Ignition delay time in in-situ combustion
Input(s)
\(M_{r}\): Volumetric Heat Capacity of Reservoir \(\left(\mathrm{BTU} / \mathrm{ft}^{3} \mathrm{~K}\right)\)
\(T_{a}\): Initial Absolute Temperature (K)
\(\mathrm{n}\): exponent
\(\mathrm{R}\): Gas Constant (BTU/mol K psi)
E: Activation Energy (BTU/K mol)
\((d h)_{a}\): Heat Generated by Oxygen (BTU)
\(\varnothing\): Porosity (fraction)
\(S_{o}\): Saturation of Oil (fraction)
\(\rho_{o}\): Density \((\mathrm{g} / \mathrm{cc})\)
\(A_{c}\): Pre Exponential Constant (1/psi K)
\(P_{o 2}\): Partial Pressure of Oxygen (psi)
Output(s)
\(t_{i g}\): Ignition Delay (s)
Formula(s)
\[
\mathrm{t}_{\mathrm{ig}}=\frac{2.04 * 10^{-7} * \mathrm{M}_{\mathrm{r}} * \mathrm{~T}_{\mathrm{a}}^{2} *\left(1+\left(\frac{2 * \mathrm{R} * \mathrm{~T}_{\mathrm{a}}}{\mathrm{E}}\right)\right) * \mathrm{R} * \exp \left(\frac{\mathrm{E}}{\mathrm{R} * \mathrm{~T}_{\mathrm{a}}}\right)}{\mathrm{E} *(\mathrm{dh})_{\mathrm{a}} * \emptyset * \mathrm{~S}_{\mathrm{o}} * \rho_{\mathrm{o}} * \mathrm{~A}_{\mathrm{c}} * \mathrm{P}_{\mathrm{o} 2}^{\mathrm{n}}}
\]
Reference(s)
Prats, M. 1986. Thermal Recovery. Society of Petroleum Engineers, New York, Chapter: 8, Page: 95.