction in 1950 (although the Turner Valley field became subject to prorationing in 1938 after years of legal challenges), a program that has seen a number of major changes over the years.
In the late 1960s Alberta's prorationing system changed fundamentally. Proratable demand, which had been allocated among pools according to productive capacity, shifted to proratable reserves (defined as the simple average of initial recoverable reserves and remaining recoverable reserves) as a basis for allocation; at the same time a new approach was adopted by reservoir engineers to establish each pool's maximum authorized production rate (maximum rate limitation or MRL in Alberta parlance). The allocation of proratable demand was subject to both a maximum and a minimum production level for each pool under prorationing. This prorationing process follows four steps:Elicit from oil buyers a forecast ("nomination") of how much Alberta oil each will purchase in the forthcoming month and total them to obtain market demand.Subtract from market demand that portion of oil production not subject to prorationing (synthetic crude, pentanes plus, heavy crude, etc.) and adjust for foreseeable inventory changes to obtain proratable demand.