Calculation Methods for Linear and Radial Steam Flow in Oil Reservoirs

The flow of oil and water in a reservoir as a result of steam injection is related to the shape of the growing steam zone. Analytical formulas describing the approximate shape of this zone have been derived both for linear flow in horizontal and dipping formations and for radial flow around injection wells in a horizontal formation. The theory is based on segregated-flow principles such as those previously used by Dupuit,1 Dietz,2 and others. The formulas take into account gravity overlay of steam zones and have been checked against results of scaled laboratory experiments, steam-injection projects in the field, and calculations with a numerical reservoir simulator. From the good agreement with the new calculation method it would seem that the shape of a steam zone is controlled mainly by one group of parameters including steam-injection rate, pressure, and effective formation permeability to steam. The equations can be used to analyze and explain field observations, such as the position of steam/liquid contacts in injection wells, estimates of effective permeability to steam in steam zones, and steam-zone thickness as noticed in observation wells. This paper shows, for example, how a cumulative oil/steam ratio for oil displaced from a steam zone depends on steam-zone pressure, injection rate, and time. With increasing oil viscosity, more bypassing of oil by steam owing to viscous forces will occur, leading to more overlay of steam zones and eventually to narrow tonguing in a lateral direction. The calculation methods provide an evaluation tool for steamdrive and steam-soak processes to reservoir engineers engaged in field operations, project design, and research.