Mathematical Model of Water- and Oil-Soluble Tracers Transfer in Studying Multistage Hydraulic Fracturing

A simplified mathematical model of two-phase multicomponent flow in the reservoir— multistage hydraulic fractures—horizontal well system is proposed. The formulation of transport problems in the well and in hydraulic fractures is simplified based on the dimensional analysis and similarity theory. The possibility of transition to a quasi-steady-state problem of distribution of the mixture components in high-permeability hydraulic fractures is shown. The dimension of the problem in reservoir is reduced by decomposing the problem into a set of problems in independent fixed stream tubes. For numerical solution of the problem, the resulting reduction in computer time reaches two orders of magnitude and can be further reduced by using parallel computing. Accelerating the solution of the direct problem is fundamentally necessary for the possibility of solving the inverse problem of identifying the porosity and permeability properties of fractures from the results of interpretation of tracer studies.