This report presents the mathematical models and computational procedure for the material balance calculation around each of the following units that constitute the METC producer gas clean-up system: gas cyclone; humidifier; electrostatic precipitator; hydrolysis unit; direct cooler; Stretford process; and final wash tower. The computation procedure is specifically designed to calculate the material balance for the producer gas clean-up system. All items to be computed by the program are listed. The process is sequential, in that the outlet stream from a unit is directly fed into the unit immediately following it. This procedure simplifies the computation because no iteration procedure is required. Two different kinds of data input are needed in each process unit calculation: preassigned data, such as temperature and pressure etc., and feed composition and flow rate. The gasifier simulation program developed earlier is integrated with this gas clean-up system simulation program through a hypothetical joint box. The present clean-up system modeling is handicapped by a lack of some crucial information, among them being: vapor--liquid equilibrium and enthalpy data for tar; proprietary process equipment performance information; and reaction kinetics information. Wherever such information is lacking, appropriate assumptions are made to circumvent the difficulty. These assumptions, however, should be verified by comparing computed values from this program with experimentally obtained data from the pilot plant.