# Pressure Control. where: p is the pressure F is the normal component of the force A is the area

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2 Basically, pressure is the measure of force acting on a unit area. Pressure acts equally in all directions throughout the fluid either a gas or liquid. For a gas inside a volume the pressure is caused by the thermal movement of the gas molecules and is the same everywhere inside the volume, assuming uniform density. Pascal proved the existence of an air column above the earth pressing down causing "atmospheric pressure" (1648) In this case the weight of the fluid causes the pressure. 1 atmosphere = 0 psig or pounds per square inch gauge = 14.7 pound per square inch absolute. For gas pressure we have two laws Boyles Law Volume increases as the pressure increases Charles Law Temperature increases as the pressure increases Both these laws are combined to produce the Ideal Gas Law PV = nrt Where P is the pressure in psia Volume is in cubic feet n are the number of moles of the gas, pound moles. R is the universal gas constant; for this case T is the Temperature in degrees Rankin; degf Now that we have pressure defined how do we control it? Pressure control can be either a self-regulating or non self-regulating process. Pressure can be exerted by either liquid or gas forces. The medium phase does not dictate the control behavior rather the forces pressurizing it and how the media is manipulated dictate the behavior. The process dynamics are determined by the methods used to control the inlet or outlet flows. The most simple pressure controller is a pressure regulator. We have several of these in the lab. A pressure regulator, either self-contained or pilot operated, is a proportional only

3 controller built into its internal design. Refer to the cross section schematic shown in figure 1. In this example, the regulator is built to control the downstream pressure. At rest or on the shelf, the regulator is fully open. When piped to its service and operating, the downstream pressure P acts on the diaphragm area A to create a force F. This force will compress the regulator spring proportionally to the spring constant. The distance traveled will be x. F = K * x The top set screw that presets the spring is used set the regulator downstream pressure. set screw K s A x Q P Figure 1 Pressure Reducing Regulator As the downstream pressure increases, the resulting force acting on the diaphragm compresses the spring and closes the internal valve. As the downstream flow demand increases, the valve has to open more to allow the backpressure to balance the spring force. Liquid Pressure Control If a centrifugal pump is used to pressurize a pipeline or a particular piece of equipment, the dynamics will behave similar to a flow loop, that is a low gain setting and a moderate reset value. The centrifugal pump curve has a flow curve that reduces the head as the flow increases. The increased flow will cause the inlet pressure to decrease, which acts to reduce the flow. This loop is considered to be self-regulating. Gas Pressure Control Gas Pressure control is quite similar to level control in that the control behavior, either self-regulation or non self-regulating, depends on the control in or out of the vessel. If a flow controller controls either the inlet or the outlet flow rate, the process is non selfregulating. This is because the other flow has one unique flow to balance the pressure. If on the other hand, either the inlet or outlet flows set through a restriction, such as an

4 orifice, the process is self-regulating. As an example consider a vessel that is pressurized by an inert gas such as nitrogen. The tank supply pressure is reduced by a pressure reducing regulator followed by an orifice. The tank is pressure controlled by venting the off gas to atmosphere. This is frequently done with flammable liquids to lower the flash point of the vapor space above the liquid surface, Figure 2. Our laboratory experiment 1 is piped in this manor. PC Orifice Pressure Reducing Regulator Vent Figure 2 Self Regulating Pressure Control In this case as the pressure increases closer to the downstream regulator set pressure, the flow through the regulator will decrease. That decreasing behavior will help contribute to reducing the rate of pressure increase. So how do we know what the pressure will be? If we consider the PV=nRT equation, (assuming constant temperature, called isothermal) what is occurring in the tank is an integration of the number of moles in the tank, that is the net number of moles is the sum of the moles flowing in minus the number of moles flowing out. The number of moles can then be used to calculate the pressure.

5 SP & PV for Press Controller PSIG Psp P Time, min Gas Flows SCFM 6 Qin Qout Time, min Figure 3 Gas Flows and Pressure for a Self Regulated Pressure Control

6 As the pressure is increased, the flow in decreases and the flow out increases. This assumes that the tank pressure is close to the regulator set pressure. Figure 3 shows the dynamic behavior for this pressure control. If, on the other hand, The inlet gas is flow controlled for a much higher pressure source and the gas is either used to pad the tank or react with one of its contents yielding an off gas flow rate that is directly proportional to the inlet gas flow, then the gas pressure could be assumed to be non-self regulating. FC PC Orifice Vent Gas Flow Controller Figure 4 Non-Self Regulating Pressure Control In this case, as the pressure in the tank increases, the action of the flow controller, assuming it is tuned to operate much faster than the pressure control loop, will be to maintain the same flow. In this case there is only one unique stable valve position. This dictates an integrating behavior therefore non-self regulating control. As the plots show, figure 5, the inlet flow was constant. After the pressure set point change, the outlet flow is equal to the inlet flow, but the tank is at a higher pressure. The gain for the self regulating pressure control was 7.5 while the reset was at 2.5 repeats per minute. For the non self regulating pressure control the gain was 20 while the reset was at 10.0 repeats per minute. As a rule, non self regulating control loops require a higher gain setting.

7 SP & PV for Press Controller PSIG 45 Psp P Time, min Gas Flows SCFM 20 Qin Qout Time, min Figure 5 Gas Flows and Pressure for a Non Self Regulated Pressure Control

8 Even though the non self regulating behavior is seen as inlet flow limiting, for small pressure changes, both loops can exhibit integrating behavior. This is because the rate of change for an increasing exponential is greatest at the start or beginning of the change. For a short interval, both self and no self regulating loops can show similar behavior. For this case, assuming integrating behavior can lead to a higher gain setting. It should be emphasized that in this case, loop instability can occur because the resulting gain may be unstable for extreme disturbances. Calculations The valve Cv factor can calculate the gas flow: Q( scfh) = 42.2C v ( P1 + P2 )( P1 G f P ) 2 Cv Q P1 P2 Gf Valve flow factor Gas flow in std. cubic feet per hour, scfh Inlet pressure psia Outlet Pressure psia gas specific gravity We can convert from scfh to pounds per hour pounds per hour = scfh * (specific gravity)/13.1 From the equation we can see that as the outlet pressure approaches the inlet pressure, the flow decreases, eventually to zero if the two are equal. This explains the pressure control's self regulating effect. We can use a similar equation for the outlet control valve. The Cv will be a function of the valve position or the pressure controller output signal. Once the two flows are known, an integrator can be used to totalize the accumulated flow in the tank. The Ideal gas law can be used to then calculate the tank pressure. Lets look at the VisSim simulation of our gas pressure control.

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