Interpretation of Simulated Falloff Tests
Authors: Onyekonwu M.O. , Ramey H.J. , Brigham W.E. , Jenkins R.M. 
Published: December 2007

Abstract
A study was made of the method for determination of swept volume and the proper average temperature to use for interpretation of combustion falloff data using the "pseudo-steady" state concept. Two thermal simulators were used for this study to include non-uniform reservoir temperature and variable saturation effects. Skin and storage effects were not included. Interpretation of the data was based on the finding that, because of the very large contrast between the conductivity of gas in the swept volume and that in the unswept sand ahead, transient effects caused by the swept volume would be characteristic of a section of very high transmissivity (kh/w). This implied that the transition period characteristics of the falloff data will form a straight Cartesian line whose slope will be related Lo the swept volume. This follows from the concept of "pseudo-steady" state. Results obtained from the analysis of simulated data showed good agreement between calculated swept volume and actual swept volume. However, the swept volume was found to include both the burned volume and also the high gas saturation zone ahead of the combustion front. Thus a volume correction is necessary to relate the swept volume to the burned volume. In addition, average temperatures within the swept volume were calculated so that the appropriate physical properties can be included in the interpretation. properties can be included in the interpretation. Graphs which can he used to make these corrections are presented for use in interpreting similar field falloff data. Although a one-dimensional radial model was used for this study, the concept should apply in multi-dimensional cases where gravity override is common.

Introduction
Many authors have applied different methods to estimate the swept or burned volume from pressure falloff analysis. These methods include pressure falloff analysis. These methods include the radius of investigation method, the semilog intersection method, the deviation time method and material balance methods. Some of these methods yield swept volume that is larger than the actual swept volume. Recently, there has been interest in using the "pseudo-steady" state concept, a material balance method, in the analysis of thermal falloff data. Due to the large contrast between the mobility of the gas in the swept volume and the fluid in the unswept sand ahead of the front, the swept sand tends to behave like a large tank closed except at the well. This phenomenon has been observed by Mangold et al in their study of geothermal reservoirs. They observed that the presence of zones of different temperatures in presence of zones of different temperatures in non-isothermal reservoirs, resulted in a fluid mobility contrast that may resemble permeability barriers during well testing.
The use of this concept has been investigated with different models. The results show that a typical pressure falloff curve will normally consist of an initial semilog straight line followed by a transition period and finally by a second semilog straight line. The transition period may contain a straight Cartesian line whose slope is related to the swept volume.
In the models used in these investigations, several assumptions were made. These include; that the reservoir temperature is uniform, no saturation gradient exists at the front, the gas in the swept volume behaves as fluid of slight but constant compressibility, and the front interface is an isopotential surface. This study used finite difference thermal simulators to relax some of the assumptions, and to evaluate the appropriate temperature to be used in the analysis of combustion falloff data. Also the swept volume as determined from pressure analysis was compared with the actual simulated volume.

THEORY
The slopes from the initial semilog straight line and the Cartesian straight lines are related to the reservoir and fluid properties by the following equations:
(1)
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