Transp Porous Med (2009) 79:67–85
DOI 10.1007/s11242-008-9280-2
A New Scheme to Describe Multi-well Compressible Gas
Flow in Reservoirs
Manuel Coronado · Jetzabeth Ramírez-Sabag ·
Oscar Valdiviezo-Mijangos · Carlos Somaruga
Received: 19 February 2008 / Accepted: 20 August 2008 / Published online: 16 September 2008
© Springer Science+Business Media B.V. 2008
Abstract In this article a steady-state approach traditionally used to describe bi-dimen-
sional incompressible fluid flow in underground formations, which is based on the superpo-
sition 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 com-
plementary 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 produc-
tion 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.
Keywords Gas flow · Compressibility · Near-well flow · Flow simulation · Streamlines
M. Coronado (B ) · J. Ramírez-Sabag · O. Valdiviezo-Mijangos
Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, 07730 México, DF, Mexico
e-mail: mcoronad@imp.mx
C. Somaruga
Facultad de Ingeniería, Universidad Nacional del Comahue, Buenos Aires 1400, 8300 Neuquen, Argentina
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