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(\rho \,c_{pt})_p \frac{\partial T}{\partial t}
- \ \phi \sum_{a = \{w,o,g \}} \rho_\alpha \ c_{p \alpha} \ \eta_{s \alpha} \ \frac{\partial P_\alpha}{\partial t}
+ \bigg( \sum_{a = \{w,o,g \}} \rho_\alpha \ c_{p \alpha} \ \epsilon_\alpha \ \mathbf{u}_\alpha \bigg) \nabla P
+ \bigg( \sum_{a = \{w,o,g \}} \rho_\alpha \ c_{p \alpha} \ \mathbf{u}_\alpha \bigg) \ \nabla T
- \nabla (\lambda_t \nabla T) = \rho_{\rm inj} \, c_{\rm inj} \, T_{\rm inj} \, q_{\rm inj}({\bf r})\, \delta({\bf r}) |
The disambiguation fo of the properties in the above equation is brought in The list of dynamic flow properties and model parameters.
The right sides of equations Equations
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–
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suggest no sources of flow
in the right side except the contacts between wells and
reservroir reservoir which is specified by well models as boundary conditions (see
below).
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