Average reservoir temperature in a cyclical steam injection process

Input(s)

$T_{i}$: Initial Temperature $(\mathrm{K})$

$T_{s}$: Temperature of Steam $(\mathrm{K})$

$f_{H D}$: Time-dependent Conduction Loss in Direction of Heated interval (dimensionless)

$f_{V D}$: Time-dependent Conduction Loss Normal to the Direction of Heated interval (dimensionless)

$f_{p D}$: Time-dependent Quantity for Heat Loss by Produced Fluid (dimensionless)

Output(s)

$T_{a}$: Average Temperature within the Heated Zone (K)

Formula(s)

$$ \mathrm{T}_{\mathrm{a}}=\mathrm{T}_{\mathrm{i}}+\left(\mathrm{T}_{\mathrm{s}}-\mathrm{T}_{\mathrm{i}}\right) *\left(\mathrm{f}_{\mathrm{VD}} * \mathrm{f}_{\mathrm{HD}} *\left(1-\mathrm{f}_{\mathrm{pD}}\right)-\mathrm{f}_{\mathrm{pD}}\right) $$

Reference(s)

Prats, M. 1986. Thermal Recovery. Society of Petroleum Engineers, New York, Chapter: 9, Page: 115.