Pressure Gradient Of Unsteady Flow Of A Viscoelastic Fluid In Eccentric Annulus With The Inner Cylinder Reciprocating Axially

During the process of polymer flooding production, flow of the produced fluid in wellbore can be regarded as unsteady flow of viscoelastic fluid in eccentric annulus with the inner cylinder reciprocating axially. The research on unsteady flow of viscoelastic fluid in eccentric annulus with the inner cylinder reciprocating axially can provide a theoretical base on optimization of working parameters for rod pumped well under polymer flooding, 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 an equation of instantaneous pressure gradient and a formula of average pressure gradient for the unsteady flow of the second-order fluid with variable coefficients in eccentric annulus with the inner cylinder reciprocating axially are established, and the corresponding numerical methods are presented. Taking HPAM aqueous solutions as examples, the instantaneous and the average pressure gradients of the flow are numerically calculated, and the influences of stroke and stroke-frequency of the inner cylinder, annular eccentricity and viscoelasticity on the instantaneous and the average pressure gradient are analyzed. The results show that as to the unsteady flow of the HPAM aquoues solution, which can be regared as the second-order fluid with variable coefficients, in eccentric annulus with the inner cylinder reciprocating axially, the influences of stroke and stroke-frequency of the inner cylinder and annular eccentricity on the instantaneous pressure gradient are obvious, and elasticity has influence on the instantaneous pressure gradients as well; the influences of stroke and stroke-frequency of the inner cylinder on the average pressure gradient are not obvious, while the influence of annular eccentricity on the average pressure gradient is obvious, and elasticity has influence on the average pressure gradient as well. A formula of stability parameter H for the unsteady flow of the second-order fluid with variable coefficients in eccentric annulus with the inner cylinder reciprocating axially 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 unsteady flow of HPAM aqueous solutions, the mass percentage concentrations of which are 0.050%, 0.100% and 0.125% respectively, in eccentric annulus with the inner cylinder reciprocating axially, based on the equation of instantaneous pressure gradient, the formula of average pressure gradient and the corresponding numerical methods established and presented, the average pressure gradients 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 average pressure gradients numerically calculated and those experimentally measured is 2.60%, so that the equation of instantaneous pressure gradient, the formula of average pressure gradient 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 unsteady flow of the second-order fluid with variable coefficients in eccentric annulus with the inner cylinder reciprocating axially is 380.