Energy-saving VPSA system utilizing direct-drive high-speed centrifugal compressors

Abstract

The present invention relates to a method and system for improving the energy and capital efficiency of a VPSA plant by optimizing a directly driven variable speed centrifugal feed compressor, a vacuum compressor and / or a product compressor to achieve a lower unit gas product production cost. More specifically, the present invention relates to a new energy-efficient VPSA process and system that employs a high speed directly driven centrifugal compressor to achieve an expanded production range. By employing a compressor sized to meet average environmental and production needs, utilizing the speed and operating range of a directly driven variable high speed centrifugal compressor, significantly lower energy consumption can be achieved over the operating life of the equipment to meet the desired production needs. Since most equipment tends to operate at less than peak production for most of the equipment's operating life. In addition, smaller sized machines can provide equipment capital savings from the initial investment.

Description

Technical Field

[0001] The present invention generally relates to energy efficient gas separation methods and systems that utilize a direct drive variable speed centrifugal compressor to pressurize and / or evacuate an adsorption vessel and further pressurize product gas within an adsorption-type gas separation system. Background Art

[0002] Separation of gases from mixtures with other gases is an important industrial process. In such processes, the objective may be to obtain a product gas that is enhanced in the gas, or to remove undesirable components from that particular product gas. For example, there are commercial scale processes for separating air into its component gases to obtain nitrogen, oxygen and argon, as well as air pre-purification processes for pre-treating air before use in other processes such as cryogenic separation of air into its component gases.

[0003] Air separation can be achieved using adsorption methods, specifically pressure swing adsorption (PSA) and vacuum pressure swing adsorption (VPSA) type methods. In PSA and VPSA methods, compressed air is pumped through a fixed bed of adsorbents that exhibit an adsorption preference for one of the main components, thereby obtaining an enhanced effluent product stream in the non-adsorbed (or less adsorbed) component. Compared with more traditional cryogenic air separation methods, adsorption methods for air separation require relatively simple equipment and are relatively easy to maintain. However, adsorption methods generally have a lower product recovery rate than many cryogenic methods. For this reason, improvement of the efficiency of the adsorption process remains an important goal. A major improvement method is to discover and develop better adsorbents. Some such adsorbents cause cycle time reduction in a given adsorption process. Therefore, new equipment that can meet the demand for reducing cycle time is needed.

[0004] There is also a continuing need for PSA and VPSA equipment with lower power consumption. The basic process employs a selective adsorbent to remove at least one component of a gas mixture, which employs four basic process steps: (1) adsorption, (2) depressurization, (3) purging, and (4) repressurization. A gas mixture containing a more easily adsorbable component and a less easily adsorbable component is passed through at least one adsorbent bed that is capable of selectively adsorbing the more easily adsorbable component at a predetermined (upper limit) adsorption pressure. The gas stream leaving the bed at this upper limit pressure is now concentrated in the less easily adsorbable component and is removed, for example, as a product. When the bed becomes saturated with the more easily adsorbable component, the bed is then depressurized to a lower desorption pressure to desorb the more easily adsorbable component, and the gas is then discharged from the system. Some processes may include additional steps, such as equalization and product pressurization.

[0005] Conventional PSA and VPSA methods use rotary positive displacement blowers for gas pressurization or evacuation in adsorption beds. These conventional rotary leaf blowers generally have lower efficiency and higher maintenance costs than centrifugal compressors, but they are indeed very well adapted to the oscillating nature of the pressure swing cycle. The attractive feature of a rotary leaf blower suitable for adsorption processes is that the power consumption is proportional to the system pressure requirement. The theoretical power consumption of the blower is proportional to the system pressure difference (i.e., there is a linear relationship between power consumption and pressure). This linear power response to system pressure requirements has made rotary leaf blowers the compression equipment of choice for the PSA and VPSA industries. However, rotary leaf blowers generate strong pressure pulsations in the system. In the absence of proper mitigation, it is known that pressure pulses from rotary leaf blowers cause severe structural damage in downstream process equipment. Although pulsation damping vessels are typically used with rotary leaf blowers, they cannot completely eliminate mismatches, and there is always a considerable level of pressure pulsations in the system.

