A Three-Phase Model For Fractured Reservoirs Presenting Fluid Segregation

Abstract

A model has been developed to describe the behavior of naturally fractured reservoirs with black oil in which high transmissibility in the fractures and low oil production rates allow the gravitational segregation of the gas, oil and water phases. The influxes of these fluids from the matrix rock to the fractures are described by functions dependent on the properties of the reservoir fluids and the matrix rock blocks. These properties are measurable by laboratory tests on cores and formation studies in the reservoir. This approach contrasts with a common trend in fractured reservoir simulation favoring the use of parameters to account for the matrix-fracture interaction; these parameters cannot be explicitly linked to the reservoir characteristics.The presented formulation results in a system of three simultaneous integra-differential equations where the dependent variables are: the dephts of the gas-oil and water-oil contacts, and the pressure at the datum. Observed and calculated variables, obtained applying the model, are in good agreement throughout the forty-five years long production history of an actual reservoir that includes a period with null production, while all the wells were closed, that resulted in an unusual fluctuation of the variables.

Multiphase Flow in Fractured Reservoirs

“…However, the approach of de Swaan (14) includes block responses which are functions of several matrix/fracture system properties. He defines (4.18) where qmfH is the matrix/fracture rate response to a unit step disturbance and x j , j=l, n are the n properties of the system defining the flow process.…”

“…A simplified case would be the advancement of water-oil contact and gas-oil contact under segregated conditions, as outlined by de Swaan (14). In general, a front tracking method should be incorporated to track fronts of any positions in the system.…”

“…One particular transfer function may be correct to use for one period of time, while another should be used for the next. de Swaan (14), however, presents an approach of integrating several interaction functions, depending on flow conditions, by using the convolution theorem.…”