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Keywords:

  • coupled differential equations;
  • high temperature-high pressure;
  • Runge–Kutta method;
  • sensitivity analysis

Abstract

In this paper, we build a model of coupled differential equations concerning pressure, temperature density and velocity in H-T-H-P (High Temperature-High Pressure) gas wells according to the conservation of mass, momentum and energy. We present an algorithm-solving model by the fourth-order Runge–Kutta method. Basic data from the Dayi Well, 7100 m deep in China, are used for case history calculations and a sensitivity analysis is done for the model. Gas pressure, temperature, velocity and density along the depth of the well are plotted with different productions, different geothermal gradients and different thermal conductivities, intuitively reflecting gas flow law and the characteristics of heat transfer in formation. The results can provide a dynamic analysis of production for H-T-H-P gas wells. © 2011 Canadian Society for Chemical Engineering