In the underground combustion process, part of the heat generated at the combustion front is carried downstream by convection. Temperature distribution in the combustion process can be obtained by including a delta function for heat generation at the combustion surface. This is similar to the hot-fluid injection model of Lauwerier. The dimensionless temperature in the reservoir, phi T1(x, t), and the overburden, phi T2(x, y, t), are as follows:
..........................................(1)
..........................................(2)
The ratio R of the heat-front velocity, u, h, to the combustion front velocity, uc, is one of the most important factors governing the temperature distribution in the pay zone. For cases of ub less than uc, no heat is carried ahead of the combustion front and the temperature at the combustion front remains constant for all times. The fraction of the heat stored between the heat front and the combustion front decreases as the time increases. This is because more of the heat is consumed in heating the formation behind the heat front and in heating the cap and bass rock.
A more advantageous condition obtains for uh is greater than uc. For this case, the formation ahead of the combustion front is preheated and the amount of heat in this region increases with time. Therefore, due to heat generation and preheating, the total temperature rise at the combustion front also increases with time. Eq. 1 also shows that the temperature at the combustion front is higher at a given time for a thinner reservoir. This seemingly paradoxical result takes place because the amount paradoxical result takes place because the amount of heat recovered from the overburden and subrock upstream of the combustion front is almost independent of the pay zone thickness. On the other hand, this heat is distributed in the pay zone, which has a heat content directly proportional to the formation thickness b. For thin reservoirs, therefore, the temperature rise in the pay zone due to heat recuperation is higher than that in thick reservoirs. For very thick pay zones (h-oo) there would be no heat recuperation, and consequently the combustion- front temperatures would be lowest.
For many cases encountered, uh is smaller than uc. Convective-heat transport. ahead of the combustion front can be achieved by increasing uh to obtain the condition uh, >uc. The wet and partially quenched combustion processes have a similar objective. The temperature at the combustion front, however, decreases as the uh/uc ratio increases. If this temperature should fall below the ignition point, the fire would die out. Consequently, at any point, the fire would die out. Consequently, at any time there exists a maximum ratio of uh/uc for which the formation ahead of the combustion front can be heated to increase oil mobility while combustion is maintained.
For the case where the heat front moves faster than the combustion front (uh is greater than uc), the downstream heat efficiency E can be derived by applying the integration method given in Ref. 3.
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Heat Localization in the Medium in Blow-Up Regime