Reservoir Engineering-General - Discussion on A Study of Forward Combustion in a Radial System Bounded by Permeable Media

The following points serve to supplement the interesting theoretical study on forward combustion by Thomas, and may be of some general interest. The mathematical model presented by the author can be viewed as a first approximation to the problem of calculating the vertical burned height profile resulting from ignition of the interval | z |<h/2 in a very thick formation. However, the assumption of a given minimum combustion temperature T, would give a better approximation to the vertical burned profile if the burning height were not constrained to stay within the ignited layer. This follows from the fact that both fuel and oxygen are present in the adjacent region, |z|>h/2, and for certain combinations of process variables the temperature is sufficiently high for complete combustion to occur. In this case, the vertical coverage will first become greater than the ignited interval before cutting back to zero as the extinction limit is approached as shown in Fig. 1. Such growth of vertical coverage is possible if the minimum combustion temperature is less than the initial source temperature (r = rj) at the edge (z = h/2) of the ignited interval. But this latter temperature is equal to one-half the source temperature for the case of infinite burned height.&apos;,&apos; Thus growth will occur initially if The fact that the vertical burned height can be greater than the ignited interval complicates the picture considerably, as can be seen by referring to Fig. 1. Here burning occurs in Region A, whereas none was possible in the original mathematical model. At the same time, there is no combustion in Region B, contrary to the assumption of burning in the entire layer |z|<h/2. This apparent inconsistency suggests that the vertical coverage derived from this simple model does not adequately represent the vertical height of the burned zone. A more compatible model will result from the actual stepwise calculation of the burning length (as a function of time) that would give rise to the specified combustion temperature. This problem can be more conveniently attacked by using the temperature distribution, given by the author&apos;s Eq. 12, expressed in the integrated form: