An implicit, three-dimensional, three-phase well coning simulator has been developed which strongly couples the well production equations to the reservoir flow equations. This strong coupling scheme allows the well production to be determined simultaneously with the reservoir pressures and saturations. The flexibility obtained allows the use of production constraints on the well production terms. This results in a highly user-oriented model. The model may be used to obtain the maximum well productivity for a given set of physical limitations and regulatory constraints, such as minimum surface pressure, maximum allowed GOR, WOR, water rate, gas rate, etc. The model can function either as a production well or an injection well and, in general, may be used to study any single-well behavior.

This paper develops the strongly-coupled formulation and discusses its utility in relationship to other implicit models. The linearization of the resulting set of finite difference equations, along with a discussion of the solution algorithm to solve the coupled system of simultaneous equations, is included. Development of the production constraints and their coupling into the reservoir equations is emphasized. Example problems of field applications of the model are included to show the utility of user supplied production constraints in determining well performance.

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