CONTROLLING POSITIVE DISPLACEMENT PUMPS

INTRODUCTION. The positive displacement pump is in some ways an even simpler device to control than the centrifugal pump discussed previously. It has the same function, namely to provide the pressure necessary to move a liquid at the desired rate from point A to point B of the process. Figure 2-1 shows a 'generic' process with a positive displacement pump (in this case a gear pump) connected to deliver liquid from A to B.

There is a great variety of positive displacement pumps. They are divided into two broad categories: Rotary and reciprocating. From the controls point of view, however, they are all similar. Their characteristic curve is so simple that it is rarely drawn. It is essentially a straight vertical line, as shown in Figure 2-2. (For some reason PD pump curves are usually shown with the pressure and flow axis exchanged. I will not follow that convention in this article.) All are constant flow machines whose pressure rises to whatever value is necessary to put out the flow appropriate to the pump speed. If the discharge is blocked, the pressure will rise until something yields -- preferably a relief valve. Close examination of the curve shows a slight counter clockwise rotation. This is due to internal leakage.

For positive displacement pumps the major cause of leakage is the small amount of reverse flow that occurs before a check valve closes and possibly past the check valve after it is closed. Leakage past the piston is negligible. Diaphragm operated PD pumps have no cylinder to leak past. Rotating PD pumps, such as gear pumps or progressing cavity pumps have internal clearances which permit a small reverse flow, called "slip" or "blowby". There is another reason why the curve may rotate to slightly lower flows at higher discharge pressures: The driver may slow down as the load increases. None of these have a significant affect in curving the slope of the characteristic enough that this slope can be used for control. For most practical purposes the slope is vertical. The system curve of the process is also shown on Figure 2-2. Its intersection with the pump characteristic defines the operating point.

As always, the process controls engineer has the responsibility of matching the capacity of a specific piece of equipment to the demands of the process at every instant in time. Rarely does the actual system curve fall exactly on the one used for design and selection. As with any two port device, there are three locations in which a control valve can be placed: On the discharge, on the suction, and as a recycle valve.

DISCHARGE THROTTLING. Discharge throttling does not work! Looking at the process from the point of view of the pump, discharge throttling rotates the system curve counter clockwise so that the modified system curve intersects the pump curve higher up. The additional pressure is dropped through the valve so that the pressure and flow to the process is (almost) exactly the same as before. The "almost" is due the small increase in internal leakage that results in an equally small reduction in flow. An increased wear rate and a shortening of the life of the machine are the only results of this approach. If the pump is seen from the point of view of the process so that the valve is considered part of the pump, the same result is obtained. To obtain a modified pump characteristic curve, the pump curve must be rotated clockwise around the intersection with the pressure axis. The problem is that this hypothetical intersection is far off the top of the operating range. It is the point where the pressure is so high that 100% internal leakage occurs. The machine would self-destruct from excess pressure if one were stubborn enough to attempt to find this point. The rotation of the curve can still be performed on paper and it amounts to a slight shift to the left. Shown in Figure 2-3, it is virtually identical to the unmodified curve. To cut a long story short, you can't control a PD pump with discharge throttling.
 

SUCTION THROTTLING. Suction throttling has the same effect on the characteristic curve as discharge throttling and doesn't work either. PD pumps have a Net Positive Suction Head Required (NPSHR) just as centrifugal pumps do. In fact their requirements are even more stringent. Therefore restrictions and pressure drops in the suction lines must be similarly avoided.
 
 

RECYCLE CONTROL. This leaves recycle control as the only means of using a valve to control a PD pump. The valve is installed in a line teeing off from the discharge and leading back to the source of the liquid, possibly a surge tank. It must be fail open , of course. Figure 2-5 shows its effects on the characteristic curves. Viewing the process from the point of view of the pump, its effect is to rotate the system curve clockwise around its intersection with the pressure axis. Note that the little "tail" at the bottom left of the modified system curve is due to the flow through the recycle valve before the discharge check valve has opened. The flow through the pump is essentially as before but the pressure to the process has been reduced. Process flow will, of course, also be reduced by the amount flowing through the recycle line.

