A Dynamic Programming Model of the Cyclic Steam Injection Process
Authors: Bentsen R.G. , Donohoe D.A.T. 
Published: December 2007

Because cyclic steam injection is a multistage-decision process, dynamic programming -characterized by a criterion function to be satisfied, a programming -characterized by a criterion function to be satisfied, a number of stages in time and space, and decisions to be made at each stage to satisfy the criterion function - may be used to predict an optimum operating policy for the specific injection project.

Introduction
The cyclic steam injection process has become the most widely applied and most successful thermal recovery technique in use today. Normally, steam stimulation is repeated several times during the life of a project. The problem is to select the optimum number and size of steam treatments so that the profits realized over the entire life of the project are profits realized over the entire life of the project are maximum. Obviously, operating costs rise directly with the frequency and amount of steam injection. Operating efficiency, on the other hand, can be adversely affected if the amount and frequency of stimulation are insufficient. Thus arises a multistage decision problem; that is, a decision must be made at each sub-period (day, for example), as to whether steam should be injected, and, if so, how much. It is desirable that these decisions be made in such a way as to secure maximum net profit before taxes. This can be achieved by dynamic programming.
To use dynamic programming, we must be able to predict not only the production rate-time curve predict not only the production rate-time curve resulting from a given simulation, but also how changes in stimulation policy will affect this curve. In this study, the effect of steam injection on well performance is estimated on the basis of a simple model performance is estimated on the basis of a simple model that takes into account both steady-state and transient flow. Oil production rate is calculated for both types of flow, and the larger of the two values is used. This allows the calculation to change to radial steady-state flow at such time as this mechanism becomes more effective than the transient mechanism.
We propose to show how dynamic programming can be used to optimize the steam soak process with respect to net profit. For this, a mathematical representation of the steam soak technique is necessary. A further objective, therefore, is the formulation of a mathematical model capable of realistically simulating the physical process.

Oil Production Response Model
The advantage of using a mathematical model is its generality and case of manipulation. However, the model must be an accurate representation of the physical process, for a solution derived from a model physical process, for a solution derived from a model can be no better than the model itself. The question now arises as to how well the model should be expected to simulate reality. In general, the simplest model should be tried first, for additional accuracy is apt to require additional cost and time. Also, the search for a high degree of accuracy may yield only greater complexity and difficulty without yielding significantly better results.
With this in mind, we kept our model as simple as possible, yet generally representative of the actual possible, yet generally representative of the actual physical process. The number of state variables is physical process. The number of state variables is limited to three, and stochastic variations in the parameters are ignored. As a consequence, use of parameters are ignored. As a consequence, use of this model should be restricted to cases in which the underlying assumptions are not severely violated.
JPT
P. 1582