# Floyd D. Jury. Director of Education

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1 Floyd D. Jury Director of Education

4 operation of any gas pressure regulator, perhaps we should analyze each of them in more detail. Restricting Element The restricting element that we use will undoubtedly be some type of valve. Regardless of the style of valve which we use, we must remember that its basic purpose is to form a restriction to the flow. It forms a bottleneck which allows us to convert from a high pressure system to a low pressure system. The pressure differential that exists across the valve represents a difference in potential energy that causes the gas to flow, just as water flows downhill. Our common sense tells us that if we increase this pressure differential across the valve, then we should thereby increase the flow of gas through the valve. In actual practice, this is true only up to a certain critical point. If we look at a typical regulator installation, such as in Figure 5, we can analyze how the pressure varies along the length of the valve under steady-state flow conditions. A6007 / IL Figure 5. Profile of Pressure Across a Valve The valve forms a major restriction in the line, and consequently its flow area is considerably smaller than that of the surrounding pipe. If we are to maintain a steady-state flow through this system, we must have just as much gas flow through the small area at the restriction as we have in the larger pipe area. It is obvious then that the velocity of the gas must be much greater at the restriction in order to maintain the flow of gas. The velocity will be the greatest at the point of maximum restriction of the flow stream. This point is called the VENA CONTRACTA and is normally located a short distance downstream of the actual orifice. This increase in velocity represents an increase in kinetic energy that must come at the expense of the potential energy which is represented by pressure. Thus, in Figure 5, we see that the pressure decreases to a minimum at the vena contracta where the velocity is the greatest. As the gas slows down again in the larger downstream piping, we gain back some of the pressure that we lost. This is called pressure recovery. If we try to increase the flow through this valve, we must, of course, increase the velocity of the gas at all points in the system. As we continue to increase the flow, we will eventually reach a point where the gas velocity reaches the speed of sound at the vena contracta. Since we cannot normally make the gas travel faster than this limiting sonic velocity, we have in effect reached the point where we can no longer increase the volume rate of gas flow through the valve simply by lowering the outlet pressure. The point where we reach sonic velocity and the flow becomes limited is known as CRITICAL FLOW, and the pressure drop that exists across the valve at that point is known as CRITICAL PRESSURE DROP. If we were to increase the pressure drop beyond the critical point by lowering the outlet pressure of the valve, we would get no further increase in flow through the valve. The actual value of the critical pressure drop varies considerably depending upon the style and flow geometry of the valve. As the gas passes through the valve, a certain amount of turbulence occurs which results in an energy loss within the valve. Part of the kinetic energy of the gas is changed into heat energy and part of it is changed into noise energy. A valve such as a ball valve or butterfly valve, that has a fairly streamlined flow pattern has a minimum of energy loss in the valve. This results in a relatively high downstream pressure recovery. This type of valve would be called a high recovery valve and is shown in Figure 6 as the solid curve. On the other hand, a valve, such as a double ported globe valve, which has a relatively turbulent flow pattern, will have a fairly high energy loss which means poor downstream pressure recovery. This type of valve would be called a low recovery valve and is shown in Figure 6 as the dashed curve. Those who specialize in the theory of fluid flow tell us that the pressure differential between the inlet and the vena contracta (P 1 P vc ) is a direct measure of flow regardless of the style of valve; whereas, the pressure drop observed across the valve ( P = P 1 P 2 ) is highly dependent upon valve style. Thus, if the two valves plotted in Figure 6 have equal flow areas, then we see that they would also have equal flow, since the pressure drop that determines the flow (P 1 P vc ) is the same for both valves even though the observed pressure drops across the valves (P 1 P 2 ) are quite different. The observed pressure drop across the valve 4

