Development of a sizing equation for a multi-stage choke valve trim

Choke valves are used to regulate the pressure from natural gas reservoirs. Traditional choke valves control the reservoir pressure drop using a single variable orifice. At choked flow conditions a shock wave forms in the vena contracta in the valve creating high downstream velocities and shock cell turbulence interaction. The high velocities increase erosion when there are sand particles in the gas. Shock cell turbulence interaction is a highly efficient noise generation mechanism and can create noise far in excess of industrial limits. Multistage (MS) technology is used to reduce high pressure in stages within a valve. Instead of a single port the MS valve uses a flow path of sequential restrictions and expansions. The segmenting of the pressure drop eliminates the presence of shock waves. This reduces the velocity (and hence erosion) and changes the primary noise generation mechanism to less efficient turbulent shear. A new MS valve geometry was developed by Cameron Flow Control. As part of this development a flow equation was required to determine the restrictive area in the valve (referred to as valve coefficient or Cv) which is necessary to control a set of reservoir conditions. The Cv of the valve is a function of its internal geometry and is complicated by the nature of the MS flow path. A mathematical model of flow through the MS path was constructed based on a series of sequential thick walled orifice plates. The choked flow conditions for the single stage geometries were investigated and linked to the gas expansion factor (Gy) and critical pressure drop ratio (τc). Experimental data and theory taken from (Rhode, 1969) was used to estimate a Cv value for the overall flow path for a series of different pressure differentials. The fluid properties were modelled using a suitable gas compressibility equation (Peng et al, 1976) and a Joule Thomson relationship (Bessieres et al, 2006) to account for changes in the expansion zones. The mathematical model did not produce a choked flow condition. Experimental tests were conducted using a model of the MS flow path, a mass flow loop and a Laser Doppler Anemometry (LDA) measurement system. The mass flow rate tests showed that the rate of change of flow rate reduced significantly at high pressure drops without the gas becoming choked. The LDA velocity measurements indicated the existence of three flow phenomena within the MS path. Computational Fluid Dynamics (CFD) was used to investigate the mechanism that caused the reduction in flow rate. Both the mass flow rate and LDA velocity measurements were used to benchmark the CFD simulations. Three large vortices were proven to exist in the restrictive channels and their size and location were shown to ultimately limit the effective flow area. A full flow test was conducted on the MS valve to finalise the sizing equation and account for any upstream or downstream geometrical effects caused by the valve body. At the outlet of the MS paths, which exited into the same volume, further vortices were seen. These proved to further reduce the overall flow rate of the valve. The primary outcomes of this research were the design of an effective MS valve (EU Patent Number: IB2008053368). As part of this, a new limiting flow mechanism was described and included as part of the sizing equation. In addition, a specific case where high inlet pressures created shock waves at the outlet was presented. Furthermore this research detailed the first use of LDA velocities measurements taken within a MS valve with a full scale design. This research expands on the state of the art knowledge of valve sizing and design.