Application of an Analytical Model for Simulating Hydraulic Systems Containing Internal Lines With Turbulent Flow

It is not uncommon for simulation models for the dynamics of hydraulic systems to contain fluid lines with turbulent flow. This paper demonstrates applications of an analytical model for pressure transients in lines with turbulent flow for lines with boundary conditions defined by hydraulic components such as pumps, valves, actuators, and restrictions; the model can be simplified for cases of laminar flow. The equations for conducting simulations with time varying inputs and for calculating eigenvalues of systems in which fluid lines are internal components are formulated. For an example demonstrating application of the equations, the model is used to simulate and optimize the performance of a hydraulic fracking system which involves the pumping of large volumes of water with additives through pipes under turbulent flow conditions into rock fissures. Specifically, the model is used to generate the frequency response of the flow transients in the pipe resulting from pump flow pulsations. This frequency response is then used to compute the eigenvalues of the system. The model is then used to conduct time domain simulations to determine the potential flow amplifications into rock fissures associated with pulsing the flow from the pump at the resonant frequency of the pressure transients in the pipe. The results reveal flow amplifications into the fissures of up to 22 times depending on the pulse shape of the input flow, the Reynolds number of the mean flow, the fluid properties of the slurry, and the length and diameter of the pipe.