5 E0441 / IL Figure 6. High and Low Recovery Valves ( P = P 1 P 2 ) is a direct measure of the pressure loss in the valve. Since it is quite difficult for us to measure the pressure at the vena contracta, we must, as a practical matter, resort to using the P across the valve as a measure of the flow instead of (P 1 P vc ). Since the P across the valve is highly dependent upon valve style, it is obvious that experimental means must be used to find the relationship between this pressure drop and the flow for any given style of valve. This is the reason for the many tables of valve sizing data published by the valve manufacturer. We said earlier that in general we could increase the flow by increasing the pressure drop across the valve. We have just discussed the fact that when we increase this pressure drop by lowering the downstream pressure, we eventually reach a critical condition where the flow no longer increases. We have reached critical flow because we have achieved the limiting sonic velocity at the vena contracta. As it turns out, we can continue to increase the flow through the valve even after we have reached the critical flow condition. We do this by increasing the inlet pressure (P 1 ) to the valve. We would still have sonic velocity at the vena contracta and we would still have critical flow through the same flow area. What we have done, however, by increasing P 1 is increase the density of the gas entering the valve and have thereby packed more standard cubic feet of gas into each actual cubic foot of volume passing through the regulator. In effect, we have not changed the cubic feet per hour of flow, but we have increased the SCFH, or standard cubic feet per hour. As you will recall, a standard cubic foot of gas is that amount of gas that will occupy a volume of one cubic foot under standard conditions of 60 o F and psia. Loading Element Except for a few of the older weight loaded units, almost all gas regulators have springs. In fact, springs and diaphragms are by far the most universally used loading elements in modern gas regulators. From a design point of view, there are several spring factors that are important such as type of material, wire diameter, spring diameter, free length, and the number of coils. From the strictly operational point of view of the gas man, however, there is only one factor of real significance. That factor is known as the spring rate. Spring rate (k) is defined as the number of pounds of force (F) necessary to compress a spring by one inch. If a certain spring requires a force of 60 pounds to compress it one inch, then we would say that the spring rate was 60 pounds per inch. Since the spring rate is a linear relationship within its normal operating range, this same spring would require 90 pounds to compress it 1.5 inches. If we took another spring and found that it would compress 2 inches under a force of 100 pounds, we could determine the spring rate by dividing the 100 pounds force by the 2 inch compression to obtain 50 lbs./in. This example suggests that we could define a simple formula that would describe this relationship. where: F = force (lbs.) X = compression (in.) k = spring rate (lbs./in.) We can easily manipulate this equation into another common form (F = kx) that will allow us to find the spring force developed for any given spring compression. This form of this simple equation is very useful in the study of gas regulators. As useful as a spring is, it can provide a loading force in one direction only. Energy must be supplied to compress the spring in the other direction. This energy usually comes from the force developed by pressure acting upon a diaphragm. A diaphragm is simply a piece of fabric coated with some type of rubber-like material. The coating provides a seal to contain the pressure while the fabric gives it enough strength to withstand the pressure. Some diaphragms are molded into special shapes but most are simply cut from flat sheets. For economic reasons the coating on the diaphragm may be much thinner on one side than the other. The 5

7 E0443 / IL Figure 8. Close-up of Diaphragm Convolution Section E0444 / IL Figure 9. Tensile Force in a Diaphragm diaphragm and shapes it into what is known as a convolution. Figure 8 provides a close-up look at how the loading pressure is uniformly distributed over the diaphragm convolution. We have to remember that this pressure is not only uniformly distributed, but also acts perpendicular to the diaphragm surface at every point. As the pressure shapes the diaphragm convolution, we can visualize a line drawn tangent to the diaphragm at any point along this convolution. As we do this, we will discover that there is one, and only one, point where the tangent line is horizontal. We can identify this as the point of horizontal tangency. A vertical dashed line is drawn through this point in Figure 8 to divide the diaphragm convolution into two sections. At this point we need to emphasize the fact that a diaphragm is basically a rubber coated fabric. The extreme flexibility of this type of material means that it can support neither shear nor compressive forces. The only force that can be sustained by any flexible material such as this would be a tension force that is always acting directly parallel to the fabric at any point. If we follow this line of reasoning in Figure 8, we can see that a horizontal tension force will exist in the diaphragm at the point of horizontal tangency. But let s look out! There is another trap here that we must avoid. It would be easy to assume that the point of horizontal tangency falls in the center of the convolution. This is only true for the one position in the stroke where the diaphragm plate is level with the flange. At other positions in the stroke, the effective area changes as the point of horizontal tangency moves inward or outward. It is easy to visualize how this effective area changes if you hold a slack piece of string between your outstretched hands to simulate the diaphragm convolution. As you move one hand up and down to simulate the motion of the diaphragm plate, you will discover the following relationship. As the diaphragm moves to COMPRESS the spring, the effective area DECREASES. As the diaphragm moves to RELAX the spring, the effective area INCREASES. This relationship will remain at your fingertips if you remember that the effective area decreases to its least amount just when it is needed most to help compress the spring. Spring and Diaphragm Effect Now let s use some of the fundamentals that we have developed about the three essential elements in order to study the operational performance of gas regulators. The pressure acting to the left of the horizontal tangent point can only be transmitted to the diaphragm plate through tension in the diaphragm material. At the horizontal tangent point, this tensile force is horizontal, as shown in Figure 9, and therefore can contribute nothing to the up and down motion or the thrust of the actuator. In other words, the area outside of the point of horizontal tangency is not effective area. Thus, when we use the formula (F = PA) for the force developed by a pressure acting on an area, we must use the effective area in the calculation. As we have just shown, this effective area is calculated using the diameter between the points of horizontal tangency on the convolutions. A6005 / IL Figure 10. Typical Self Operated Regulator 7