[0006] In the past, fixed speed centrifugal compressors, with and without inlet guide vanes (IGVs) and with variable frequency drives (VFDs), have been considered for PSA and VPSA processes because they have higher efficiencies when compared to conventional rotary lobe blowers. Centrifugal compressors typically need to be able to operate at high speeds and follow a highly dynamic variable pressure cycle while maintaining optimal efficiency to take advantage of high adiabatic machine efficiency. Variable speed control and / or IGVs, or a combination of both, must be employed to meet variable feed flow conditions. When the PSA or VPSA cycle pressure deviates from the design pressure condition of the fixed speed centrifugal compressor, the stage efficiency drops significantly, especially when operating at a pressure ratio close to 1 (blocking). This results in an increase in average power consumption and a decrease in the overall average compressor efficiency throughout the PSA or VPSA cycle.

[0007] However, this technology has not been successfully employed in the past. The use of conventional fixed speed centrifugal compressors with and without IGVs is not ideal because they cannot follow the faster ramps and ramps required for the cyclic pressure swing adsorption process. Conventional variable speed centrifugal compressors may have an improved operating range and improved energy savings and flow reduction compared to the use of IGVs, but cannot quickly adapt to the transient flow conditions of a PSA or VPSA cycle (due to the large inertia of the gears and the large, slow running conventional induction motors).

[0008] In recent years, PSA and VPSA methods have made several progresses. Some of these progresses include: (a) a significant reduction in the ratio of the top adsorption pressure to the bottom desorption pressure, and (b) a reduction in cycle time (usually less than one minute), resulting in a reduction in adsorbent inventory. An important factor in the total energy demand of a PSA or VPSA process is this ratio of adsorption pressure to desorption pressure. The delivery pressure during bed adsorption by a feed air compression device and the suction pressure during desorption by an evacuation device change continuously with the cycle. In order to achieve the lowest possible total power consumption for a cycle such as this, it is desirable that the feed compression device and the evacuation device operate at peak efficiency over a wide range of pressure ratios.

[0009] VPSA equipment is usually designed and sized to meet maximum production requirements under maximum ambient temperature conditions. However, due to changes in consumer demand and environmental conditions, VPSA equipment is usually operated below design capacity. Typical VPSA turndown operations are achieved by extending the cycle step time, but without changing the feed flow rate and the adsorption and desorption pressure ranges. In addition, a product recycle stream is also used to ensure machine operation. Therefore, VPSA operation is not as energy-efficient in turndown mode as at the design point. The purpose of the present invention is to improve the energy efficiency and capital efficiency of VPSA equipment by optimizing directly driven variable speed centrifugal feed compressors, vacuum compressors and product compressors, so as to minimize the initial equipment capital investment and achieve low unit production costs and lower overall energy efficiency during the life of the equipment. Summary of the invention

[0010] The present invention relates to a method and system for improving the energy and capital efficiency of a VPSA plant by optimizing a directly driven variable speed centrifugal feed compressor, a vacuum compressor and / or a product compressor to achieve a lower unit gas product production cost. More specifically, the present invention relates to a new energy-efficient VPSA process and system that employs a high speed directly driven centrifugal compressor to achieve an expanded production range. By employing a compressor sized to meet average environmental and production needs, utilizing the speed and operating range of a directly driven variable high speed centrifugal compressor, significantly lower energy consumption can be achieved over the operating life of the equipment to meet the desired production needs. Since most equipment tends to operate at less than peak production for most of the equipment's operating life. In addition, smaller sized machines can provide equipment capital savings from the initial investment. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 A typical VPSA apparatus is shown with three pieces of rotating equipment.

[0012] Figure 2 A compressor performance map is shown for an exemplary V30C compressor driven by a high speed motor and a VFD.

[0013] Figure 3 A compressor map of an oxygen product compressor is shown. DETAILED DESCRIPTION

[0014] Centrifugal technology is based on dynamic compression. In a dynamic compressor, gas such as air, oxygen, nitrogen and / or other gases are drawn between the blades of a rapidly rotating impeller and accelerated to high speed. The air is then discharged through a diffuser, where the kinetic energy is converted into static pressure. Most dynamic compressors are turbo compressors with axial or radial flow patterns and are designed for larger volume flows. The performance of a dynamic compressor is very dependent on environmental conditions, such as:

[0015] 1) Inlet temperature

[0016] 2) Inlet pressure

[0017] 3) Relative humidity (RH)

[0018] 4) Cooling water temperature

[0019] Lowering the air inlet temperature increases the air density, resulting in higher free exhaust volume (ACFM), higher compressor power consumption, and a higher available turndown range. Likewise, increasing the air inlet temperature decreases the air density, resulting in lower free exhaust volume (ACFM), lower compressor power consumption, and a lower available turndown range.

