Accumulation Terms

The general form of the mass accumulation term that includes equilibrium sorption on the solid grains is:

$M^\kappa\quad=\quad\varphi\sum_{\beta}{S_\beta\rho_\beta X_\beta^\kappa}+(1-\varphi)\rho_R\rho_lX_l^\kappa K_d$ (4-2)

where $\varphi$ is porosity, $S_\beta$is the saturation of phase $\beta$ (e.g., $\beta$ = gas, aqueous, non-aqueous phase liquid/oil), $\rho_\beta$is the density of phase $\beta$, and $X_\beta^\kappa$is the mass fraction of component k in phase $\beta$, $\rho_R$is the rock grain density, and $K_d$ is the aqueous (liquid) phase distribution coefficient. The total mass of component k is obtained by summing over the fluid phases $\beta$. The heat accumulation term in a multiphase system is

$M^h\quad=\quad(1-\varphi)\rho_RC_RT+\varphi \sum _\beta S_βρ_βu_β$ (4-3)

where $C_R$is the specific heat of the rock grains, T is temperature, and $u_\beta$is the specific internal energy of phase $\beta$.