Theory And Application On Flow In Multi-layer Reservoir

A series of new problems are essentially needed to be solved at fine development of oil field, such as measurements of vertical permeability and other formation parameters at different depths of a thick oil layer, the method of separate layer water injection and the pressure interpretation method of gas well considering temperature effect. These problems are all related to the law of fluid flow in multi-layer reservoirs. The heterogeneous reservoir is divided into layers with different formation parameters and thermodynamic parameters in this paper, and the law of fluid flow in these layers is studied. Lots of tests are carried out at oil fields, and physical and mathematical models are built up. The results have been applied to fine development of oil field after the problems are solved.The analytical pressure formula of a single-layer reservoir considering vertical flow is first given to solve the problem of measurements of vertical permeability of a thick oil layer on the basis of basic equation of fluid mechanics in porous media. The corresponding log-log type curves are drawn and the pressure interpretation method is built up. The law of fluid flow in multi-layer reservoir has some extent similarity with that in single-layer reservoir. Cross flow between neighboring layers, horizontal and vertical flow in layers are considered on the assumption of that pressure and vertical flow of the neighboring layers are equal, and fluids only flows through perforations of top layer in wellbore,which means fluid is not permitted to flow into other layers. Seepage equations and corresponding definite conditions are transformed to dimensionless forms by defining some dimensionless parameters. They are solved by using the method of separation of variables in the Laplace space and then solutions in the real space are given by Laplace inversion. Log-log type curves are drawn for pressure interpretations and the profiles of the curves are controlled by the dimensionless parameters. The test technology of vertical permeability is studied and some field tests are carried out, that is the first try at China.The fluid flow at separate layer water injection can be considered as three parts, which are the pipe flow in the well bore, throttle flow in the water distributor and the seepage in the reservoir. In the study of the pipe flow, the relationship between the wellhead pressure and the wellbore pressures of the layers is built up through the Bernoulli equation. In the study of throttle flow, the flow in the water distributor is simulated by numerical methods and it is found that the total pressure loss is proportional to the square of the flow rate into the water distributor. In the study of the seepage in the reservoir, the wellbore pressure formulas of the vertical well and the vertically fractured well are derived with infinite boundary and constant flow conditions. Considering all the three types of flows, the relationship between wellhead pressure and tap diameters of water distributors of different layers is proposed. Finally an effective method named pressure rise method is given to adjust flow rates of the layers. When changing the wellhead pressure, flow rates and pressures of the layers can be measured. On the basis of the measurement the water injection indexes are calculated. Then proper wellhead pressure and tap diameters will be calculated through water injection indexes and flow rates of the layers. The wellhead pressure should be as small as possible when the flow rate error limits are satisfied in order to reduce the costs.The temperature in gas well bore is not constant and the position of the pressure gauge is usually higher than the one of the gas production layer. As a result temperature difference between them causes additional pressure. This effect should be considered in pressure interpretation. The formation is divided into many layers according to thermodynamic parameters and single layer has uniform thermodynamic parameters. The vertical heat conductivity in the layers is ignored and only the horizontal heat conductivity is considered. The vertical heat conductivity in the well bore is also ignored and only the vertical heat convection is taken into account. The heat transfer of gas well can be considered as three parts, the vertical heat convection in the well bore, the horizontal heat conductivity between the well bore and the formation and the horizontal heat conductivity in the formation. The temperature distribution can be calculated on the basis of the heat convection equation in the well bore, the heat conductivity equation in the formation and the integrated heat conductivity coefficient. The temperature of the gas producing layer is considered as constant because the thickness is too small compared with other layers. Pseudo pressure is used to obtain the well bore pressure formula of the gas well, and the final result is corrected by the additional pressure. Finally the log-log type curves are drawn and the pressure data is interpreted.