Temperature increase with time during in-situ combustion process

Input(s)

$S_{o}$: Saturation of Oil (fraction)

$\emptyset$: Porosity (fraction)

$\mathrm{n}$: exponent

$\rho$: Density of Oil $\left(\mathrm{lb} / \mathrm{ft}^{3}\right)$

$A_{c}$: Pre-exponential Constant $(1 / \mathrm{F} \mathrm{psi})$

$P_{O 2}$: Partial Pressure of Oxygen (psi)

$M_{r}$: Volumetric Heat Capacity of Reservoir (BTU/F $\mathrm{ft}^{3}$ )

E: Activation Eergy (BTU/lbm mol)

R: Gas Constant (BTU/lbm mol F)

$T_{a b}$: Absolute Temperature (K)

Output(s)

$\frac{d T}{d t}$: Temperature Increase with Time $(\mathrm{K} / \mathrm{s})$

Formula(s)

$$ \frac{\mathrm{dT}}{\mathrm{dt}}=86,400\left(\frac{\mathrm{S}_{\mathrm{o}} * \rho * \emptyset * \mathrm{~A}_{\mathrm{c}} * \mathrm{P}_{\mathrm{O} 2}^{\mathrm{n}}}{\mathrm{M}_{\mathrm{r}}}\right) * \exp \left(-\frac{\mathrm{E}}{\mathrm{R} * \mathrm{~T}_{\mathrm{ab}}}\right) $$

Reference(s)

Prats, M. 1986. Thermal Recovery. Society of Petroleum Engineers, New York, Chapter: 8, Page: 95.