Injection of liquid industrial wastes into confined underground saline aquifers can offer a good disposal alternative from both environmental and economic considerations. One of the needs in choosing from among several disposal alternatives is a means of evaluating the influence such an injection will have on the aquifer system. This report describes a mathematical model to accomplish this purpose.

The objective of the contract was to develop a three-dimensional transient mathematical model which would accurately simulate behavior of waste injection into deep saline aquifers. Fluid properties, density and viscosity are functions of pressure, temperature and composition to provide a comprehensive assessment tool. The model is a finite-difference numerical solution of the partial differential equations describing

1. single phase flow in the aquifer,
   
2. energy transport by convection and conduction, and
   
3. compositional changes in the aquifer fluid.
   

The model is not restricted to examining waste disposal operations. It can be used effectively to evaluate fresh water storage in saline aquifers, hot water storage in underground aquifers, salt water intrusion into groundwater flow systems and other similar applications.

The primary advantages of the present model can be summarized as:

1. The model is user-oriented for easy application to full-scale evaluation needs.
   
2. The model is fully three-dimensional and transient.
   
3. The model is comprehensive accounting for density and viscosity variations in the aquifer due to temperature or compositional changes.
4. The model includes the effects of hydrodynamic dispersion in both the temperature and compositional mixing between resident and injected fluids.
5. The model energy balance includes the effects of pressure. This can be important in deep aquifer systems where the viscous pressure gradient is significant.
6. The model uses second-order correct space and time approximations to the convective terms. This minimizes the numerical dispersion problem.
7. The model is extremely flexible in providing a wide choice of boundary conditions. These include natural flow in the aquifer, aquifer influence functions around the perimeter of the grid in recognition that the gridded region does not have no-flow boundaries, heat losses into the overlying or underlying impermeable strata, and the wellbore heat and pressure drop calculations coupled to the aquifer flow equations.

The limitations of the present techniques are:

1. The use of the second-order correct finite-difference approximations introduces block size and time step restrictions. These restrictions, though considerably less stringent than explicit methods cause, depend upon the magnitude of the dispersivity.
2. The comprehensive nature of the model makes the computer time and storage requirements significant.
3. The model, because of its complexity, is not as efficient in reducing down to solve simpler problems as a specially written model would be.

Included in the report are detailed descriptions of the approach used in the model, validation tests of the model, and a typical application of the model. A comparison volume documents the input data requirements, program structure, and an example problem for the model. '