[0020] A decrease in inlet pressure will reduce the air density at the compressor inlet. Like higher temperatures, this will result in lower free discharge, lower power consumption, and less available turndown. And an increase in inlet pressure will increase the air density at the compressor inlet, resulting in higher free discharge, higher power consumption, and higher available turndown.

[0021] Adding water vapor to the air makes it humid and reduces the density of the air. This is because the molar mass of water is less than the molar mass of air. Therefore, an increase in relative humidity reduces flow and power, and a decrease in RH will increase flow and power.

[0022] Finally, cooling water temperature affects suction capacity, such that cooler water increases flow and power, and warmer water decreases flow and power.

[0023] VPSA equipment is typically designed and sized to meet maximum production requirements under conditions of maximum ambient temperature. However, due to changes in consumer demand and environmental conditions, VPSA equipment is typically operated at less than design capacity, thereby reducing the efficiency of the turndown operation. Contrary to the conventional design philosophy of sizing equipment to meet maximum capacity requirements under maximum ambient conditions, the present invention reduces equipment capital by designing VPSA equipment for average production requirements and environmental conditions, speeding up the machine when necessary to meet maximum capacity requirements. The variable speed compressor is suitable for achieving the required flow and pressure requirements to produce the average production requirements while maintaining optimal compressor efficiency. When the production requirements exceed the average production requirements, the compressor speed is increased to increase the flow to meet the production requirements. The average production requirements of the system typically range from about 50% to about 90% of the maximum design capacity requirements of the system at the highest ambient temperature. In another embodiment, the average production requirements of the system typically range from about 60 to about 90% of the maximum design capacity requirements of the system at the highest ambient temperature, about 70 to about 90% in another embodiment, and about 80% to about 90% in yet another embodiment.

[0024] The present invention relates more specifically to gas separation processes and systems, such as PSA or VPSA adsorption systems, which have at least one container containing at least one adsorption bed therein. The adsorption bed contains at least one adsorbent material. In some embodiments, at least one adsorption bed is cyclically pressurized by at least one feed compressor and sometimes evacuated by at least one vacuum compressor, wherein at least one feed compressor or at least one vacuum compressor is a centrifugal compressor driven by an associated high-speed induction motor designed for variable high-speed operation. In such embodiments, the compressor that is not a centrifugal compressor may be a rotary vane blower driven by an induction motor. In some embodiments of the present invention, the adsorption bed is cyclically pressurized by at least one feed centrifugal compressor driven by an associated high-speed induction variable speed motor, and evacuated by at least one vacuum centrifugal compressor driven by an associated high-speed induction variable speed motor. More specifically and in accordance with the present invention, the centrifugal feed compressor and / or the centrifugal vacuum compressor are driven by a high-speed induction motor driven by a direct drive for variable speed operation, so that the compressor and high-speed induction motor combination can accelerate from low speed to high speed and decelerate from high speed to low speed at a faster rate required for the shorter cycle time of the current PSA or VPSA system and method.

[0025] The use of a variable speed controlled high speed permanent magnet motor or induction motor allows an order of magnitude improvement in the ability to accelerate and slow down a centrifugal compressor in a PSA or VPSA process over a conventional low speed induction motor / gearbox system. The use of a high speed motor allows the elimination of the necessity of a gearbox and thus also the elimination of the necessity of a lubricating oil system. Thus, the centrifugal compressor can be carried on oil-free bearings. Furthermore, in some embodiments, it is expected that the efficiency of the drive system proposed by the present invention will be improved by more than 7 percentage points with the elimination of gear and bearing oil friction losses, lubricating oil system losses, and the ability to improve lead / lag power.

[0026] In order to achieve high efficiency for a centrifugal compressor, the compressor must be operated along a peak efficiency line. The peak efficiency line is a line drawn on a compressor performance map. As discussed herein, the compressor performance map (i.e., pressure ratios at various speeds relative to mass flow) is generated by the isentropic work coefficient at various speeds for a specific inlet temperature of the compressor. The peak efficiency line represents the locus of points corresponding to all peak efficiency points of the compressor operating curve at different speeds. By operating along the peak efficiency line, the compressor is able to operate in the most efficient mode in terms of its power consumption.

