Mass-Balance Equation

The mass and energy balance are based on the general idea of conservation of mass and energy in any space. The amount of mass/energy remains constant--it is neither created nor destroyed during any chemical, physical or/and biological processes. The basic mass- and energy balance equations solved by TOUGH codes can be written in the general form:

$\frac {d}{dt} \displaystyle \int _{V_n}M^kdV_n=\int_{\Gamma_n}F_ k\centerdot \bold{n}d\Gamma_n+\int _{V_n}q^kdV_n$ (4-1)

The integration is over an arbitrary subdomain $V_n$ of the flow system under study, which is bounded by the closed surface $\Gamma_n$. The quantity M appearing in the accumulation term (left-hand side) represents the mass of component k (e.g., water, brine, gases, tracers, radionuclides, VOCs) or energy (k = h) per volume. F denotes mass or heat flux, and q denotes sinks and sources. n is a normal vector on the surface element $d\Gamma_n$, pointing inward into$V_n$ . Each term constituting the equations is described in detail in the following subsections.