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.