  This research paper explores application of multivariable regression models
using only reservoir temperatures for predicting oil and gas production in a
Toe-Heal-Air-Injection (THAI) enhanced oil recovery process. This paper
discusses effects of statistical interaction between thermocouples by using
second degree quadratic polynomials, which showed significant production
forecast accuracy. Interactions among thermocouples statistically include
temperature of larger reservoir areas, hence improving the predictive models.
The interaction of two thermocouples can be interpreted as temperature gradient
of combustion zone as moving forward during THAI operations life cycle.
  Second degree polynomial regression including interactions showed major
prediction improvement for both oil and natural gas productions compare to
simple regression models. Application of Poisson regression slightly improved
prediction accuracy for oil production and was less effective on improving
natural gas production predictions. Quadratic Poisson regression models showed
realistic production prediction method for both oil and gas production values,
due to the nature of Poisson probability distribution which is non-negative for
rates and count values.
