A New Scheme to Describe Multi-well Compressible Gas Flow in Reservoirs

In this article a steady-state approach traditionally used to describe bi-dimensional incompressible fluid flow in underground formations, which is based on the superposition principle and on streamline tracing, has been generalized to compressible gases. The original formulation is very valuable since it requires short computation time, a minimum of reservoir information, and provides a multi-well flow description. Therefore, it results complementary to large computer simulation codes and analytical modeling. To generalize the approach, the superposition principle has been modified to account for gas density variations. An equation for the density has to be incorporated, which is treated as a pressure equation. A well influence radius has been introduced. Beyond that radius the gas pressure is assumed to become the reservoir average pressure. By considering non-interfering wells the velocity superposition principle is restored, and the pressure equation can be solved using a Kirchhoff integral transformation. An analytical expression for the velocity is obtained, which can be straightforwardly introduced in the original streamline tracing code. Further, two additional phenomena are added in the new formulation to account for non-bi-dimensional effects: (i) a gas source around production wells due to the gas released by the oil as it moves to production wells and (ii) a gas sink around injection wells, due to the gas that leaves the horizontal layer when moving radially away from injection wells. Analytical expressions for the gas velocity combining compressibility and these effects are derived. An ideal-like gas case has been analyzed. The approach was applied to real reservoir data. The well influence radius shows strong sensitivity to the system parameters; therefore, high data precision is required.