The effect of compressibility on flow start-up of waxy crude oils

Abstract

The current work presents a mathematical model to simulate the flow start-up of gelled oils in pipelines. The model comprises the conservation equations of mass and momentum and an elasto-viscoplastic constitutive equation to account for thixotropy of the material. The flow is considered one-dimensional, laminar and compressible and the cross-section shear stress is admitted to vary linearly so that the constitutive equation can be integrated along the pipe radius. The balance equations are solved by the method of characteristics, the constitutive equation by the finite difference method and finally they are altogether integrated iteratively. Two kinds of boundary conditions are investigated: a constant inlet pressure and a constant inlet flow rate. Two time-scales are identified in the current study: the pressure wave propagation time and the material response time. It can be anticipated that the ratio of this two times are quite important on the restart time in case of a constant pressure boundary condition and on the magnitude of the maximum pressure for a constant flow rate boundary condition.