5 Multi-phase flow

Control valve sizing theory for multiphase flow is not nearly as well developed as it is for single-phase fluids. Sizing control valves for a pure liquid or gas flow can be done using existing standard sizing equations based on flow dynamics and valve-specific sizing coefficients. When a control valve is sized for a two-phase flow, which is usually a mixture of liquid and gaseous fluid, no generally accepted standard method exists. This is because, in two-phase flow, liquid and gas cannot be mathematically described in a simple and exact way at the same time. Also, experimental research requires a lot of tests with different kinds of mixtures and mass fractions using various valve types. For this reason, it is not possible to size valves for multi-phase flow with the same accuracy as for single component streams.

A large part of this section concentrates on sizing control valves for a particular multi-phase fluid, i.e. pulpstock. Valmet's flow control business line has done a lot of the basic research on determining the behavior of pulpstock flow through control valves. As a result of this research, this manual now introduces a method for sizing control valves for pulpstock flows. This method can be applied to all rotary control valve types.

Phase changes in the liquid and gas, vaporization of the liquid, or condensation of the gas into liquid make it difficult to calculate mass fractions and effective density. These factors in sizing accuracy are especially evident with single-component two-phase flow. When the pressure decreases and the temperature is almost constant, the liquid tends to evaporate whereby the mass fraction of vapor and the required valve capacity increase. On the other hand, something called the metastability phenomenon tends to 'slow down' the phase change. In this phenomenon, the liquid does not vaporize at once in the vena contracta although the thermodynamic equilibrium of the substance would indicate this. Instead, vaporization occurs only after the vena contracta.

Paper and pulp mills use a large number of control valves for throttling the flow of pulpstock. As the selection process determines the pumping energy 'burnt' in the control valve and the piping, the costs of both building and running the process are largely determined by how the throttling control valves are sized and selected. Correct selection of the pulpstock control valves can determine the the optimal size selection of pumps and piping. In the past, over-dimensioning of pumps and valves has been used for all the uncertainties in the behavior of the pulpstock flow. Rough correction coefficients have been used to account for the greater capacity (C_v) requirement of pulpstock compared with water. However, new studies go a long way towards predicting how pulpstock exactly behaves in control valves. Furthermore, they significantly help improve the accuracy of sizing calculations. Previous studies, mainly performed to evaluate consistency effects on pipe flow, indicate that pulpstock flow behavior is highly dependent on flow velocity, as shown in figure 70.

When the flow velocity of the pulpstock is very small, it flows in the pipe like a solid plug and forms 'rolls' which spin between the plug and pipe wall. As the flow velocity is increased, the flow changes into a plug flow, in which the fibers no longer touch the pipe wall as there is a narrow boundary layer between the plug and the pipe wall. In this area, the pressure loss remains relatively constant in spite of flow velocity changes, and it can even have an inverse relation to the flow velocity increase (unstable area in figure 71). As the flow velocity is further increased, the thickness of the boundary layer increases, and turbulence starts to appear in the boundary layer and on the surfaces of the pulp plug. The centre of the pulp plug remains plug-like. This is called mixed flow. When the flow velocity is further increased, the pulp plug disappears and the whole flow cross-section becomes turbulent.

The three basic forms of pulpstock flow are illustrated in figure 72.

Note also that at high flow velocities, as in figure 71, the pressure loss of the pulpstock can be lower than that of water.

 

 

Valmet's flow control professionals have performed over 2000 measurements of pulpstock flow through control valves. These tests were performed on three different types of quarterturn control valves in three different sizes (50 mm/2", 100 mm/4" and 200 mm/8"). The pulp stocks used were bleached kraft (sulphate pulp), thermo-mechanical pulp, and recycled pulp. The tests resulted in an empirical correction coefficient (k), which is presented in appendix J. The coefficient (k) is determined by equation (82).

The following relationships have been established in the pulpstock flow through control valves:

• The coefficient (k) increases with the increase in differential pressure.

• The coefficient (k) decreases with the increase of pulp consistency.

When the consistency is lower than 2%, there is very little difference between water and pulp flow rates, and sizing can be done without a correction coefficient (k), using water sizing equations only.

Control valve sizing for pulpstock applications is performed using an 'equivalent water flow rate' and water sizing equations. The 'equivalent water flow rate' is derived from equation (83).

After calculating an equivalent water flow rate, the sizing is done utilizing standard IEC/ISA sizing equations for water, as presented in chapter 3.

Figure 73 shows an example of an installed flow characteristic for a 10% mechanical pulp control valve in a typical process piping system.

Figure 72 shows that when the valve opening is already relatively large, the actual flow decreases if the valve is further opened. This kind of situation has to be avoided in order to maintain the fluid flow control of the process.

In the described case, we advise to set the valve maximum opening at about 55% to guarantee process controllability, and to use a valve with an expanded outlet. When the valve maximum opening is set at 55%, increasing the valve opening, the capacity (C_v) increase produces a constantly larger flow.

A typical two-phase flow of a liquid and solids is wet slurry, a mixture of a liquid and solid particles. Suspensions are slurries if the particle sizes are so small that the mixture remains unseparated for a long time. Suspensions can be treated as non-Newtonian fluids, where basic liquid equations can be applied to the calculated 'apparent viscosity' for the suspension.

Settling slurries are suspensions in which particle size is bigger than 0.25 mm (0.01 in). These can be calculated as liquids, as long as the two phases can be assumed to flow through the control valve as a homogenous mixture, with the densities of different phases close to each other, and viscosity small enough to guarantee effective mixing. In that case, the density (ρ) is taken as the effective density (ρ_E) weighted mass ratios of liquid and solids.

Solving the two-phase flow of suspensions is complicated because it is a complex flow type. It involves calculating the 'apparent viscosity' and determining the necessary parameters as well as a liquid calculation taking into account the Reynolds number. The details of the calculation are not presented here but are available from valve manufacturers.

A typical two-phase flow of dry slurry is a mixture of gas and solids. This kind of mixture is rarely controlled by conventional valves due to mechanical problems like erosion and plugging. If a control valve is to be sized for dry slurry, equation (78) gives the best results, although it is slightly conservative. In this case, the density of the mixture is taken as the effective density in equation (77), where the liquid is replaced by a solid.