A Note on Compressor Stability and Control (1)

Variable Speed or Variable IGV?

I have encountered quite regularly with the question "which compressor control method is the best?" Surprisingly, there are some answers that absolutely refer to one of the methods (for example "Variable Speed" or "Variable IGV") failing to consider the application. This article (published by me on LinkedIn) is intended to briefly demonstrate why selecting compressor control method depends greatly on the application.

The article is available on LinkedIn via:

A Note on Compressor Stability and Control; Variable Speed or Variable IGV?

The PDF version can be accessed here:

Pump Off-Design Operation

Pump Off-Design Operation; a Review on Karassik's Paper

The well-known pump consulting engineer, Igor Karassik, has reviewed (in his 3-part paper) the issues encountered when a centrifugal pump is operating at flows other than BEP. Here is a brief review and summary of those.

It should be noted that with modern pump designs the limitation of pumps due to minimum flow is greatly improved but still these guidelines are helpful in understanding the concepts.

1. Motivation

Pump operating point is the intersection of its curve and system curve and can be changed by altering either one or both of these curves:

• Pump (head-capacity) curve is altered by variation of pump speed;
• System (resistance) curve is altered by throttling pump discharge.

Although pump is able to operate at either case as long as it is provided with adequate NPSHA, there are several issues associated with such an operation.

2. Operation at High Flows

This happens in two cases:

• An over-sized pump; pump curve may intersect system curve at a much greater capacity than required system flow; required capacity can be met by throttling back;
• A parallel operation of two pumps when one pump is taken out of service because of a decrease in demand; single operating pump curve may intersect system curve at a much higher capacity compared to required capacity and may reach pump run-out point.

In either case uncontrolled pump operation can lead to cavitation (if NPSHA is inadequate) and power consumption increase (for low specific speed pumps).

3. Operation at Low Flows

This is the case usually encountered when there is a reduction in process flow demand and can have several consequences:

• Operation at lower efficiency;
• Higher radial thrust hence higher load on radial bearing;
• Temperature rise of pumped liquid;
• Internal recirculation (both in suction and discharge);
• Higher power consumption (for high specific speed pumps);
• Pump becoming air-bound.

Pump final minimum flow can be determined considering all above-mentioned effects.

4. Radial Thrust

Operation of pump at flows other than BEP causes non uniform pressure profile around the impeller and this imposes a resultant radial force on shaft and bearing. Generally, radial thrust is a function of total head and impeller width and diameter. Below diagram shows that how changing the single volute design to modified concentric casing or double volute design helps reducing radial thrust at off-design operation.

Radial thrust in volute pumps

5. Temperature Rise

Operation of a pump at reduced flow will be with reduced efficiency. The difference between pump hydraulic power and diver power represents power losses within the pump (neglecting minor losses) which are converted into heat and transferred to the liquid. This causes the liquid temperature to rise and if the power losses are high (at very low flows) the temperature can reach very high values (even in excess of boiling temperature).

Rate of temperature rise can be predicted for shutoff conditions (with engineering estimations) using following formula:

In which "BHP₀" is brake horsepower at shutoff, "W_W" is net weight of liquid in pump [lb] and "C_W" is specific heat of liquid (1.0 for water).

If liquid is flowing through the pump, temperature rise at pump discharge can be calculated from:

In which "e" is pump efficiency. This formula can be used to draw temperature rise curve on pump performance curve. Below diagram presents such an example.

Centrifugal pump performance curve including temperature rise curve

6. Internal Recirculation

Recirculation at suction and discharge areas of impeller occurs at certain flows below BEP and causes a great increase in pressure pulsations. Internal recirculation at the suction is most frequently the cause of pump problems.

6.1. Suction Recirculation

Mechanism: Increasing impeller eye diameter (to reduce NPSHR) leads to lower entrance velocities. In turn, peripheral velocity of impeller at the eye is increased and at some capacity distortion of the velocity triangles causes the flow at the outer eye diameter to reverse and flow back out of the impeller.

Consequences: Very intense vortices are formed as a result of internal recirculation; with high velocities at the core, static pressure is significantly decreased locally. The consequences are intense cavitation, severe pressure pulsations, noise and damage to impeller material.

