## Valve Design for Flow Control

Valves regulate fluid flow regulating a pressure drop in a flow line. Valves are a common final control element for a process control system to maintain pressure, temperature, composition, or other process quantities. There are many types of valves with strengths and weaknesses for particular applications. For example, some valves are better suited for applications where the valve is mostly for starting and stopping flow in a pipeline. In this case, a type of valve design that has low pressure drop is desired and a ball valve or gate valve may be selected. In other cases, it is desirable to precisely maintain a flowrate into a process and a globe valve may be the preferred solution. When backflow is a concern, a swing-check valve can be installed to ensure that fluid only flows in one direction. Each valve has unique performance characteristics.

#### Valve Design Equation

The valve design equation relates the pressure drop \Delta P_v across the valve to the volumetric flow rate q.

$$q = C_v f(l) \sqrt{\frac{\Delta P_v}{g_s}}$$

The C_v is a measure of the size of a valve and valve suppliers have different valve body sizes, each with a different C_v value. The valve position or lift l is adjusted to regulate flow through the valve. The lift function f(l) depends on the type of trim installed. The trim is relatively easier to modify but the size of the valve C_v cannot be adjusted without replacing the valve body. Rearranging to solve for P_v gives the pressure drop across the valve as a function of flow q.

$$\Delta P_v = g_s \left(\frac{q}{C_v f(l)}\right)^2$$

#### Linear Flow to Lift Relationship

In designing a valve for a particular process, it is important to maintain a linear relationship between lift l and flow q. A nonlinear relationship makes flow control tuning more complicated that requires gain scheduling, piecewise linearization in the control software, or other measures to compensate for the nonlinearity. Equal percentage valves are popular valve trims to compensate for typical process nonlinearity and create a combined valve + system response that is linear.

#### Valve Trim

There are several types of valve trim that influence the f(l) function. A linear value trim is f(l)=l but this is rarely used in practice. An equal percentage valve trim is f(l)=R^{l-1} with R=20 to R=50. An equal percentage valve trim opens more at higher flow rates and compensate for typical processes that have higher pressure losses at higher flow rates. The valve exercises show why this is needed.

#### Valve Positioners

Valve positioners measure the valve travel and automatically adjust the actuator to precisely lock in on a commanded valve opening. Valve positioners improve the precision with which a valve can follow commands. It is an inner feedback loop with the valve to match a valve opening set point.

#### Valve Design

A valve design involves selecting the type of valve, the body size C_v, and trim that gives a particular lift function f(l). A few key concepts are important in valve design:

• Pressure is generated by pumps and dissipated over valves and the system. The pressure generated by a pump is equal to the sum of the pressure drop across the valve and system.

$$\Delta P_{pump} = \Delta P_v + \Delta P_{system}$$

• Most systems have a quadratic relationship between pressure drop and flow.

$$\Delta P_{system} \propto q^2$$

• The pressure drop across the valve should be 1/3 to 1/4 of the total pressure drop at typical operating conditions. High pressure drop means that too much pumping energy is consumed by the valve. Low pressure drop means that the valve is oversized and may have a hard time with fine-tuned flow adjustments and the valve is too large (and expensive) for that particular application. Pumps with variable frequency drives can also be used to regulate the flow and avoid the parasitic valve pressure drop all together.

Assignment

See the Valve Design Exercise for further details on valve design calculations.