# 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.

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