The Application of Improved Numerical Techniques to 1-D Micellar/Polymer Flooding Simulation

Date

1981-08

Authors

Ohno, Takamasa

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Abstract

Three examples of three phase flow models which have been developed are compared under various conditions. Although the dif-ference in oil recovery and surfactant trapping among the models was rather large with constant. salinity, a salinity gradient produced high oil recovery and low surfactant trapping with all three models. Since surfactant trapping is important and it is highly uncertain, this is another reason for designing a micellar flood with a salinity gradient, or something equivalent to a salinity gradient. The semi-discrete method was applied to a 1-D micellar/polymer flooding simulator. By using a semi-discrete method, the time step size can be controlled and varied to be as large as pos-sible without sacrificing accuracy. The stability limit can also be detected with this method. The method is tested and compared with the fully discrete method in various conditions such as differ-ent phase behavior environments and with or without adsorption. In the application of the semi-discrete method, four different ODE in-tegrators were used. Two of them are explicit methods while the other two are implicit methods. Although the implicit methods did not work as well as the explicit methods, there may be some improve-ment possible. With respect to the computation time, one of the explicit methods which is based on the· Runge-Kutta approximation worked best. Although the method can save 20 to 30% computation time under some conditions, compared with the fully-discrete method, the results are highly problem-dependent. To improve the computation time, two methods are suggested. One is to check the error only in the oil or water component rather than all components or any other one component such as surfactant. The other is to check absolute error instead of relative error and multiply by a small conservative factor to the calculated time step size. The stability was analyzed for the oil bank, and for the surfactant front. The former imposes a rather constant limitation on the time step size continuously until the plateau of the oil bank is completely produced: Although approximate, the stability analysis for the surfactant front suggests an unconditional local instability, which is caused by the change in the fractional flow curve due to the surfactant.

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