Numerical Simulation Of Three - Dimensional Three - Phase Percolation Of Average Capillary Force In J - Function

With the development of technologies for low-permeability reservoir recovery, the research on numerical simulation of low-permeability reservoir has become the focus of attention recent years, in which, most studies involve the reservoir stress sensitivity and low-speed non-Darcy flow simulation. However, compared to conventional ones, this kind of reservoir has lower porosity and permeability which leads to a higher capillary pressure, the impacts of capillary pressure on multi-phase flow within the pore-throat should not be ignored. By adopting the mercury injection data of the low permeability sandstones, the J function was fitted, from which the average capillary pressure can be calculated, this average capillary pressure comprehensively reflects the reservoir physical properties. Based on the black-oil model, the mathematical model of oil-gas-water three-dimensional flow taking J function into account to get average capillary pressure was established and deduced, then the finite difference method was used to discretize and solve this model, and programming by Fortran90made this numerical reservoir simulation realized. In the simulation, the average capillary pressure of each grid at each time step was calculated by the J founction of Penglaizhen formation, which involves the influences from porosity, permeability, fluid saturation, and wetting contact angle, etc. A series of simulation schemes were designed to study the impacts of the capillary pressure and rock wettability on the multi-phase flow in the reservoir:1. Comparative simulation of water flooding with and with no capillary pressure to analyze how capillary pressure works on the sweep efficiency.2. Comparative simulation of vertical flow with and with no capillary pressure to study how capillary pressure influences the vertical equilibrium of oil-gas-water.3. A relatively low permeability zone was assumed to locate between the injection well and production well, the wettability of the zone was controlled by setting the value of contact angle in the J function, water flooding was simulated with the varying contact angle in the zone, accordingly, influences from different levels of wettability on the sweep efficiency and residual oil distribution were studied. The results prove:(1) for the water-wet reservoir, capillary pressure acts as the driving force and boosts the oil recovery, the daily oil production rate and recovery ratio are both lager than the case with no capillary pressure, the situation is similar to gas production.(2) Capillary pressure acts against the gravity, making oil, gas and water more vertically well-distributed; conversely, if there is no capillary pressure, the vertical difference would be more obvious:large amounts of gas flows to the top layer, while most of water and oil flow to the bottom due to gravity.(3) During the water flooding, if there exists a relative low-permeability zone obstructing the flow path between the injection well and the production well, the water injected would divides into two paths, one is trying to penetrate the low-permeability zone, the other is making a detour, the terminus of either way is the production well; the water allocation for the two ways depends on the wettability of the low-permeability zone, with the wettability changing from water-wet to oil-wet, it becomes increasingly difficult for water to get into the zone, as a result, more oil gets trapped in this zone. When the wettability of the zone is weak water-wet, water flooding of these two paths can form the most effective combination, and get the highest oil recovery rate. The research contents of this dissertation provide a theoretical basis for the water flooding in the heterogeneous reservoir with the variable wettability.