It should be noted that if NPSHR at the vortex (which is not possible to be calculated mathematically) does not exceed NPSHA, frequently no damage occurs by pump operation in recirculation zone.

Some Notes:

• Larger impeller eye diameter is equivalent to lower NPSHR, higher suction specific speed (N_ss or S) value and higher capacity at which recirculation takes place;

Safe operation zone for normal ("A") and high ("B") suction specific speed

• If damage to the impeller is at pressure side, it is caused by internal recirculation. Otherwise, damage at suction side is due to classic cavitation (caused by inadequate NPSHA);
• Trimming the impeller will move the best efficiency point to a lower flow value but will not reduce the flow at which suction recirculation will occur;
• Minimum flows for pumps handling hydrocarbons need not be selected as conservatively as for cold water pumps;
• Do not specify NPSHR values which result in suction specific speeds of above 9000 (for water) or 11000 (for hydrocarbons) [Again it is emphasized that such a consideration might not be critical with modern pump designs];
• The flow at which suction recirculation starts can be predicted as a function of  suction specific speed and hub-to-eye diameter ratio (h₁/D₁) using below curve:

Suction recirculation flow

6.2. Discharge Recirculation

Mechanism and Consequences: Like suction recirculation it causes hydraulic surge and local cavitation at the impeller tips. Another consequence of discharge recirculation is axial instability which is because of pressure fluctuations outside the impeller shrouds. This can cause a failure of ball thrust bearing (due to lower clearance).

Vane Passing Syndrome: discharge recirculation should not be confused with vane passing syndrome; a phenomenon caused by interaction between moving impeller tips and stationary volute tongues and diffuser vanes. A hydraulic shock occurs as impeller vanes pass the stationary parts. Shock wave magnitude (and the resulted pressure fluctuations) increases with impeller tip velocity and pump size and frequency is a multiple of pump speed and the number of impeller vanes.

Near the central part of the vane (at first stage) shock pressure is momentarily reducing local pressure to less than vapor pressure and causes cavitation erosion. Negative effects of vane passing syndrome can be eliminated by increasing the gap between vane tip and stationary part keeping in mind that too much a gap lowers pump efficiency. The minimum recommended gap is 4% to 6% of the impeller diameter.

6.3. Final Remarks on Internal Recirculation

Following tables present comparisons between classical cavitation and suction recirculation and also vane passing syndrome and discharge recirculation:

 

7. Power Consumption

Power consumption increases for a high specific speed pump as its flow is decreased. If the motor is not selected satisfying lower flow end of curve, it will be overloaded. On the other side, selecting a motor for 0% high specific speed pump flow is not economical and so a minimum allowable flow is dictated.

8. Entrained Air or Gas

Effect of entrained air or gas in the pump liquid on performance and minimum allowable pump flow is presented in below diagram.

 Effect of entrained air on pump performance

9. Minimum Flow By-Pass

If the pump is required to operate below its minimum permissible flow (because of process requirements) then a by-pass line should be installed from discharge line in pump side of check and gate valves. Normally it should not be led directly back to pump suction as there should be some means of heat dissipation.

It should be noted that if the minimum flow is established for reasons other than permissible temperature rise (such as internal recirculation) then it would be normally around 25% to 50% of design flow and temperature rise won't be significant and a major portion of the by-pass may be led back to the suction piping.

Reference: I. Karassik, 1987, "Centrifugal Pump Operation at Off-Design Conditions", Chemical Processing Magazine

Turboexpander Performance (2)

A Note on Turboexpander Aerodynamic Design

Turboexpander polytropic efficiency can be expressed as a function of its specific speed (as defined below):

In which N is turboexpander rotational shaft speed, Q₂ is turboexpander discharge flow and Δh is the ideal enthalpy reduction through the turboexpander.

Turboexpander polytropic efficiency is increased with the increase of its specific speed up to an optimum value. This trend suggests two methods to increase turboexpander efficiency (and hence its power generation):

1. Increasing turboexpander shaft speed (N);
2. Increasing turboexpander number of stages (or decreasing Δh).

Turboexpander shaft speed is limited by the capability of its hydrodynamic bearing. To increase the speed to values higher than this limit, magnetic bearings (with higher capital cost) have to be utilized. On the other hand, increasing the number of stages also means a higher capital cost. These costs need to be justified and balanced by the increase in turboexpander power generation capacity.

