A permeation theory of in-situ coal gasification is developed, and a mathematical model is derived for the process. Predicted gas compositions, gas flow rates, and temperature profiles are in good agreement with field test data. For example, experimental gas compositions deviate no more than 3 to 4 mol% from calculated values. On the average, agreement is much better. The major purpose of the permeation theory is to provide a basis for quantitative understanding of in-situ coal gasification and to lead to important general conclusions concerning the nature of the process. The well instrumented Hanna 2, Phase 2 test was essential in providing needed Phase 2 test was essential in providing needed information to confirm the theoretical conclusions. This test was conducted near Hanna, WY, during 1976 and was the best instrumented and most successful held test ever conducted up to that time. PART 1: DEVELOPMENT OF THEORY PART 1: DEVELOPMENT OF THEORY The dilemma of rapidly decreasing reserves of natural gas in the U. S. and the need for a clean, easily transported fuel has spurred much interest in the production of gas from coal. One of the most promising methods of coal gasification was promising methods of coal gasification was demonstrated by field tests conducted for the last 5 years by the Laramie Energy Research Center at Hanna, Wy. In fact, Phase 2 of the Hanna 2 test (completed in May 1976) was perhaps the most successful in-situ coal gasification test ever conducted. It more complete description of this test is given later. The experimental data are presented in Part 2 to confirm the theory developed presented in Part 2 to confirm the theory developed in this section. Since May 1976, other successful field tests have been reported by the Alberta Research Council, Texas Utilities, and the Lawrence Livermore Laboratory. NEED FOR A THEORETICAL MODEL Before this study, no physical theory was available that successfully predicted field test data. Many of the most important features of underground coal gasification (UCG) were poorly understood or not understood at all. For example, the heating value of gas produced during the Hanna field tests was much higher than that reported for previous field experiments at other locations; the previous field experiments at other locations; the reasons for this anomaly were unknown. It was widely believed that the optimistic results from the Hanna field experiments might be peculiar or specific to the Hanna area. However, the development of a theory of UCG and successful field experiments with the linked, vertical well process at other locations now are proving this assumption false. The need for a theoretical understanding of UCG has become readily apparent. A more thorough interpretation of field test results required the development of a theoretical mathematical model for the process. In addition, design capability must be developed before UCG can become a commercial process. This capability is essential for carrying process. This capability is essential for carrying out economic studies and risk analyses as well as engineering design. The design method must determine many variables, such asgas composition,gas heating value,air injection rate requiredgas produced per unit volume of air injected,coal consumption rate,effect of coal composition,effect of coal bed thickness,effect of ash content,effect of moisture content,effect of varying pressure and air injection rate, andwell spacing and configuration. The theory developed in this study provides definite information concerning Items 1 through 10 as well as several items not listed. Item 11 can be determined by a two-dimensional extension of the methods described here. Not infrequently, design methods were developed empirically on the basis of experimental data. In fact, the Soviet Union has used this approach to UCG. A theoretical predictive method, however, is more desirable because much less costly field testing is required to validate the method. Once the method is fully validated, it can be used to predict UCG behavior even under operating predict UCG behavior even under operating conditions never tested previously. SPEJ P. 300