Determination of the length of fractures in multistage hydraulic fracturing using the stream tubes model

The mathematical statement and efficient high-speed algorithm for solving the inverse problem of interpreting tracer studies of the lengths of fractures of multi-stage hydraulic fracturing are given. The case of fractures of infinite permeability is considered. Solving the forward problem requires numerical modeling of multi-component flow. To reduce computational costs, the spatial problem is decomposed into a set of problems of reduced dimension along the stream tubes. At a high level of accuracy, such a model reduces computer calculation time by two orders of magnitude. A stable algorithm for solving the inverse problem is presented. The evaluation of sensitivity of the quasi-solution of the problem to measurement error is given.