A stimulation job entails high pressure pumping of proppant and sand into a well-bore in order to induce hydraulic fractures in the subsurface formation, typically, along horizontal wells. There may be 10-25 reciprocating pumps connected at the surface and during simultaneous operation these naturally give rise to high pressure pulsations over the piping system. These pressure fluctuations induce acoustic and mechanical resonance that leads to excessive vibration, which in turn can cause considerable wear and damage to the pump and piping network, potentially with catastrophic consequences. In this work, we present a robust control strategy designed to prevent this eventuality.
The reciprocating pumps employed in stimulation job frequently operate at pressures in excess of 10,000 psig, with pressure fluctuations in hundreds of psig. In a typical reciprocating pump design, rods connected to a crank drive multiple plungers which are offset in phase. Plungers accelerate between maximum positive and negative velocities in a sinusoidal curve. Subsequently, pressure and flow follow sinusoidal characteristics. The pressure and flow rate variation is mitigated due to combination of flow from multiple (three or five) plungers designed to be out of phase within a multiplex pump. When the piping system comprises elbows, tees, or diameter changes, the pressure pulsations can lead to piping vibrations, a phenomenon termed acoustic-mechanicalcoupling. If the vibration-inducing frequency (or the pump pressure pulse frequency) matches the natural frequencies of the piping system, it induces mechanical resonance; and the vibration forces, stresses, and amplitudes can be excessive.
Transient fluid flow in piping networks leads to another source of acoustic resonance. The pressure pulses from the pumps induce wave-guided acoustic modes in the pipes that travel at the wave speed along the pipe. When these bounce off a reflecting surface (such as a valve or a bend in the pipe) they generate standing waves that may produce resonance. The wave speed is calculated using the known acoustic modes in a fluid-filled pipe, which is dominantly the tube wave but could also include the flexural wave. Resonant conditions are achieved when the pump frequency matches the acoustic natural frequency of the fluid-piping system.
Experimental results based on pressure measurements in the time and frequency domains were used to characterize various pumping systems. In particular, experiments were conducted on a 2-pump system to address the issues of fatigue and premature failure (of piping iron and pumps) caused by pressure pulses and resultant vibrations. Furthermore, to study the transient dynamics of a particular pumping system, and to mitigate excessive pulsations, a 10-pump Flowmaster® CFD simulation model was developed using the experimental data. Starting with a rigorous reciprocating pump model, and using fluid properties from NIST REFPROP, a transient fluid flow model with field scale piping layout and fixtures was developed. This model was incorporated in an optimization framework and used to minimize the peak-to-peak (P2P) pressure differential observable at the missile outlet with active pump speed and phase control. Notably, as simulation-based P2P objective function is highly nonlinear, a robust control strategy was introduced to minimize the observable P2P variation. As a reduction in the P2P pressure pulse leads to a concomitant reduction in vibration, this results in reduced maintenance costs and safer field operation. The control strategy and test results based on a 10-pump simulation model will be presented.
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