| This work addresses the prediction of the long-term temperature and pressure variations of natural gas that is stored cyclically in underground formations.;A knowledge of such variations during injection and withdrawal is important for two reasons. First, an increase in pressure accompanied by a decrease in temperature (possible near the bottom of the wellbore during injection) may cause hydrate formation and condensation in the wellbore, thereby increasing the possibility of flow restriction. Second, economic considerations dictate the need for a knowledge of gas temperature upon withdrawal. In each case, a major variable is the time of flow, bringing the need for an unsteady-state solution that depends on the history of the system.;The model addresses three distinct, but coupled, regions of interest: the well column, the rock formation surrounding the well, and the gas-storage region in the vicinity of the wellbore. In the well column, Euler's method is used for solving the differential equations of momentum and energy, together with equations for frictional dissipation and heat transfer with the surrounding rock formation. In this rock formation, the finite-element method is used for solving the transient heat-conduction equation. In the storage region, the finite-element method is also used for solving for pressures and temperatures.;An interactive computer program is developed that accurately calculates the long-term temperature and pressure changes in the coupled three-region system. Features include variable gas compositions, injection/withdrawal schedules, geothermal temperatures, and well casing/tubing arrangements.;Within the context of the finite-element method, three different element types were examined: a linear triangle, an isoparametric quadrilateral, and a new element with a logarithmic basis function to match the logarithmic nature of the gas pressure profile in the reservoir, which thereby reduces the number of required elements. A test case of annual injection and withdrawal was used to test the reproducability of results between the different element types. In addition, a match of actual field data was performed, which gave results within 2.2% of known recorded values. |
