Gas-Coning by a Horizontal Well

The problem of gas-coning by a horizontal well is solved in the framework of a model which accounts for the movement of the gas-oil boundary. The main result is a plot of critical time versus rate. The model assumes an infinitely long horizontal well in the oil-zone. Both fluids are incompressible and gas is at all times in static equilibrium. Flow of oil is then two-dimensional in the plane perpendicular to the axis of the well. In this plane, the gas-oil interface is a line which forms a moving boundary and the problem of calculating the flow of oil is a moving-boundary problem. The introduction of boundary-fitted orthogonal coordinates transforms the moving boundary problem into two classical boundary-value problems and one initialvalue problem. The boundary-value problems are solved analytically. The initialvalue problem, which controls the movement of the boundary, is in the form of a non-linear integro-differential equation. For small rates this equation is solved by transforming it into an infinite system of ordinary differential equations, and using acceleration of convergence as a method of closure. For large rates an iteration method is used.