How to Size a Relief Valve

Positive displacement (PD) pumps do not function well if the discharge is blocked. Unlike centrifugal pumps, they have little tolerance for flow restriction. A piston pump will try to continue stroking regardless of whether its discharge valve is open or closed. This means that something will have to give—a tripped motor, ruptured casing or worse. Centrifugal pumps also do not operate well with a valve, but they can at least tolerate a brief closure. In fact, some require a closed valve pressure reading during performance tests at the factory. This difference is the result of the design of both pumps. No internal motion occurs to displace the fluid inside a centrifugal pump. The impeller simply keeps spinning the fluid if the valve is closed. In a PD pump—such as a piston pump—the displacing motion acts on the fluid, and the fluid must exit the pump. For these reasons, a PD pump needs to have a relief valve (either internal or external), which could be set to open when a certain pressure is reached. This is necessary to protect the pump. Unfortunately, because of pressure pulsations inside a PD pump, knowing at which pressure to set the release valve to open is difficult. Should it be average, maximum or minimum pressure? An example of such a dilemma—raised during a recent conversation with a colleague in the industry regarding release valve pressure settings—is shown in the next section.

Release Valve Pressure Settings

From an email sent to Lev Nelik: I am responsible for determining the adequacy of existing relief valves on the discharge of some of our PD pumps. The original design basis of the release valve sizing was to match the design flow rate of the pump. The engineering and construction contractors I am currently working with say that this design is deficient and should be larger by a factor of π/2 (π = 3.14) to account for the rotary action of the driver acting on the piston in this pump. I cannot find references to this requirement in the open literature and wanted to ask your opinion. -Tom Morrison, BP Lev Nelik responds: A release valve opening should be capable of passing the full flow at the set pressure of the valve. For example, if the pump has been moving 1,000 gallons per minute (gpm) at 100 psi and the relief valve was set to protect/bypass at 120 psi, then when it opens, the entire 1,000 gpm should flow through it. The changeover from main flow to bypass will not be instantaneous because it cannot be in practice. For example, at 120 psi, the valve may just begin to open, and full flow is reached by 123 psi, but not at 150 psi. Different designs of release valves can narrow or widen this “band,” but in general, it should be a relatively sharp change from main discharge flow to bypass. Tom Morrison responds: Thank you for the prompt reply and information. From your response, it looks like pump vendors would design the release valve for the normal, full-flow design condition. There is a specific nuance to the example you mentioned that I want to make sure that I clarify and understand. For a piston-type displacement pump, the instantaneous flow rate varies through the shaft revolution. In mid-stroke, a maximum rate of (design flow x π/2) is reached while the flow drops to near zero at the end of the stroke. So, for the 1,000 gpm case, the instantaneous maximum would be more than 1,500 gpm. If the release valve passes 1,000 gpm at 120 psi, wouldn’t the pressure need to jump significantly higher than 120 psi to pass the 1,500 gpm? I am not advocating raising the release valve size to 1,500 gpm because then it would chatter on every stroke of the pump. I would like to confirm that no one in the industry designs these release valves for any more than the normal full-flow design rate. Thanks again for your insights. Lev Nelik responds: Any pump operating point is an intersection between the pump curve and system curve. There could be only three types of systems: static head (pressure), friction or a combination of both. The flow through the piston pump changes, as shown by the equation below: Q = Q_max x sin (2πx) Its change is like a sequence of steady-state steps, with rapid transient flows to be neglected (unless discussing water hammer and/or similar transient rapidly changing effects, when the system does not have time to adjust to the pump changes and lags). Consider, as an example, a friction system in which piston flow is 1,500 gpm, resulting in 100 psi. When the piston is at the end point, flow is, as you noted, 100 gpm, which would cause system resistance and make the pressure 44 psi, per affinity laws: (1,000/1,500)² x 100 = 44 psi The pressure will essentially fluctuate between 44 psi and 100 psi, which is why you would indeed see pressure pulsations in the system (a problem with PD pumps). For this reason, one or more dampeners are usually installed on PD pumps to make an averaging effect with the use of, for example, accumulators. If the discharge is partially blocked and the pressure rises to an average of 200 psi, the spikes would be from 277 psi to 122 psi. If the setting of the valve is accomplished with the pulsation dampener in the system at 190 psi and the spring opens with a force resulting in 190 psi multiplied by the spring cap, then all flow (same fluctuating 1,000 gpm to 1,500 gpm) will go to the bypass release valve. If, however, there is no dampener, then the spring will chatter when the pressure is at 122 psi. It will close the release valve, and at 277 psi it will obviously open. In such a case, the user would observe this happening and set the spring to open at a lower value, such as 122 psi. This way, the release valve never closes. In fact, the user will likely not notice the piston pump pulsation, as you described, but will only be watching the practical result to get the spring set. When his gauges show the (average) pressure, he will stop turning down the spring cap and leave it at that point so that the release valve will be open when he (practically) had it set. PD pump manufacturers follow the same process—setting the spring to open and fully bypass not at calculated instantaneous values but at the actual gauge readings (time-averaged damped). They, of course, deal with the internal release valves, but external release valve manufacturers follow similar steps. Similar logic can be used for the pure static pressure (injection) or a combined system. I did not bother getting the numbers calculated too exactly, nor drafting a quick sketch of this, but I think you get the main point. Tom Morrison responds: This was an awesome response, and I appreciate your not getting down to the “nth” decimal place with your calculations. You addressed your response at the exact level of detail I was hoping for and provided enough detail that I could follow along precisely. If you would allow me to summarize back to you what I think I read, I would say the following. The concern I asked you about is real, and the manufacturers incorporate this knowledge into the somewhat-iterative setting of the spring in the internal release valve to dampen out the pulsation effect. For good design practice, one or more pulsation dampeners are necessary to properly dampen this swing for this type pump. In my revalidation of the external relief valve on the pump discharge, I should check the sizing against the normal design flow of the pump, not the instantaneous flow indicated by the Q = Q_max x sin (2πx) term you showed in your response.