Steam Drive Model for Hand-Held Programmable Calculators
Authors: Jones Jeff 
Published: December 2007

Summary
This paper presents a model based on works published by Van Lookeren and Myhill and Stegemeier. The first portion of the model calculates an optimal steam rate (to the nearest 5 B/D) for a given set of steam and reservoir parameters by the method proposed by Van Lookeren. The second portion of the model uses the optimal steam rate (or a given steam rate) and related data calculated in the first portion in conjunction with additional inputs to calculate the oil production history. A modification to the Myhill-Stegemeier model is introduced that significantly improves correlation of model predictions with field results in 14 projects reported in the literature. Included in the paper Is a complete program listing for Texas Instruments Inc.'s TI-59 calculator with a PC-100 printer, as well as operating instructions and an example problem.

Introduction
For many years, various investigators have attempted to provide steamflood models that yield acceptable results yet are applied readily by the average engineer. These calculation methods have taken several forms including (1) a digital computer program by Effinger and Wasson and a "cookbook" graphical method proposed by Fairfield, each presenting easier ways of applying the basic Marx and Langenheim steam-zone growth model, (2) analytical models by Mandl and Volek, Neuman, Myhill and Stegemeier, and Van Lookeren that account for gravity override and steam-front shape factors ignored in the simpler models, and (3) a novel curve-matching model by Gomaa based on parametric studies done with a numerical simulator. All of these methods have drawbacks ranging from oversimplification to cumbersome application, and most include significant handwork for more than a few calculations.An obvious need exists for a model that can be used on a hand-held calculator with as much automatic documentation and as general application as practical. This paper presents such a model for use with a TI-59 programmable calculator and a PC-100 printer.

Model Description

Injection-Rate Optimization Model
The model consists of two integrated components that can be used separately or as a set. The equations for the first component are described in detail in Appendix A, with user instructions in Appendix B. The purpose of this program is to calculate and document steam parameters including Ts, Ps, is, fs, hn, degrees API, and ks. Eq. A-1 is the same equation proposed by Van Lookeren for calculating the effects of segregated flow on vertical steam sweep efficiency. This equation can be used to optimize steam injection rate if the investigator has access to pressure vs. rate data for a given injection project.With such data, it is possible to calculate a maximum EI as a function of an optimal injection rate, which Van Lookeren shows maximizes vertical sweep. It is assumed that the various injection parameters remain constant so initial injectivity tests in a new project probably will not be very useful. However, experience has shown that useful pressure/rate extension data are available when cold-oil-viscosity-dominated cold-oil-mobility effects subside and reservoir-permeability-dominated hot-oil mobility controls injectivity, usually within a year of continuous injection.
JPT
P. 1583^