Numerical Calculation For The Flow Of A Viscoelastic Fluid In Concentric Annulus With Isometric Ring Slots On The Inner Cylinder

Polymer injection is one of the effective technology for EOR, in which the technology of separated layer polymer injection achieved by injection allocation with concentric ring depressurization slots on it is an important technical way which can help polymer injection and cost control. Flow of polymer aqueous solution in injection allocation with concentric ring depressurization slots on it can be regarded as flow of viscoelastic fluid in concentric annulus with isometric ring slots on the inner cylinder. The research on the flow of viscoelastic fluid in concentric annulus with isometric ring slots on the inner cylinder can provide a theoretical base on optimization of working parameters for the technology of single string separated layer polymer injection with concentric ring depressurization slots on the string, which is of engineering importance.A viscoelastic fluid model of the second-order fluid with variable coefficients is used to describe rheology of the produced fluid, and the governing equation and a formula for calculation of pressure drop for the flow of the second-order fluid in concentric annulus with isometric ring slots on the inner cylinder under the cylindrical coordinate system are established, and the corresponding numerical methods are presented. Taking HPAM aqueous solutions as examples, the apparent viscosity, the stream function, the velocity and the pressure drop of the flow are numerically calculated, and the influences of slot width, slot depth, slot interval, slot number and elasticity on the apparent viscosity, the stream function distribution, the velocity distribution and pressure drop are analyzed, respectively. The results show that as to the flow of the HPAM aquoues solution, which can be regared as the second-order fluid with variable coefficients, in concentric annulus with isometric ring slots on the inner cylinder, the influences of slot width, slot depth and elasticity on the apparent viscosity distribution are obvious, while the influence of slot interval and slot number on it are not obvious;the influences of slot width, slot depth and elasticity on the stream function distribution are obvious, while the influence of slot interval and slot number on it are not obvious;the influences of slot width, slot depth and elasticity on the velocity distribution are obvious, while the influences of slot interval and slot number on it are not obvious;the influences of slot width, slot depth, slot number and elasticity on the pressure drop are obvious, while the influence of slot interval on it is not obvious. A formula of stability parameter H for the flow of the second-order fluid with variable coefficients in concentric annulus with isometric ring slots on the inner cylinder under the cylindrical system is also established, and taking HPAM aqueous solution as an example, the stability parameter H of the flow is numerically calculated and analyzed. Through the experiments of the flow of HPAM aqueous solutions, the mass percentage concentrations of which are 0.050%,0.100% and 0.125% respectively, in concentric annulus with isometric ring slots on the inner cylinder, based on the governing equation, the formula for calculation of pressure drop, the formula of stability parameter H and the corresponding numerical methods established and presented, the pressure drop numerically calculated are compared with those experimentally measured, and the critical maximum value of the stability parameter H of the flow is determined. The results show that the maximum average relative errors between the pressure drop numerically calculated and those experimentally measured is 4.12%, so that the governing equation, the formula for calculation of pressure drop and the corresponding numerical methods established and presented in this paper can be testified to be correct, and the critical maximum value of the stability parameter H of the flow of the second-order fluid with variable coefficients in concentric annulus with isometric ring slots on the inner cylinder is 395.