A quasi-quantum-mechanical percolation model, which imitates the process of oil displacement by water from the oil reservoir, is suggested. The Hamiltonian describing the irreversible evolution process of the percolation lattice, which models the oil reservoir, is constructed. With the help of the computer calculations for the rectangular plane lattice, the time development of the process under consideration is observed. The authors consider the critical behaviour within the time interval t₁<or=t<or=t₂ where time moment t₁ corresponds to the percolation phase transition (when water appears in the production wells for the first time) and time moment t₂ corresponds to the moment when the development of the percolation process is stopped (when only water begins to flow through the production wells).