[0027] The performance map may also be in the form of a lookup table or reference table generated from the isentropic work coefficient.The performance map and resulting optimum efficiency line may be stored in a programmable logic controller (PLC) and integrated with the PSA and VPSA systems.

[0028] Using the design method of the present invention, one or more centrifugal compressors are sized for average product demand, where speed can be increased to meet higher capacity requirements. It is important to design the compressor impeller with a flat efficiency curve characteristic to minimize the reduction in efficiency when the machine is operated outside of design conditions.

[0029] As mentioned previously, VPSA units are typically designed to meet maximum production requirements, even though consumers typically require small amounts of oxygen production most of the time. Environmental conditions, temperature, and altitude can have a significant impact on VPSA unit production. With a direct-driven variable speed centrifugal compressor, the VPSA unit can be designed for average production requirements and environmental conditions using compressor speed, speeding up the machine when needed to meet maximum capacity requirements. This design approach provides financial and power savings compared to conventional design principles to meet maximum capacity requirements.

[0030] Although it should not be construed as limiting, the present invention is implemented in a PSA or VPSA adsorption process for separating a gas (e.g., air) into oxygen and nitrogen. Other gas separation processes that may benefit from the use of the present invention include, but are not limited to, PSA and VPSA separations involving the recovery of gases such as O2, N2, CO2, H2, Ar or He.

[0031] Using the V30C compressor as an example, it is possible to increase flow by about 50% at a constant pressure ratio while still maintaining high efficiency. If additional flow is required, the machine can be pushed further toward the throttle at the expense of efficiency. Of course, one needs to size the motor to have enough power to meet the increased flow.

[0032] like Figure 1 As shown, a VPSA plant typically has three pieces of rotating equipment. A feeder (22) provides air to the plant. Air is separated to produce oxygen. A vacuum machine (50) removes waste nitrogen from the plant. The product compressor (73) raises the pressure of oxygen from the plant to the supply pressure desired by the consumer. Typically, the feeder and vacuum machine are Roots-type rotary blowers. These machines operate at a fixed speed and the flow rate cannot be changed once installed. Therefore, once a VPSA is designed and built, the amount of oxygen produced cannot be increased. Typically, for single-stage compression, the product compressor is a reciprocating compressor or a fixed-speed centrifugal compressor. Similar to conventional feeders and vacuum machines, conventional product compressors, once selected and installed, cannot be adjusted to increase oxygen capacity. If less oxygen product is needed, the compressor will operate in a recirculation mode through a recirculation line (77) together with a recirculation control valve (75, 76), and the machine will consume the same amount of power as if it were producing 100% of capacity. In other words, capacity reduction will not generate any energy savings by the product compressor.

[0033] Using a centrifugal compressor with a high speed motor and VFD, a VPSA plant can be designed and the rotary gear can be selected to produce a certain amount of oxygen and also produce more oxygen by increasing the compressor speed when needed due to customer demand or changing environmental conditions. Higher capacity is achieved by increasing the speed of the compressor by adjusting the motor speed via the VFD. The three machines will need to be adjusted together, i.e., if the feed machine speed is increased to add more air to the plant, more vacuum capacity will be needed to remove the additional waste nitrogen and more product compressor capacity will be needed to handle the additional oxygen produced by the plant.

[0034] U.S. Patent Nos. 7,785,405 and 8,529,665 teach operating a centrifugal compressor with a high speed motor and VFD by adjusting the feed and vacuum machine speeds to maintain operation on a peak efficiency line as the VPSA pressure varies with the cycle. It is very important to operate along this peak efficiency line to capture the full power advantage of these machines. However, if additional oxygen is required due to changes in customer demand or environmental conditions, the operating line can be shifted toward throttling by increasing the speed of the compressor. The increase in speed is achieved by applying a multiplier to the calculated speed.

[0035] For a centrifugal product compressor with a high speed motor and VFD, unlike a feed and vacuum machine, the compressor will be operated at the compressor's design point (pressure, flow and speed). Similar to a feed and vacuum machine, the flow from this machine can be increased by increasing the speed while maintaining the same outlet pressure.