9 spring is in its most relaxed state and the valve plug is fully open, the effective area of the diaphragm will have to be something greater than 80 in 2. A typical value might be 100 in 2. When we previously assumed a constant effective area, we found that our example regulator had a 4 psi proportional band. Let s see how the change in effective area would affect the proportional band. be much less change in effective area with valve travel, and consequently, the proportional band of the regulator will be smaller. The major disadvantage of this approach is the higher cost of the molded diaphragm. We can also narrow the proportional band by installing a spring with a lower spring rate, but we might introduce problems with valve plug chattering because of the lower stiffness. Another way might be to install a larger valve size so that the valve travel can be reduced. We could also install a different regulator whose effective diaphragm area is greater. This would theoretically reduce the proportional band, although we would almost certainly run into problems of exceeding the spring s capacity for travel or initial compression. The last two methods also have the disadvantage of requiring a major change in hardware. We see that the proportional band of our regulator increased an additional 0.4 psi as a direct result of the change in effective area of the diaphragm. Thus, droop and proportional band are caused by both spring effect and diaphragm effect, as we can see from the plot in Figure 11. Pilot Operated Regulators So far we have only discussed self operated regulators. This is the name given to that class of regulators where the measured pressure is applied directly to the loading element with no intermediate hardware. There are really only two basic configurations of self operated regulators that are practical. These two basic types are illustrated in Figures 4 and 10. E0445 / IL Figure 11. Plot of Droop Due to Spring and Diaphragm Effect From a performance point of view, it is desirable to keep the proportional band as narrow, or small, as possible. One way that will help is to minimize or eliminate the diaphragm effect. In actual practice this is done quite frequently by using a molded diaphragm with deep convolutions rather than a simple flat-sheet diaphragm that has quite shallow convolutions. You can show yourself quite easily why the deeper convolution minimizes the effective area change by performing the string trick again that was suggested in the last section. As you move one end of the string up and down, you will notice that for a given amount of valve travel, the change in the position of the horizontal tangent point of the convolution is much less with a deeper convolution. This means that there will If the proportional band of a given self operated regulator is too great for a particular application, there are a number of things that we can do. From our previous examples we recall that spring rate, valve travel, and effective diaphragm area were the three parameters that affected the proportional band. In the last section, we pointed out the way to change these parameters in order to improve the proportional band. If these changes are either inadequate or impractical, the next most logical step is to install a pressure amplifier in the measuring or sensing line. This pressure amplifier is frequently referred to as a pilot. A typical pilot amplifier consists of a double diaphragm assembly that is rigidly fastened together as shown in Figure 12. This complete diaphragm assembly moves up and down under the action of the spring, the loading pressure (P L ) and the controlled pressure (P 2 ). As the diaphragm assembly moves, it modulates the flow through the supply pressure nozzle according to changes in P 2. The maximum opening of this variable orifice must be larger than the fixed orifice shown as a hole through the upper diaphragm. 9

