STOMP components comprise the subsurface systems of interest. Available components and component phases vary based on the operational mode (Table 1). The component mass conservation equation equates the time rate of change for each STOMP component mass within a control volume with the flux of that component mass crossing the control volume surface. Phase partitioning of components are computed assuming equilibrium conditions for all modes of STOMP (except HYDTKE). This implies that in geologic media the time scale for thermodynamic equilibrium is significantly shorter for component transport.
Table 1. Equilibrium components and component phases for STOMP modes in liquid (l), gas (g), NAPL (n), precipitated salt (p), hydrate (h), and ice (i) phases.
The lefthandside of the equation represents the volumetric integral of the mass accumulation term for component (j) in all phases (γ) over the node volume. The righthandside of the equation represents the surface integral of flux terms over the node volume as well as the volumetric integral of source/sink terms.
Where the mass accumulation term is
and component (j) can exist in the aqueous (l), nonaqueous liquid (n), gas (g), hydrate (h), ice (i), and precipitated (p) phases under equilibrium conditions, depending on the operational mode.
The flux is a combination of advective and diffusive components:
For the oil component,o, the mass conservation equation is modified to include mass accumulation of sorbed oil to the rock/soil phase.
In STOMPW, WAE, WS, WASE, and WAS, there is an osmotic flux term, which accounts for the flow of aqueous fluid by osmotic pressure for simulations with coupled salt transport.
The mass conservation equations, shown above, are discretized by assuming a piecewise profile to express the variation in primary variables between node points and integrating over the node volume. The mass accumulation terms (i.e., lefthandside terms) are integrated over the node volume according to
Defining flux directions parallel to the surface normal allows the surface integrals to be converted to summations over all node surfaces.
where west (W), east (E), south (S), top(T), and bottom (B) node surfaces are considered.
This transformation strictly requires an orthogonal grid system for the flux directions to be aligned with the surface normals. Nonorthogonal systems will yield mass balance errors.
The mass conservation equations are discretized in time using a fully implicit scheme, where the time levels are indicated with superscripts. The primary unknowns for the mass conservation equations are intrinsic properties at node volume centroids (node grid point) for time level t+δt.
The residual equation for each component is then the difference between lefthandside and righthandside.
Dissolution of water in the NAPL phase is neglected in all operational modes except STOMPHYDTKE.
Dissolution of air in the NAPL is neglected.
In WaterOil (WO) and WaterOilAir (WOA) modes, oil exists in the diffusive pore space as liquid oil in the NAPL phase, dissolved oil in the aqueous phase, and as oil vapor in the gas phase.
Salt transport occurs by advection and diffusiondispersion through only the aqueous phase.
Following the low solubility assumption for dissolved air and oil in the aqueous phase, water diffusiondispersion through the aqueous phase is neglected.
Symbols(In order of appearance) 

time, s  
volume of element n, m^{3} 

mass accumulation term for component j , kg/m^{3}  
surface of element n, m^{2}  
advective flux of component j, kg/m^{2}s  
unit surface normal vector  
mass fraction of component j in phase γ  
specific mass source of phase γ, kg/m^{3} s  
diffusive porosity 

density of phase γ, kg/m^{3} 

saturation of phase γ  
Darcy velocity vector of phase γ, m/s  
diffusivedispersive flux of component j for the phase γ, kg/m^{2} s  
relative permeability of phase γ  
intrinsic permeability, m^{2}  
kinematic viscosity of phase γ, Pa s  
pressure of phase γ, Pa  
acceleration of gravity, m/s^{2}  
unit gravitational direction vector  
molecular weight of component j, kg/kg mol  
molecular weight of phase γ, kg/kg mol  
phase tortuosity for phase γ  
diffusion coefficient of component j for phase, m^{2}/s  
mole fraction of component j in phase γ  
total porosity  
area of surface, m^{2} 
Subscripts  

phase index  
aqueous liquid phase  
nonaqueous liquid phase  
gaseous phase  
hydrate phase  
ice phase  
precipitated salt phase  
solid phase  
node surface index 

negative surface (west, south, bottom)  
positive surface (west, south, bottom) 
Superscripts  

component index  
oil component  
water component  
salt component  
upwind weighting scheme  
harmonic weighting scheme 