Modeling of Wave Propagation in Drilling Fluid

The study presents a one-dimensional (1D) numerical model of wave propagation as well as transmission/reflection phenomena in Newtonian and non-Newtonian drilling mud flow associated with oil/gas drilling activities. Propagation of wave formed due to back pressure changes by means of a choke is investigated. In general, the reflection and transmission of pressure waves at intersection of conduits with different cross sections or in case of partial blockage typical of drilling practices is multidimensional and caused by nonuniform boundary conditions over the cross section. The 1D approach is investigated to approximate the multidimensional reflection and transmission of pressure pulse at areal discontinuity in conduit. The approach is facilitated by introduction of a local force exerted by solid wall on the fluid at the intersection of the conduits into conservative form of the equation for momentum conservation. In addition, nonconservative formulation of momentum equation was explored. To solve the differential equations, MacCormack numerical scheme with second-order accuracy is applied to the nonlinear Euler and 1D viscous conservation equations. A grid refinement study is performed. It is shown that nonconservative form of the conservation laws results in more accurate prediction of transmission and reflection in case of areal discontinuity. The results of the numerical modeling are presented in terms of pressure wave propagation and attenuation upon reflection and transmission at consequent interfaces.