[0036] Figure 2 A compressor performance map is shown for an exemplary V30C compressor driven by a high speed motor and a VFD. The map was generated in accordance with the PTC-10 test protocol. The machine was operated at a constant speed. The flow and pressure were varied using a suction throttle as the machine moved from throttle to surge at said constant speed. Data points were collected using temperature, pressure and flow measurements to form a curve of flow to pressure ratio. The temperature measurements were used to determine the efficiency of the machine at each point along the curve and to determine the peak efficiency point for said speed. The test was repeated at various speeds from 40% to 110% of the compressor design speed to form a complete performance map.

[0037] The design point of the compressor is shown on the plot. The design point includes the flow, pressure ratio, and speed at which the compressor impeller is designed to operate to meet the process requirements. For a typical compressor utilizing a fixed speed motor and gearbox, the compressor operates at or near the design point. For a compressor driven by a high speed motor and VFD, the compressor can be operated across the plot, including at different speeds along the peak efficiency line. The compressor can also be operated at a higher flow at the same head by increasing the speed of the motor. This provides flexibility for a compressor that is designed for a specific flow and pressure, but operates at a higher flow if the process requirements change.

[0038] from Figure 2 , line 1 shows the peak efficiency point at all speeds. This includes the design point of the compressor and the line along which it is desired to operate the machine to maintain maximum efficiency. Figure 2 Line 2 in shows the higher flow operating line where the machine can be run to provide more flow to the process.

[0039] Traditionally, if customer demand or environmental conditions dictate a higher flow situation, the equipment and associated compression equipment are designed to produce the higher flow rate.Process turndowns would be used for normal operating situations or normal environmental conditions.

[0040] However, in the case of a direct-drive centrifugal compressor and a high-speed motor with a VFD, the equipment can be designed for normal (line 1) flow conditions and then turned up for higher flow conditions (line 2). Operating in this mode will use a smaller compressor and be lower capital. It can also run at lower power for average demand because a compressor designed for average flow is more efficient when operating at the design point than a larger compressor operating in a turned-down mode.

[0041] Figure 3 A compressor map for an oxygen product compressor is shown. The design point of the compressor is shown on the map. The design point includes the flow, pressure ratio and speed at which the wheel is designed to operate to meet the process requirements. For a typical compressor using a fixed speed motor and gearbox, the compressor operates at or near the design point. For a compressor driven by a high speed motor and VFD as described in the patent, the compressor can operate within the entire map range. The compressor can also be operated at a higher flow at the same head by increasing the speed of the motor. This provides flexibility for compressors that are designed for specific flows and pressures, but operate at higher flows if production requirements change.

[0042] With a traditional product compressor, the compressor will be designed to meet the highest customer demand or worst case ambient conditions. When demand is lower, the compressor flow to the customer is reduced by recycling the exhaust gas back into the inlet of the compressor. This uses the full power of the compressor as if it were at a higher flow. Therefore, even when product demand is reduced, the product compressor will always be running at peak power. With a centrifugal compressor with a high speed motor and VFD, the compressor can be sized for average flow or average ambient conditions, and then for higher demand or worst case ambient conditions, peak production can be achieved by increasing the compressor speed via the VFD to increase the motor speed. This concept is used in Figure 3 , where the compressor design point is shown. At this speed, the compressor will produce the flow rate under normal conditions. Then, for higher demands, the speed of the compressor is increased, which moves the compressor's operating point toward the right, producing more flow at the same pressure. This saves both capital and power, because a smaller compressor can be used to meet higher demands, and a compressor operating at the average design point uses less power than a larger compressor operating in recirculation mode.

[0043] The compressor capital and power impacts for an oxygen VPSA plant are shown in Tables 1 and 2 assuming an average production demand of 75% of peak demand.

[0044] Table 1: Conventional compressor capacity sized for peak demand relative to planned average demand Capital impact

[0045]

[0046] Table 2: Sizing of Roots and Centrifugal VPSAs based on peak demand relative to planned average demand Power comparison of conventional compressors

[0047]

[0048] From Tables 1 and 2, it is clear that a VPSA unit with a compressor sized for average production demand presents a capital advantage. For peak demand production, a machine sized for average conditions will consume slightly higher power because the machine will be operating at slightly less than peak efficiency. However, in the true unit operating window, the impact of the power increase will be minimal. Units designed for average demand will have great potential for energy savings over the unit’s operating life because most units will be operating below peak demand for most of the time.