Viewing the pump from the process gives a different perspective on the same phenomenon. This time it is the pump curve that is rotated counter clockwise around its intersection with the flow axis. This modified pump curve gives the effect of greatly increased internal leakage. From the point of view of the process, this is exactly what is happening. Note that I have not used the same operating points in Figure 2-3 as I did in Figure 2-5. It is simply impossible to show any significant reduction in flow on a curve representing the effects of discharge throttling.

Recycle control is an efficient method of control for PD pumps. Since the flow rate is essentially constant, the power requirement is roughly proportional to discharge pressure. Since the effect of recycle is to drop the discharge pressure, it results in significant reductions in power requirement. Nevertheless there is still wasted power in proportion to discharge pressure times recycle flow.

Recycle valves experience rather severe service if the pressure drop is high. Cavitation will destroy them if they are not appropriately selected. Two approaches exist to deal with this problem: The first solution is to drop the pressure in many small stages through the use of many twists and turns in the valve trim. The second is to tolerate the resulting cavitation by shooting the liquid as a jet through a small hole in the middle of a disk. The jet then blasts directly into the discharge piping. The line diameter is often increased immediately downstream of the valve and the wall thickness is also increased. In this way the jet cavitates down the middle of the pipe. It makes a terrific racket.

In either case it may be necessary to put a fixed restriction downstream of the valve. It should be sized so that the ratio of the high to intermediate pressure is the same as the ratio of intermediate to low pressure. Keep in mind that the restriction will reduce the rangeability of the valve by making it act like a quick opening valve. This is because the restriction becomes the dominant factor in the line once the valve is about half way open. From that point on, the valve has little control.

Recycle lines for PD pumps should be run back to the suction vessel. This allows any entrained bubbles to escape. If they do not, they can build up to the point where pump capacity is impaired. It may even vapour lock.

SPEED CONTROL. Speed control is an obvious method of controlling the flow rate of PD pumps since flow is essentially proportional to speed. Pressure can also be controlled by sliding up and down the system curve. Any point on the system curve can, in theory, be reached. Most drivers, however, have low speed limits which limit the turndown of the system.

Variable speed electric motors are somewhat modified versions of normal motors. They require special provision for cooling and lubrication at low speed. In addition, they require specialized electronic power supplies called "invertors". These units provide power of the appropriate frequency and voltage. They are, unfortunately, still quite expensive and do not have the reliability of control valves. There is another reason why large variable speed electric drives are seldom used with reciprocating pumps. The large inertia of the system means that speed changes cannot be made quickly. If it is possible for a valve in the process side to close suddenly, a variable speed electric cannot reduce speed fast enough to prevent a severe pressure rise. A recycle valve will be required to protect the pump, as detailed below in the section on machine protection. A more simple type of electronic control is frequently used for small chemical injection pumps.

OTHER MEANS OF CONTROL. The great variety of types of PD pumps results in a variety of specialized means of flow control. A pneumatic actuator may be used to vary the geometry of the crank arrangement of a reciprocating pump so that each cycle displaces a greater or lesser amount of cylinder volume. Direct acting diaphragm pumps driven by compressed air or some other gas can be controlled by regulating the gas supply. There is also a technique known as "lost motion" whereby the crank arrangement first compresses a spring or volume pocket before it begins to work on the piston or diaphragm. These specialized methods are usually integral parts of the equipment and the controls engineer simply connects a pneumatic or milliamp signal to the appropriate input port. None of these methods changes the essentially constant flow nature of the pump curve. (The flow is still "constant" but at a different value.)

The efficiency of hydraulic or eddy current couplings is about the same as that of recycle control. This is because the torque on both sides of the coupling is proportional to D P. The power lost in the coupling will be proportional to torque times the reduction in speed. In other words, all unused power is being dumped. If the pressure does drop with a reduction in net discharge flow, then there will be a power savings. A valve is a cheaper way of accomplishing the same thing.

