# 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.

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