Tuesday, April 14, 2009

Defining Control Valves Pressure Drop





In many design guides there are some recommendations on how to assign pressure drop for the control valve (20-30 percent of the system friction loss- or 10-15 psig minimum), but they don’t say why.
For many, the reason is obvious- but for many others is not. If I were the one who wrote that design guide, I would have taken the pain up front and described the whole story, because many mistakes (as many as the number of control valves in a plant to be pessimistic) could have been avoided, many pumps could have been ordered with proper margin, and many reworks could have been eliminated. The fact is so simple that it was assumed to be obvious, but because the volume of related work to this simple topic is humongous, we cannot afford not to understand it properly (well, we can still afford not to understand many scientific facts, because they have no immediate impact in our everyday lives).


Hydraulic Path (see Figure 1):
A pump is used to transfer a liquid from a low pressure source to a high pressure destination. It adds the required energy (or pressure) to the flowing liquid to increase its pressure and to overcome the pressure drop on its path. Why do we need a control valve? Because in operating plants streams flow rates do not stay the way we define them in the H&M balance table (or steady state simulation). They keep changing for many reasons –and- we may want to change them as well. The pumps are also capable of working for a range of flow rates (see the typical centrifugal pump curve, Figure 2-1). For smaller flows (than normal) the same pump provides higher discharge pressures, and for higher flows it cannot increase the pressure to that extent.

Now, it’s time to introduce two major components of the hydraulic path:
Static Loss (or gain) – and- Dynamic Loss (there is no dynamic gain)
The Static components do not change with changes in flow, but the Dynamic components do change with flow. Figure 1 provides some clarifications:
Pressure Balance:
P1 + Static Head 1 - suction line friction loss - ∆P1 + ∆P pump - ∆P Control valve -discharge line friction loss - ∆P2 - ∆P3 - Static Head 2 = P2
Re arranging:
P2 - P1 - Static Head 1 + Static Head 2 = ∆P pump - ∆P Control valve -suction line friction loss - discharge line friction loss - ∆P1 - ∆P2 - ∆P3
The left hand side of the equation is a constant value, because P1, P2, and the static heads are constants, and they do not change with chnages in flow. So, we may call them the “Static Components”. The right hand side should be therefore that same constant value overall, but its components do change with changes in flowrate, and that’s why we may call them the “ Dynamic Components”. (System dynamic loss is not limitted to the line friction loss, it also includes any other equipment or piping element which has a pressure drop. Sounds obvious, but (believe me) does’t hurt to emphasize.)
Dynamic losses change with flow based on below formula (which it stemmed from the Bernoulli’s law): (∆P @ Q2) = (∆P @ Q1) * (Q2/Q1)^2 (flow ↑ ---> ∆P ↑)
So, we now know how our hydraulic system demand on pressure (which is provided by the pump) changes within a desired range of flow (normal, turndown, and rated conditions, and anywhere in between). We also knew the system constant pressure demand (left hand side – or- static component of the hydraulic path). Our job is to initially specify adequate ∆P for the pump, and secondly to calculate (estimate) the control valve ∆P, which satisfies the above pressure balance.
Some guidelines recommend to put aside 20-30% of system “Dynamic Losses” for the control valve (Dynamic Loss: line friction loss + heat exchanger(s), heater, piping elements, any other equipment ∆P in the path). So, we intentionally add to the system friction loss and therefore need a pump which delivers higher pressure than what we actually need. But why are we doing this? Because we need the system to be under our control in term of flow rate, and the control valve is doing this job for us. We need this manoeuvring room in addition to the system demand. This room becomes larger at smaller flow rates (higher pump discharge pressure and higher control valve ∆P), and is minimum at rated flow (lower pump discharge pressure and lower control valve ∆P).
Now, control valves ∆P should be at least 10-15 psi to operate properly. So, if 20-30% of system dynamic loss becomes less than 10 psi, the 10 psi value is selected as a minimum.
Question: Dynamic loss changes with flow. What flow rate is this dynamic loss referring to? The highest (some recommend normal flow, it’s really a matter of preference- but it shouldn’t be the smallest flow), because it gives the higher ∆P across the control valve- and therefore higher pump discharge pressure (If we underestimate the system dynamic loss – or- fail to understand which parts of the system are the main cause of dynamic pressure drop, chances are the pump won’t be able to overcome the higher pressure drops at higher flow rates, even with the control valve wide open).
Let’s go back to the pressure balance equation:
P2 - P1 - Static Head 1 + Static Head 2 = ∆P pump - ∆P Control valve -suction line friction loss - discharge line friction loss - ∆P1 - ∆P2 - ∆P3
This equation is valid and should be satisfied at all times (meaning all flow rates). We know dynamic loss increases proportional to flow rate squared. We also have some clue to estimate control valve ∆P. So, the pump ∆P could be calculated from the above equation. As mentioned earlier, centrifugal pumps come with a characteristic curve (Figure 2). When we are sizing the pump, we don’t know about the curvature of that famous curve (it comes later from the pump vendor), so we may assume a linear relation between flow and pump ∆P (or ∆H, see Figure 2-2). The two points which represent this line could be the rated point, and the shut off point (Q= 0 gpm, ∆H= 1.25 ∆H rated), and this assumption provides more conservative estimates in pump and control calve sizing. To find the pump discharge pressure at any other flow rate, we may use this line.

It is important to define the system in not just one point (normal flow), but to specify a wider range of operation (from turn down to normal to rated), because it is important for purchasing the control valve, which is supposed to control the flow rate at various conditions. With referring to the pressure balance equation, it’s clear that at turndown condition, pump delivers higher pressures – and- the dynamic losses are also minimal, therefore control valve ∆P must be the highest (or the control valve is less opened).
Also, at rated condition, the pump delivers the lower discharge pressure- and – the dynamic losses are at their highest value. Therefore control valve ∆P must be the lowest (or at its maximum recommended opening).
Question: How do we come up with the 20-30% dynamic loss recommendation on the control valve ∆P? It’s a matter of economy and practicality. We don’t necessarily want to oversize the pump, and then drop the extra pressure (energy) through the control valve, but we still want to have available extra pressure when system dynamic (friction) loss increases. Also, from control valve functionality point of view, too much a difference between turndown and rated cases pressure drop may affect the functionality of the control valve. So: not very high, not very low, just as much as covers all our needs.

Some points to add:
1- Don’t let the “complexity” (J ) of the hydraulics software you are working with, keeps you from thinking through and using your own judgement. Many of these programs are written by engineers, and not software specialists, so they might not be adequately robust- which means you actually need to unnecessarily learn some tricks to overcome the program bugs-which to me is a waste of time rather than acquiring any additional value. It’s better to master the concept, and not being a slave to some random dazzling softwareJ.
2- For complex circuits, it is very important to properly identify the destination point. The destination point pressure must be thermodynamically defined fixed value. No further obstacles (dynamic losses) should be after the destination point in your pump’s path, because you will exclude that portion of the dynamic losses and under estimate the required control valve ∆P. For instance, a heater with massive pressure drop cannot be a destination point in your circuit. You will end up assigning 10 psi ∆P for the control valve. A cause for entertainment – but not for the designer.
3- Once more, when a high dynamic loss is expected in a hydraulic system, it means the friction loss difference is significant between turndown and rated cases- which also means, this difference should be absorbed by the control valve. A control valve with a wide range of ∆P (even the pump discharge pressure is higher at turndown, and that also adds to the need for a control valve capable to offer wide a wide range of ∆P, please take another look at the pressure balance equation).

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