A Parametric Study for the Friction Factor in the Critical Zone of Flow for Crude Oil Pipelines

Crude oil pipelines can occasionally experience flow regimes in the critical section where the flow changes from a laminar streamlined flow to a transitional zone with the onset of turbulence where the Reynolds number is located in the range 2100 to 3000. In this range of operation the flow is considered unstable and currently there is no definitive method for evaluating the friction factor with certainty. The result for modeling purposes is that pressure predictions are rendered somewhat less reliable than if the pipe operated in either the laminar or transition zone or fully turbulent zones. In the critical zone, one approach for both providing a reasonable estimate and for maintaining numerical stability is to use a weighted average of the laminar and transitional friction factor equations. This paper intends to quantify the uncertainty in pressure prediction using this approach, by comparing with estimates for the friction factor based on actual instrumented data during both steady state and transient modes of operation in the critical zone. The first step in attempting to achieve this goal reliably would be to provide a verification base state where the uncertainties in all input parameters such as fluid properties, pipe roughness, temperature, elevation profile, pipe internal diameter, and distances have been reduced as feasibly as possible. The approach taken here involves application of the non-linear regression method, Levenberg-Marquardt. Historical data from an actual operating NPS 16 multi-station blended crude pipeline system was available to assist in this parametric study.