Application of Factorial Design Analysis to Producing Well Pressure-Drop Modelling
Authors: Gregory G.A. 
Published: March 2010

Abstract
This paper demonstrates how the proper use of fractional factorial design analysis can generate not only useful information regarding a complex computer model, but possibly a simple linear approximation of the computer model that is useful for prediction purposes in its own right.
A single four-variable equation is presented which, under Identifiable conditions, can be used in place of the computer model of Aziz et al(2) to predict the pressure drop in oil and gas producing wells with acceptable accuracy.

Introduction
EXPERIMENTATION based on factorial design has long been an integral component of many industrial research studies. One class of design that is particularly suited to preliminary investigations, designated as the 2n factorial design, consists of those experiments in which each factor appears with only two different values, or levels. Although this limits the degree of detailed information which can be obtained concerning the effect of a given factor on the observed response, it does permit an over-all quantitative estimate of the relative importance of various factors and their possible interactions in the form of a simple linear model Furthermore, it is possible to reduce the amount of experimentation required by using only a fraction of the total possible combinations that are formed by selecting one level for each factor.
Even so, these designs have not been widely used in the petroleum industry to study variables influencing the production of oil and gas. The cost of obtaining field data normally rules out many of the experiments because of the number of data points required to take maximum advantage of the statistical analysis. However, although experimentation in the classical sense may be restricted by economic considerations, Sawyer et al. (1) recently demonstrated a way in which factorial experiments can be used effectively in oil and gas recovery problems. The application consists of performing the "experiment" on a complex mathematical modal, with the "experimental data" in fact being the predictions of this complex model for the various factor level combinations indicated by the experimental design. The objective of such a study is to generate a "sub-model" (i.e. a simple mathematical model of the original complex model). This "sub-model", provided it is a reasonable approximation over some limited range of the variables, can be used in hand calculations to pre-select the conditions under which the complex model should be used to best advantage. The result may be a significant saving in the amount of computer time required in a conventional search for optimum conditions using only the complex model.
This paper reports the results of applying the above echnique to the model for the prediction of pressure drop in wells producing oil and gas, recently published by Aziz, Govier and Fogarasic(2). It is further demonstrated that the resulting sub-model may be a highly useful predictor in its own right.

Selection of Independent Variables
In most real systems of interest, a large number of independent variables can be identified.