Locating a Burning Front by Pressure Transient Measurements
Authors: Kazemi Hossein 
Published: December 2007

Abstract
A pressure fall-off test on the injection well of a forward combustion project may permit us to calculate the distance to the burning front. In the mathematical description and analysis of test data, we have considered the effect of temperature on the thermodynamic properties of reservoir fluids. The temperature distribution predicted by Chu for a combustion wave has been used in analyzing a field test. Numerical solutions were obtained by simultaneous solution of the flow equation, the continuity equation and the equation of state. Although this analysis concentrated on isotropic systems, the results can be extended to systems having directional permeability.

Introduction
Conventional pressure fall-off tests have been used extensively to determine reservoir characteristics in gas- or water-injection projects. Such tests consist of injecting fluid into the formation at a constant rate until steady state is nearly achieved, then discontinuing injection and measuring the bottom-hole pressure as a function of time. A plot of pressure vs the logarithm of time (measured from the instant of shut-in) yields a smooth curve characterized by three distinct regions (Fig. 1): Region 1 reflects the permeability alterations in the vicinity of the wellbore; Region II reflects the reservoir characteristics further away from the wellbore; and Region III, the characteristics in the displaced fluid bank. The curves in Regions II and III are straight lines, the slopes of which are proportional to the reciprocal of the flow capacity of the formation behind and ahead of the interface as shown by Eq. 1, respectively:
.....................(1)
If the two-phase interface is a circular cylinder, and if the portion of the formation occupied by the injected fluid is homogeneous, the distance to the interface may he calculated by Eq. 2:
.................(2)
Several analysts use an assumed value for .Eq. 3 may also be used to calculate the distance to the interface:
....................(3)
The coefficient of the logarithmic expression on the righthand side is the transmissibility ratio between the regions behind and ahead of the front, and is equal to the ratio of the inverse slopes of the straight lines in the plot. A pressure fall-off test can also be applied in a forward combustion project to locate the position of the burning front. The shape of the pressure fall-off curve is different from that in a conventional test. This is because the fluid properties are functions of position caused by variations in temperature in the tested zone. Also, irregular geometry in both the reservoir and the combustion front (tonguing of the combustion front) can produce similar effects. Van Poollen reported the first fall-off test on a thermal project, but he did not consider the effect of temperature variations. In this work a new method is presented which includes the effect of temperature in the analysis, and a technique is proposed for locating the burning front.
THEORY ASSUMPTIONSThere are several assumptions implicit in this development:the formation is horizontal, of uniform thickness and homogeneous;before breakthrough, the burned-out zone is circular in an isotropic system, and vertical conformance is 100 per cent (although the analysis is concerned primarily with isotropic systems, it is shown that the results can be extended to systems having directional permeability);the burning front has infinitesimal thickness in the radial direction;the region behind the burning front contains only air, while in the region ahead of the front there are flue gases, hydrocarbon and water vapors and liquid hydrocarbons and water (Fig. 2);
JPT
P. 227ˆ