Development of an analytical model for steamflood in stratified reservoirs of heavy oil
Abstract
The use of analytical models to predict reservoir behavior depends on the similarity between the mathematically modeled system and the reservoir. Currently, there are not any models available for the prediction of steamflood behavior in stratified reservoirs based on the characteristics of reservoirs found in the Colombian Middle Magdalena valley, because the existing analytical models describe homogenous or idealized reservoirs. Therefore, it is necessary to propose a new model that includes the presence of clay intercalation in zones submitted to steamflood. The new analytical model is founded on the principles describing heat flow in porous media presented in the models proposed by Marx and Langenheim (1959); Mandl and Volek (1967), and Closmann (1967). Then, a series of assumptions related to the producing and non-producing zones and steamflood were determined, thus defining the system to be modeled.
Once the system is defined, the initial and boundary conditions were established to contribute to find specific solutions for the case described. A set of heat balancing procedures were proposed from which a series of integro-differential equations were found. These equations were solved by using the Laplace transform method. The mathematical expressions were defined for the calculation of parameters such as volume of the heated zone, the rate of instantaneous and cumulative heat losses, and the oil rate and recovery factor. We can find differences when comparing the model response with the simulation, because in the mathematical model, we cannot include phenomena such as drop pressure, relative permeability and the change of oil viscosity with temperature. However, the new analytical model describes approximately the steam zone behavior, when the heat flow in the clay intercalations is not in stationary state.
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