Dead Time and Process Lag in Control System

The first thing you need to do, Boss, is decide whether you are controlling flow, or whether you are controlling pressure. What is the requirement from the Process perspective, please, Matey?

Good question Crabtree,

Gas is supplied from a distant source up to 40 bar pressure, normally varies between 25 to 35 bar. User requirement is intermitant (for 15 min in an hour) but at 17-18 bar. So, buffer vessels are installed in upstream of PCV to supply huge quantity for short duration at required pressure. FCV has to cotrol the flow rate at that pressure. Distance between PCV and FCV is about 500 m. Pipe size is mainly DN 500, but small lengths of smaller sizes are also involved.

Hope it is clear.

Thanks kilowattO for the clarification,

Now can you please suggest how to compute the dead time and lag time for the case I had explained? Please see more information at #3. Thanks in advance.

Thanks KilowattO for beatiful graphical dipiction. GA.

The PCV should open immediately so as to sustain the pressure in the pipeline. A second or two, perhaps?

Yes, I also wish the same, but it is not happening. Flow control valve (FCV) can be put on some default open position, say 50%; so that once the system starts taking flow (by opening an ON/OFF valve in downstream), the required flow rate can be attained quickly. This results in drop in upstream of FCV. My question is:

1. How fast the pressure drop travels up to PCV (500 m away) to be sensed by pressure transmitter?

2. Once sensed, how long PCV will take to start opening?

3. Once PCV starts opening, how long it will take to feed required flow rate?

4. What are the solutions to curtail dead time and process lag? Can we take pressure transmitter before FCV as input for PCV, is there any adverse effects?

Ahah, so it isn't really a flow control valve, it is merely a modulating valve with some predetermined position set elsewhere; there is no flowmeter to use as the measuring element as part of an automated system. So now the answers are:-

A1) It depends upon the pressure of the gas, the flowrate, size and length of pipe and a host of other factors.

A2) Almost immediately; a second or two?

A3 & 4) If the pressure drop along the pipe is such that the modulating valve is fully open in order to achieve the flowrate, then the pressure control valve won't be able to sustain the pressure needed to achieve the flowrate. If the valve has, as suspected from the above, a fixed position, then the answer is that the pressure control valve can never do the job of flow control, and a set flowrate will never be achieved without operator intervention from the device that sets the modulating valve position. In such a situation, any calculation is not worth the paper on which it is printed.

GA PWSlack for a good response, but I want to clarify that FCV is really a flow control valve using a flow element and set point is 500 Nm3/min. Its default open position is to facilitate quickly attaining the set flow. Once flow rate is more than set value, it starts closing. Job of PCV is maintain 17-18 barg pressure in its downstream. Now, I think you can answer better. I am interested in methods to determine dead time and process lag.

Since this is an operating system, the bump test will be the way to determine the dead time and lag time.

One concern I have is the 2 loops fighting each other. In a situation like you describe, the pressure controller should typically be tuned for 3 times faster response (Ki) than the flow loop. Otherwise your system will just oscillate.

Thanks & GA KillowattO,

Bump test of FCV show about 3 sec dead time and hardly 2 sec lag time (Lag time could be much more if there is no default opening of FCV). Similarly for PCV also it can be found. I wanted to cross check it with some theoretical models if some one suggests. FCV and PCV both may have there own specific dead time and lag time. But here there is one more important factor. That is the time taken for pressure drop (after FCV opens) to travel 500 m upstream up to PCV to provide input to PCV to open (to make-up the pressure drop). How to calculate this time?

Very approximate view....

1. Velocity of sound in air ~ 330 m/s. Proportional to inverse square root of molecular weight.
2. 28 for N2 versus 18 for NH4 gives 330/√(18/28) = 410 m/s.
3. Time for pressure wave to travel 500m is 500/410 ~ 1.2 seconds.

Not surprising the valves have slow response compared to 1 second, since great risk of supporting an organ pipe oscillation with timed "puffs" (2.4 seconds for wave to travel to far end, then reflect back to valve).

From a different point of view, pipe contains ~ 200 cubic meters gas. Set intial flow rate works out as 4 cu m/second. So 2% of volume/second gives about 2% pressure drop/second.

Thanks Ano.Poster for your input.

Is the pressure waves travel at the same velocity as sound? If yes, then will it take same time to travel 500 m distance (opposite to the direction of flow) even if there is a restriction like pinched (partially open) ball valve in the the middle?

From a different point of view........ How 2% of volume/second gives about 2% pressure drop/second. I could not get your calculations.

Pipe volume for 500 m length is about 90 cubic meters. Set flow rate of 500 Nm3/min works out to 8.3 Nm3/sec or about 0.5 cu m/sec at 17 barg pressure and 30 C temp. Before FCV fall in pressure was observed at the rate of 0.14 bar/sec immediately after the flow started. Can you please redo the calculations with this information.

Thanks a lot 67model for an exhaustive but still a 'to the point' answer. It has cleared many of my doubts. It deserves many GA's, but I can offer only one.

In my question there are two control valves, 500 m apart. Both may have their own dead time & lag time depending on control characteristics. Pressure drop is caused by FCV at the end but PCV is sensing it 500 m away in upstream to respond. As you have rightly pointed out the rate of pressure drop may diminish while travelling upstream at the rate of velocity of sound, the response of PCV will be based on diminished one. As I mentioned about the restrictions like partially closed valve at #14, its effect may be alarming.

Based on your observations, I have following more questions:

1. Knowing the rate of pressure drop before FCV and pressure drop due to friction for piping, fittings & other components, can we roughly calculate % opening of ball valve in the middle?

2. Can we decide to take pressure before FCV as a feed to operate PCV? What could be the other problems assuming all the valves in between PCV & FCV are full bore ball valves and they are kept fully open position.?

I tries to paste a sketch of piping here, but could not succeed, will try to send with PM. I can describe in words below:

Start from 6" PCV, 6"+10" pipe with reducer (5 m), 10" ball valve, 10" check valve, reducer+20" pipe (200 m), 20" ball valve, 20" pipe (250 m), reducer+16" pipe (50 m), Unequal 'T'+12" pipe (40 m), reducer+8" pipe in several segments (5 m), 8" ball valve, 8" 'Y' strainer, 8" ball valve, 8" ball valve, 8" FCV and 8" ball valve at the end.

GA. Thanks a lot 67model for your response.

The requirements of receiving consumer downstream of FCV is intermittent for 15 min in an hour. Flow rate required is around 8 Nm3/s (+/-10%). Pressure before FCV is important, should be above 13 barg, else auto closure.

Earlier someone commented that PCV's response should be 3 times faster than FCV, may be due to the reasons that "the PCV can react more slowly to the demand, with a total lag of several seconds".

The "3 times faster" that I mentioned is a rule of thumb. The loops have to have a different frequency response, or the system will oscillate. If the flow loop is faster, and the pressure drops, then the flow loop cannot compensate for the lack of pressure. If the pressure loop is faster, then it will supply the flow loop with the required pressure to operate properly.

GA & thanks Kilowatt0 for clarification. Can you please comment on some of the unanswered questions raised in this discussion.