A Fractal Irreducible Water Saturation Model For Capillary Tubes And Its Application

With the increasingly prominent contradiction between international energy supply and demand,tight sandstone reservoirs have become an important area of global unconventional oil and gas exploration and development.Tight sandstone reservoirs are dense,with complex pore structures and strong heterogeneity.It is difficult to accurately calculate the irreducible water saturation of reservoirs.In view of the quantitative evaluation of irreducible water saturation in tight sandstone reservoirs,the tight sandstone reservoir of Xujiahe Formation in Sichuan Basin is taken as an example,combining with the experimental data of rock physical properties,nuclear magnetic resonance and mercury injection,the reasons of the poor accuracy of the existing irreducible water saturation determination method in low-permeability tight sandstone reservoirs are analyzed.Based on this,a method for quantitatively evaluating the irreducible water saturation of the reservoir using mercury injection data is proposed by introducing the fractal geometry theory into the capillary tubes model.And the new method is applied to the calculation of irreducible water saturation in the target area.Using core physical property analysis data,mercury injection experimental data,and NMR experimental data,combined with previous research results,the reasons for the low accuracy of mercury injection method and nuclear magnetic resonance experimental method for calculating irreducible water saturation in low-permeability tight sandstone reservoirs are analyzed.It is considered that there are two main problems in the existing method for determining irreducible water saturation.First,the experiments are conducted under the conditions of normal temperature,and the influence of temperature on the irreducible water saturation is not considered.The second is that the critical pore-throat radius is determined to be 0.2?m in the existing experimental method.It is suitable for sandstone reservoirs with medium-high porosity and permeability,but it is not suitable for low permeability tight sandstone reservoirs.The experimental research and numerical simulation are used to study the calculation of irreducible water saturation in tight sandstone reservoirs.Based on the capillary tubes theory,the irreducible water saturation model of the rock is deduced,and the fractal geometry theory is introduced to characterize the characteristic parameters in the capillary tubes model.Finally,a fractal irreducible water saturation model for capillary tubes is established.Five tight sandstone samples with different physical properties are selected.High pressure mercury injection capillary pressure experiment and weighing experiment have been performed on all of these samples.The irreducible water saturation results calculated by the conventional mercury injection method and the new model under experimental conditions are compared with the irreducible water saturation obtained by weighing method.Combined with the comparison results,the constructed fractal irreducible water saturation model is verified.The results show that the irreducible water saturation calculated by the new model is more accurate and the new model can be used to calculate the irreducible water saturation of tight sandstone.Using the mercury injection experimental data and core physical property analysis data,several representative rock samples with different pore structures are selected.Based on the constructed fractal irreducible water saturation model,the irreducible water saturation response values of tight sandstone samples with different pore structures under different temperatures and different critical pore-throat radius are simulated respectively,and the effects are summarized.It is considered that when the temperature is constant,the greater the maximum displacement pressure is(the smaller the critical throat throat radius is),the smaller the rock irreducible water saturation is.And the more complicated the pore structure is,the greater the decreasing extent of the irreducible water saturation is.For hydrophilic rocks,when the maximum displacement pressure(critical pore-throat radius)is constant,the higher the formation temperature is,the smaller the irreducible water saturation is.The decreasing extent of irreducible water saturation firstly increases with the increasing of the complexity of rock pore structure and then decreases.In this paper,the low-permeability tight sandstone samples from different areas are selected,and the residual water saturation under different centrifugal forces(50psi,100 psi,150psi,200 psi,250psi and 300psi)is measured,respectively.According to the relationship between the decreasing extent of residual water saturation(the residual water saturation corresponding to the lower centrigual force minus the residual water saturation corresponding to the higher force)and centrifugal force,the critical pore-throat radius of the low permeability tight sandstone is determined to be 0.1?m.The new irreducible water saturation model is applied to the calculation of the irreducible water saturation of the gas layer in tight sandstone reservoir of Xujiahe Formation in Sichuan Basin,the irreducible water saturation calculated under experimental conditions and reservoir conditions is compared with the waxing sealing water saturation.The results show that the irreducible water saturation calculated by the new fractal irreducible water saturation model is more accurate on the condition that the influence of temperature and maximum displacement pressure on the irreducible water saturation is considered,which is helpful for the evaluation of irreducible water saturation in tight sandstone reservoirs.