Volumetric heat capacity of a reservoir

Input(s)

$\mathrm{M}_{\mathrm{s}}$: Volumetric Heat Capacity of Solids (btu/ft ${ }^{3} \mathrm{~F}$ )

$\emptyset$: Porosity (fraction)

$\mathrm{S}_{\mathrm{o}}$: Oil Saturation (fraction)

$\mathrm{M}_{\mathrm{o}}$: Volumetric Heat Capacity of Oil (btu/ $\mathrm{ft}^{3} \mathrm{~F}$ )

$\mathrm{S}_{\mathrm{w}}$: Water Saturation (fraction)

$\mathrm{M}_{\mathrm{w}}$: Volumetric Heat Capacity of Water (btu/ft $\mathrm{ft}^{3} \mathrm{~F}$ )

$\mathrm{S}_{\mathrm{g}}$: Saturation of Gas (fraction)

f: Fraction of non-condensable Gases (fraction)

$\mathrm{M}_{\mathrm{g}}$: Volumetric Heat Capacity of Gases (btu/ft ${ }^{3} \mathrm{~F}$ )

$\rho_{\mathrm{s}}$: Density of Solids $(\mathrm{g} / \mathrm{cc})$

$\mathrm{C}_{\mathrm{w}}$: Isobaric Specific Heat of Water (btu/lb F)

$\Delta \mathrm{T}$: Temperature Differential $(\mathrm{K})$

$\mathrm{L}_{\mathrm{v}}$: Latent Heat of Vaporization (btu/lb)

Output(s)

$\mathrm{M}_{\mathrm{r}}$: Volumetric Heat Capacity of Reservoir (btu/ft $\mathrm{ft}^{3} \mathrm{~F}$ )

Formula(s)

$$ \mathrm{M}_{\mathrm{r}}=(1-\varnothing) * \mathrm{M}_{\mathrm{s}}+\varnothing * \mathrm{M}_{\mathrm{o}} * \mathrm{~S}_{\mathrm{o}}+\varnothing * \mathrm{~S}_{\mathrm{w}} * \mathrm{M}_{\mathrm{w}}+\emptyset * \mathrm{~S}_{\mathrm{g}} *\left(\mathrm{f} * \mathrm{M}_{\mathrm{g}}+(1-\mathrm{f}) *\left(\frac{\mathrm{L}_{\mathrm{v}} * \rho_{\mathrm{s}}}{\Delta \mathrm{T}}+\rho_{\mathrm{s}} * \mathrm{C}_{\mathrm{w}}\right)\right) $$

Reference(s)

Prats, M. 1986. Thermal Recovery. Society of Petroleum Engineers, New York, Chapter: 12, Page: 164.