Calculation of the flow rate between wells in the flow model of an oil reservoir using streamlines

To analyze the waterflooding system of an oil reservoir and predict the effectiveness of geological and technical measures, information is required on the distribution of injection rate between the reacting production wells and the reservoir boundary. The most reliable methods for calculating these characteristics are methods based on hydrodynamic modeling of flow. Modern commercial software implement algorithms for these purposes based on the construction and analysis of streamlines. At the same time, there are no reliable estimates of the accuracy of these algorithms and recommendations for choosing the optimal parameters in the available literature.In this paper, we propose an algorithm for calculating the proportions of the distribution of the total well flow rate between the surrounding wells and the reservoir boundary using streamlines. Streamlines are constructed on the basis of a finite element solution to the flow problem averaged over the formation thickness and determine the boundaries of the streamtubes connecting the corresponding wells. The flow rate through the flow tubes is calculated by numerically integrating the Darcy velocity field of the indicated two-dimensional problem. The algorithm was tested on idealized examples of waterflooding elements of typical well placement schemes, when the exact distribution of the proportions of fluid injected into the formation is known, and on the example of comparison with the solution of the problem of simulating the injection of a tracer into the reservoir. Recommendations for the selection of starting points for tracing streamlines are presented, which allow achieving a minimum level of error in determining the mutual influence of wells in a wide range of the computational grid resolution of the flow model.A more general application of the described method without significant changes is to equip the high resolution flow model along fixed stream tubes with their rate characteristics.