The Research Of The Capillary Effect On The Multi-phase Flow In Tight Oil And Gas Reservoir

Tight oil and gas reservoirs have great potential for development,and it is becoming more and more important in the oil and gas reservoirs development industry.It is a complex porous coupled system composed of matrix and multi-scale fractures.Strong heterogeneity is one typical feature of the tight reservoir.Especially,the capillary pressure in matrix is usually very large due to its small porosity and low permeability.On the contrary,the capillary pressure in the fractures is very small or even negligible compared to the matrix.The multiphase flows in this coupled system display nonlinear characteristics caused by the heterogeneous capillary pressure,which differ from the Darcy’s law.The capillary pressure may be discontinuous at the matrix-fracture(or matrix-wellbore)interface when the multiphase fluids flow across the matrix-fracture(or matrix-wellbore)interface,and due to this,complex flow phenomenon across the interface will occur.Theoretical analysis shows that under the assumption of zero capillary pressure in fracture,three flow patterns can be distinguished for the two phase steady flow across the matrix-fracture interface:(1)When the pressure difference between matrix and fracture can overcome the capillary end effect,both two phase will flow from matrix to fracture and wetting phase saturation will rapidly rise to 1 at the matrix side of interface,which causes the divergences of non-wetting phase pressure gradient and phase saturation gradient.(2)When matrix pressure is higher than fracture pressure,but the pressure difference cannot overcome the capillary end effect,only the non-wetting phase that can flow from matrix to fracture.(3)When fracture pressure is higher than matrix pressure,both two phases will flow from fracture to matrix.In this situation,the wetting phase pressure at the interface is discontinuous.The heterogeneity of capillary pressure will cause complex flow phenomenon across the interface,resulting in drastic changes or divergences of physical quantities near the matrix-fracture(or matrix-wellbore)interface,which makes it very difficult for high-precision reservoir numerical simulations.The existing reservoir numerical simulation models generally show poor accuracy in calculating such interfacial flows.Based on the classification of the flow patterns and the corresponding interface conditions mentioned above,this thesis focuses on the effect of the heterogeneity of capillary pressure on the two-phase flow in tight reservoirs.The research contents are as follows:1.A new numerical well model for low permeability gas reservoir is constructed.The traditional numerical well model for two-phase flow is directly extended from the single-phase one.Since it does not fully consider the drastic changes of physical parameters near the matrix-wellbore interface,it may bring significant errors.Based on the analytical equations of one-dimensional radial flow considering the capillary end effect,an alternative numerical well model for low permeability oil or gas reservoirs is constructed.Numerical examples show that the proposed model can reflect the dramatic changes of saturation and oil or gas phase pressure in the vicinity of the production well both for two flow patterns,and therefore can predict the gas and water productions accurately at different grid scales.It means that the prediction results of the proposed well model are less dependent on the grid sizes.The calculation results also show that the capillary end effect will cause serious water-block phenomenon near the matrix-wellbore interface,which makes the water accumulate near the production well and impedes the oil or gas outflow from matrix to the production well.2.Based on the capillary end effect,the nonlinear characteristics of the two-phase steady flow in core experiments are analyzed.In this thesis,a rigorous mathematical analysis is performed by using one-dimensional steady flow equation,and the following conclusions are drawn.If the pressure difference is small enough,the influence area of the capillary end effect covers the whole core,and the curve of the flow rate vs.the pressure difference presents a nonlinear relationship of concave function.With the gradual increase of the pressure difference,the function curve gradually tends to be linear,and a pseudo-threshold pressure difference can be obtained by extending the linear section.In this thesis,it is proved mathematically that the pseudo-threshold pressure difference is a finite value.By analyzing the influence of relevant parameters(core permeability,phase permeability curve,fluid viscosity,etc.)on the pseudo-threshold pressure difference,it is found that the lower the core permeability,the more significant the non-linearity of the flow rate curve and the larger the pseudo-threshold pressure difference.When the wettability is neutral,the pseudo-threshold pressure difference will be quite small.It can be predicted that the hindrance of capillary pressure will be greatly reduced in the tight reservoir with neutral wettability.In addition,the influence of boundary layer effect on two-phase flow in tight reservoirs is also studied.The results show that even considering the boundary layer effect,the heterogeneity of capillary pressure is still an important cause of non-linear flow.The analysis based on the capillary pressure heterogeneity in this thesis provides a new perspective for the research of two-phase nonlinear flow in tight reservoirs.3.In the natural tight reservoirs,matrix and natural fractures coexist.There is still huge difference between the capillary pressure in matrix and in natural fractures.For the same reason,the heterogeneity of capillary pressure also has an important impact on the macroscopic flow in the coupled system,and the flow presents a significant nonlinear characteristic.In this thesis,the macroscopic nonlinear two-phase flow in the direction perpendicular to the fracture is discussed based on the assumption of the evenly distributed natural fractures.The results show that the wetting phase has a threshold pressure difference,which increases with the increase of fracture density.Under the condition of small pressure difference,the function curve of the non-wetting phase flow rate vs.pressure is a convex function.It will tend to be linear with the increase of the pressure difference,but the pseudo-threshold pressure difference still exists.In addition,the influences of the saturation,the permeability and the boundary layer effect on the function curve are analyzed.The results show that the water saturation and the permeability in matrix have great influence on the nonlinear characteristics of the flow.With the increase of the water saturation,the capillary pressure decreases and the nonlinear characteristics weaken.With the decrease of the matrix permeability,the heterogeneity of capillary pressure increases and the nonlinear characteristics of the flow also increases.When the boundary layer effect is considered,the nonlinear characteristics are significant even under a small pressure difference.