Following table shows simulation results for three different proposed turboexpander designs with the same process conditions. Results show that how turboexpander power generation is increased via either increasing number of stages or utilizing magnetic bearings (and therefore designing the turboexpander for higher shaft speeds).
 

Preliminary turboexpander aerodynamic design

 

Following points should be considered when optimizing turboexpander design using such an approach:

• Maximum allowable shaft speed (limited by hydrodynamic bearing) for the specific turboexpander process design conditions;
• Optimum specific speed value for the selected turboexpander design.

PS Contact me for more details on turboexpander design conditions, simulation and preliminary aerodynamic and mechanical designs.

Turboexpander Performance (1)

Turboexpander Design and Off-Design Performance

Turboexpanders are being widely applied in cryogenic and power recovery cycles. In both cases there exists a fluid that has to be expanded to meet the process requirements. This is based on high chilling effect of expansion process in a cryogenic cycle. An example of such an application is medium-sized natural gas liquefaction (or LNG) plants. In a power recovery cycle, there is an end user with a specific fluid pressure requirement and turboexpander duty is to reduce the pressure to match the demand. Gas pressure reduction stations at the inlet of cities or power plants are examples of such an application.

For both cycles, power generated by turboexpander shaft (either driving a compressor or generating electrical power through a generator) is considered as a by-product intending to increase the overall efficiency.

In most turboexpanders applications, inlet gas conditions (flow, temperature, pressure and molecular weight) are varying. This variation can be intense for gas pressure reduction stations supplying gas to household sector as natural gas demands is much higher in cold seasons of the year. As turboexpander efficiency (same as any other turbomachinery) is highly affected negatively when operating in off-design conditions it won't operate efficiently throughout a year if the process designer fails to select the optimum design conditions for turboexpander operation. This can be done only if the process designer is familiar enough with turboexpander off-design performance.

Turboexpander off-design performance can be predicted using efficiency correction factors:

In which C_Q, C_P, C_T and C_MW are correction factors due to deviation of flow, pressure, temperature and molecular weight with reference to design values respectively. Typical turboexpander efficiency correction factors are given in the below diagrams for constant speed operation of turboexpander (such as electrical power generation application). Similar curves exist for turboexpander variable speed operation (like compressor drive application). This factors and how they affect determining turboexpander design point are briefly discussed below.

 

Turboexpander efficiency correction curves

 [Source: Bloch, Soares, 2001, "Turboexpanders and Process Applications", Butterworth-Heinemann]

Flow:

Although flow correction curve is nearly symmetrical and either lower or higher flow causes the same reduction in turboexpander efficiency but lower flow means that lower power can be produced at turboexpander shaft. So turboexpander design flow should be determined such that as much as possible flow can be passed through it during the year.

If flow variation is too high that causes the turboexpander to operate at very low flows (and hence very low efficiency) in some months of the year, then it might be economically feasible to select two turboexpanders and operate only one (and keep one stand-by) in low-flow situation.

Pressure:

It can be seen from the diagram that the reduction in turboexpander efficiency is negligible with increase of pressure relative to design pressure. This leads to the conclusion that if lowest inlet gas pressure is selected as design pressure, then turboexpander will operate with maximum efficiency (from inlet pressure point of view) throughout the year.

Temperature:

Unlike flow and pressure, temperature is an inlet gas parameter that can be controlled. That is done via a pre-heater normally considered upstream of the turboexpander. The need for pre-heating arises from the above-mentioned chilling effect of gas expansion process in a turboexpander; this can cause gas to be chilled to lower than its allowable temperature and may result in droplet formation. So turboexpander inlet gas temperature is determined (by calculation) considering its discharge temperature to be minimum allowable gas temperature. This temperature then should be maintained by controlling gas pre-heater.

Molecular Weight:

Molecular weight is a function of gas composition and its design value should be based on average gas components mole percent.

It should be noted that the exact design conditions can be determined based on these guidelines with the help of an economic analysis considering turboexpander power generation and pre-heater required energy for a 1-year operation. This requires the simulation of turboexpander performance with inlet gas parameters variations taken into consideration.