[0049] A more energy-efficient alternative to using the proposed direct-drive high-speed centrifugal compressors is to size the compressors based on peak customer production demand. When customer production demand is below peak levels, the machines will operate in a less efficient turn-down mode.

[0050] An intermediate option would employ only direct-drive, high-speed permanent magnet or high-speed induction centrifugal compressors as product compressors, while using conventional positive displacement Roots-type blowers to pressurize and depressurize the adsorption vessels. The centrifugal product compressors could be sized for average demand, while the Roots-type blowers would need to be sized to meet peak customer production demands.

Claims

1. An adsorption system for gas separation, comprising: a. at least one container, said at least one container containing at least one adsorption bed, said adsorption bed comprising at least one adsorption material; b. at least one compressor configured to be driven by an associated motor comprising a direct drive high speed permanent magnet motor or a high speed induction motor designed for variable speed operation, wherein the at least one compressor comprises a product compressor to achieve a desired product pressure at average and peak production capacities, wherein the product compressor is a positive displacement compressor or a dynamic compressor; and c. means for receiving data signals of conditions in said system and for communicating with said high speed induction motor driving said at least one compressor in response to said conditions, enabling the at least one compressor to operate at a specified speed; d. wherein the at least one bed is configured to be cyclically pressurized and depressurized during operation, e. wherein the at least one compressor is sized to meet an average production requirement under ambient conditions of the system, wherein the average production requirement ranges from 50% to 90% of the maximum capacity requirement of the system at maximum ambient temperature; f. Wherein the speed and pressure ratio of the at least one compressor is increased when the product production demand exceeds the designed average production demand of the system.

2. The system of claim 1, wherein the at least one compressor is a reciprocating compressor, a screw compressor, a Roots compressor, or a centrifugal compressor.

3. The system of claim 2, wherein the at least one compressor is a centrifugal compressor, and the speed and pressure ratio of the at least one compressor can be increased to achieve the desired discharge product pressure and flow rate.

4. The system of claim 1, wherein the system is a PSA or VPSA system.

5. The system of claim 4, wherein the PSA or VPSA system is configured to recover at least one gas selected from the group consisting of: O2, N2, CO2, H2, Ar, or helium.

6. The system of claim 3, wherein the system is a dual-bed VPSA system comprising a feed centrifugal compressor and / or a vacuum centrifugal compressor, wherein each compressor is powered by an associated high-speed permanent magnet motor or a high-speed induction motor.

7. The system of claim 3, wherein the system is a dual-bed VPSA system including vacuum compressors, wherein at least one of the compressors is powered by an associated high-speed permanent magnet motor or a high-speed induction motor.

8. The system of claim 2, wherein the associated motor of the at least one centrifugal compressor is in communication with at least one associated variable frequency drive, and the at least one associated variable frequency drive is in communication with the means for receiving a data signal.

9. A system according to claim 6, wherein the associated motor of the at least one feed centrifugal compressor communicates with at least one associated variable frequency drive, and the at least one associated variable frequency drive communicates with the device for receiving data signals, and wherein the associated motor of the at least one vacuum centrifugal compressor communicates with at least one associated variable frequency drive, and the at least one associated variable frequency drive communicates with the device for receiving data signals.

10. The system of claim 2, wherein the conditions in the system include inlet and outlet pressures of the at least one centrifugal compressor and an inlet temperature of the at least one centrifugal compressor.

11. The system of claim 8 or 9, wherein the means for receiving a data signal is configured to determine a pressure ratio of the at least one centrifugal compressor.

12. A system according to claim 8 or 9, wherein the device for receiving a data signal transmits a speed of operation in response to a pressure ratio and an inlet temperature of the at least one centrifugal compressor to the high-speed permanent magnet motor or high-speed induction motor of the at least one centrifugal compressor during operation.

13. The system of claim 8 or 9, wherein the high-speed permanent magnet motor or high-speed induction motor is directly coupled to the at least one centrifugal compressor so that the at least one centrifugal compressor can operate at or near a predetermined efficiency line.

14. The system of claim 13, wherein the predetermined efficiency line is an optimum efficiency line represented by a locus of points corresponding to peak efficiency points of a compressor operating curve at different speeds and process conditions of the at least one centrifugal compressor.

15. The system of claim 11, wherein the pressure ratio is a ratio of an outlet pressure to an inlet pressure.

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