Air Entrapmemt In Porous Media Under Capillary Rise And Dynamic Displacement Conditions

Aquifers containing trapped gas are called quasi-saturated aquifers,in which the saturation of trapped gas is the main factor affecting the permeability coefficient of quasi-saturated aquifers.The current research on gas trap only has microscopic trap mechanism,but lacks macroscopic trap dynamics,and the establishment of trap dynamics requires capillary rise mathematical model as the basis.The existing capillary rise equations all directly use unsaturated Darcy’s law,and lack the establishment of capillary rise mathematical model based on soil water flow equation.At the same time,there are two empirical formulas for estimating trap gas saturation in quasi-saturated aquifers,which take initial water cut and displacement rate as variables.The theoretical relationship between these two empirical formulas has not been studied.The theoretical derivation of trap dynamics model and the study of the theoretical relationship between these two factors are of great theoretical significance to the understanding of gas traps in quasi-saturation.In this paper,the trapping behavior of gas in two different processes,capillary rise process and dynamic displacement,is carried out,and trap dynamics are constructed on the basis of solving the analytical solution of the vertical one-dimensional capillary rise control equation,and the theoretical relationship between two types of empirical formulas based on trap dynamics is obtained.The paper has achieved the following concrete results:(1)The mathematical model of capillary rise is established and the analytical solution is obtained.The analytical solution of the capillary rise mathematical model is obtained by referring to two kinds of solving methods for vertical infiltration of soil water.The capillary rise mathematical model can obtain the moisture content at any height at any time,and at the same time can calculate the flow velocity of water on the diving surface to obtain the displacement rate at any time.(2)Based on the mathematic model of capillary rise,the gas trap dynamics equation of capillary rise process is established.Based on the mathematical model of capillarity rise and the Land experience model,the trap dynamics were constructed.The derivation of this model is not only an improvement of the Land model,but also an innovative construction of the trap dynamics model to make the gas trap in the process of capillarity rise more clear.(3)The theoretical relationship between two kinds of trap gas saturation empirical models is obtained.Two types of trap gas theoretical models were derived through the kinetic theory.The experimental data were substituted to verify the theoretical model and the empirical model.It was concluded that the initial gas content and displacement rate had a competitive relationship on the influence of trap gas saturation,and they were dominant in different time periods.