Work done during the second quarter of this contract is presented. The coal reaction models developed during the first quarter have been coupled with the fluid mechanics of the gasifier to formulate the conservation equations that describe the performance of the gasifier. This completes the set of equations needed for continued development of the computer programs. These equations are all presented in this report; they include: (1) gas and particle species mass conservation; (2) gas and particle momentum conservation; (3) gas and particle energy conservation; (4) mass source due to coal devolatilization; (5) mass source due to char reactions; (6) species mass source due to gas phase reactions; (7) equations describing momentum and energy interactions; and (8) equations describing gas phase properties. Work has continued on the development of the pulsating coal gasifier computer code by modifying the Baum-Levine solid rocket combustion instability program. The gas and particle conservation equations were normalized and expressed in a vector form suitable for numerical integration. Modifications of all of the subroutines necessary to perform the numerical solution using the Lax-Wendroff method have been completed. Subroutines needed to compute the various mass source terms due to coal reactions, as well as boundary routines, input/output routines, etc. will be completed during the third quarter of this contract. 17 refs., 1 fig., 3 tabs.