12 in order to balance either an increase in orifice size or an increase in P 1 A family of curves is shown in Figure 17 for a given orifice size which clearly illustrates that there is a different outlet pressure curve for each inlet pressure on a typical service regulator. E0448 / IL Figure 16. Basic Service Regulator Without Velocity Boost To get tight shutoff the regulator uses soft seats which must be tightly compressed. This compression force can only come from the action of P 2 acting on the diaphragm, which means that P 2 must rise enough at zero flow to hold the seal tight. This lock up pressure can be clearly seen on the performance curves in Figure 15. The amount of pressure rise that we get in this lock up region is directly dependent upon the stiffness of the elastomeric material on the valve plug. For economic reasons the house service regulator is usually a single port valve as shown in Figure 16. If we look at the upstream or inlet pressure (P 1 ) we can see that it is producing a force that is trying to open the valve. The controlled pressure (P 2 ) is acting on the back side of the valve plug trying to close it, but in a typical application, P 1 is much greater than P 2. This leaves us with a rather large unbalanced force that is acting to open the valve plug. The only way that we have to balance this force is by P 2 acting on the diaphragm. If we get any kind of variation in the inlet pressure, then we can see that we will also get a variation in our controlled pressure. One easy way that we can decrease this variation in P 2, due to fluctuations in P 1, is to use a mechanical lever ratio connecting the diaphragm assembly to the valve plug. In a typical service regulator, this lever ratio is about three to one. This means that P 2 only has to vary one third as much as before in order to balance fluctuations in P 1. The lever only reduces the effect of valve unbalance, it does not eliminate it. Since the magnitude of the unbalanced force on the valve is directly proportional to the valve area, it is to our advantage to select an orifice size which is no larger than necessary to pass the required flow of gas. The magnitude of the unbalanced force on the valve also increases when P 1 increases. Thus, even though the lever system is helping to reduce the effect of valve unbalance, we still must have an increase in P 2 Most house service regulators control pressures in the vicinity of a few inches of water column, yet since each individual gas company s pressure setting may be slightly different, we need some method of adjusting the setpoint pressure. We know from our previous discussions that P 2 acting on the diaphragm must provide a force that will balance the spring compression force. We can use the adjusting screw on top of the spring, as shown in Figure 16, to increase the total compression force in the spring. P 2 must then also increase in order to balance the larger spring force and hold the valve plug in the proper position. Thus, by changing the initial compression in the spring, we can adjust P 2 to operate at any setpoint value that we wish within a certain range defined by the load limits on the spring. Another factor that we frequently need to take into consideration when working with service regulators is the weight of the moving parts in the regulator. When installed with the regulator spring on top, the weight of the spring and diaphragm assembly produces an additional downward force that must be balanced by an additional increase in P 2. If this same regulator was turned upside down, the weight of the moving parts would then operate in the opposite direction and the setpoint pressure would change. Since, in this upside down position, the weight is opposed by the spring instead of the pressure, we can use the initial compression in the spring to support the weight of the parts. The upper casing of the regulator is designed so that it will hold the spring properly, but it also protects the regulator parts from exposure to the weather, dirt, etc. Just as important, it also keeps a cushion of air above the diaphragm. As the diaphragm assembly moves up and down, the air in this upper casing must move in and out through the vent hole, otherwise, the compression and rarefaction of air in the upper casing would interfere with the diaphragm movement. If we restrict the flow of air in and out of the upper casing by just the right amount, we can damp the tendency of the diaphragm assembly to go into a sustained oscillation. This type of oscillation is called hunting or buzzing. This is why a regulator will sometimes buzz when we remove the closing cap to adjust the spring. When we close the cap again, the regulator stops buzzing. The same thing can sometimes happen if the vent hole is enlarged for some reason. 12

13 B2367 / IL Figure 17. Variation of Controlled Pressure with Changes in Inlet Pressure on a Tyical Service Regulator Conclusion It should be obvious at this point that there are a great many important fundamentals to understand in order to properly select and apply a gas regulator to do a specific job. Although these fundamentals are profuse in number and have a sound theoretical base, they are relatively straightforward and easy to understand. As you are probably aware by now, we made a number of simplifying assumptions as we progressed. This was done in the interest of gaining a clearer understanding of these fundamentals without getting bogged down in special details and exceptions. By no means has the complete story of gas pressure regulation been told. The subject of gas pressure regulation is much broader in scope than can be presented in a single document such as this, but it is sincerely hoped that this paper will help the gas man to gain a working knowledge of some fundamentals that will enable him to do a better job of designing, selecting, applying, evaluating, or troubleshooting any gas pressure regulation equipment. 13

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