"Stroke Counting" is a method used when fixed amounts of liquid must be injected at specific intervals such as in batch processes. An electronic device is used to count the number of revolutions of a PD pump. After a sufficient number has been counted, the pump is shut off. When this method is used for pH control, the correct number of strokes can be calculated from a titration curve.

MEASUREMENT. The most common application for PD pumps is in high-pressure service. The flow rates vary from extremely small to moderately large. Pressure control is very common. Since the control valve tees off the discharge header, it is not significant where the sensing transmitter is placed. Keep in mind that the discharge will be pulsating. The pulsations may be relatively small for a rotary pump or they may be extremely large for a simplex (single cylinder) reciprocating pump. The degree of pulsation also depends on the effectiveness of the hydraulic pulsation dampeners that are often supplied with the pumps. If pressure or flow control is critical, the control systems engineer should encourage the biggest economical discharge dampeners. Small pulsation dampeners, called snubbers, should be installed on all instrumentation such as pressure gauges, switches and transmitters. This will extend their life as well as improve the signal. Many transmitters have built-in adjustable electronic damping. These should be adjusted so that the time constant is approximately twice the period of the expected pulses at the lowest speed. The phenomenon known as "aliasing" makes digital control systems such as a distributed control system (DCS) especially sensitive to pulsations. Aliasing can be best explained with the help of a diagram as shown in Figure 2-7. The rippling curve shows the actual flow rate of the discharge as it varies with time. The Xs show the points at which the DCS samples the measurement. The DCS gets the totally misleading impression that the system flow is slowly rising even if the average is quite constant. The usual reading the DCS gets is one of totally random fluctuations. Analog damping, either hydraulic or electronic, is absolutely essential for digital control. It prevents aliasing by filtering out high frequency components before they are sampled.

Flow control measurements have similar problems to pressure measurements. An additional problem arises in the case of an orifice plate or similar head type measuring system. Since the D P varies with the square of flow rate and it is the D P that is averaged, the resulting signal is not the average of the flow rate. Rather it is the square root of the average of the square of the flow rate. (Electrical engineers recognize this as the RMS -- root mean square.) As long as the shape of the pressure signal, over time, does not change, flow will be proportional to, but not equal to, root D P. The more cylinders in the pump, the smoother the waveform will be and the closer the measured to the actual reading. Discharge pulsation dampeners also help considerably. The measured flow on "ideal" (undamped, pure sinusoidal flow waveform) simplex and duplex pumps is 11% higher than the actual flow. An "ideal" triplex pump yields a measurement that is 1% high.

Flow measurements on the discharge of high pressure pumps should be avoided. This may not be possible if the pump has a recycle loop that returns, as it should, to the suction vessel. In that case remember that the flow sensor will experience not only high pressure but also a high level of pulsation. Turbine meters are easily damaged. I am told that coriolis-type mass flow meters do well in this service.

Certain classes of reciprocating pumps, known as metering pumps, have a very precise volume of liquid delivered with each stroke. The RPM of the pump can be used as an accurate flow measurement. However, individual calibration is required if this accuracy is to be realized. Note that even small amounts of entrained air or other bubbles can cause serious errors. Metering pumps are commonly applied for chemical injection. There is a simple way to calibrate them if extreme accuracy under varying conditions isn't an issue. A large glass cylinder is teed into the suction piping. If a valve between the cylinder and the supply is closed, the time it takes the pump to draw down the level by a fixed volume can be used to calculate a flow rate. The cylinder also serves as a level gauge to a supply tank. In some applications the fact that the pump is capable of developing high pressure isn't even an issue. It may be metering directly into an open tank or a low pressure line. In such cases the pump may need a back pressure valve on the discharge to ensure that the check valves seat properly. This item is usually supplied by the vendor as part of the pump package.

PD pumps are not generally used for level control in the process industries. The great variety of types of PD pumps invariably provides exceptions to every generalization. The direct acting, pneumatically powered diaphragm pump is one of these exceptions. It is ideal for sumps containing sludges. The pump can be controlled by an entirely pneumatic control system thus eliminating all electrical connections. This has the added advantage of being absolutely safe in hazardous locations.