Displacement of viscous fluids in a set of parallel pipes

The process of pumping water in a formation filled with a more viscous fluid is considered using the simplest model of the interwell space described by a set of parallel pipes. The fluids are assumed to be immiscible with a sharp interface in each pipe. The main task is to recover the parameters of the interwell space from a given displacement characteristic, namely, displacement data for each fluid. An explicit solution of the direct problem is presented for the model under study. It is shown that the problem of medium recovery, which is, in fact, an inverse problem, can be solved up to a one-parameter family. Additionally, a topology is found in which the inverse problem is stable.