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.