Patent Publication Number: US-8540498-B2

Title: Compressor-expander set critical speed avoidance

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a Divisional of U.S. Ser. No. 12/047,938 filed Mar. 13, 2008, now U.S. Pat. No. 8,360,744 issued Jan. 29, 2013, entitled COMPRESSOR-EXPANDER SET CRITICAL SPEED AVOIDANCE and is hereby incorporated by reference herein in its entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates generally to a control scheme. More particularly the present invention relates to a method and apparatus for limiting a time of operation in a critical speed zone of turbomachinery. This invention also relates to an antisurge scheme for a recycle compressor when a compressor-expander set trips. 
     2. Background Art 
     Most turbomachines, such as compressors, gas turbines, steam turbines, and expanders inherently exhibit at least one critical speed where the rotational speed of the turbomachine excites a natural frequency of the turbomachine. Extended operation at such critical speeds must necessarily be avoided. 
     When the critical speed or speeds reside below the normal operating region of the turbomachine, a startup procedure involving high angular accelerations through the critical speed or speeds is carried out, thus minimizing the time of operation in a neighborhood of the critical speed or speeds. This neighborhood around a critical angular or rotational speed is known as a “critical rotational speed zone,” and is thus defined for the purposes of this application, including the claims. Critical speed zones for a particular turbomachine are disclosed by the turbomachine manufacturer. 
     Critical speed zones residing within the normal operating speed range of a particular turbomachine are less common than those residing outside this normal operating speed range. 
     An improved cryogenic process for liquefying natural gas is disclosed in U.S. Pat. No. 6,308,531 by Roberts et al., and is hereby incorporated in its entirety by reference. The process is also described in a paper presented at the 2007 LNG 14 conference. The title of this paper is “Technical Challenges during the Engineering Phases of the Qatargas II Large LNG Trains” by Chavez et al., which is also hereby incorporated in its entirety by reference. The improved process includes a gas refrigeration cycle using nitrogen for a refrigerant. As is well known to those of ordinary skill in this art, a gas refrigeration cycle makes use of a compressor and an expander or turbine. The expander is used to drop the pressure of the gas, but also serves to extract energy from the refrigerant via shaft power. Shaft power derived from the expander is used to provide at least a portion of the required refrigerant compressor power. Gas refrigeration cycles are covered in many undergraduate thermodynamics textbooks such as  Fundamentals of Engineering Thermodynamics  6 th  ed. by Moran and Shapiro, John Wiley &amp; Sons, Inc., publishers, ISBN-13: 978-0471-78735-8 which is hereby incorporated in its entirety by reference. 
     The gas refrigeration cycle used for producing Liquid Natural Gas (LNG) in the Roberts et al. process is a regenerative cycle. That is, a heat exchanger is used to cool the high pressure stream upstream of the expander using the relatively cold low pressure stream downstream of the cooling load. 
     A departure from text-book gas refrigeration cycles in the Roberts et al. LNG application is the use of a first compressor, driven by the expander, and a second compressor driven by a separate driver. Because of the energy provided by the second compressor to the gas stream, the expander produces sufficient power to fully drive the first compressor. 
     The gas refrigeration cycle of the Roberts et al. LNG process is the coldest of a plurality of cascaded refrigeration cycles. Hence, the gas refrigeration cycle is used to subcool the liquid natural gas below its saturation temperature. 
     Typically, a plurality of gas refrigeration cycles, arranged in parallel, is used in the LNG process. The compressors in the compressor-expander sets may be operated using a load-sharing algorithm such as those disclosed in U.S. Pat. No. 5,743,715 to Staroselsky et al., which is hereby incorporated in its entirety by reference. 
     Turbocompressors generally experience unstable operation at low flow rates. The instability takes the form of either stall or surge, with surge being the most common for industrial compressors. In surge, the flow through the compressor suddenly reverses direction. This results in large thrust loads that can damage thrust bearings and cause vanes to contact the compressor shroud. Relatively hot gases from the discharge side of the compressor are drawn back into the compressor where more energy is added from the rotor, increasing the gas temperature even more. Repeated surge is to be avoided. Surge control algorithms are described in the Compressor Controls Series 5 Antisurge Control Application Manual . . . Publication UM5411 rev. 2.8.0 December 2007, herein incorporated in its entirety by reference. 
     A control system for the refrigeration processes in the Roberts et al. LNG process is needed. A challenging aspect for this control system is avoidance of critical speeds for the compressor-expander sets used in the gas refrigeration loop. These compressor-expander sets typically have a plurality of critical speed zones, some of which reside within the normal operating speed range of the compressor-expander sets. Extended operation in these critical speed zones must be avoided, but the gas refrigeration process must not be disrupted. 
     When a compressor-expander set trips or is shut down for any reason, including that of residing too long in a critical rotational speed zone, the second compressor, driven by a separate driver, may be pushed toward surge. 
     There is, therefore, a need for an improved control system for a compressor-expander set. 
     BRIEF SUMMARY OF THE INVENTION 
     A purpose of the present invention is to provide a method and apparatus for avoiding operating a compressor-expander set in a critical speed zone longer than a predetermined time while maintaining the process at its set point or set points. 
     The following description assumes a gas refrigeration cycle wherein the refrigerant is nitrogen, a representative process in which a compressor-expander set is used. The instant control method and apparatus is by no means limited to gas refrigeration cycles or to a particular fluid used in the system. 
     Most often, a plurality of compressor-expander sets is provided to produce the nitrogen mass flow rate needed to subcool the natural gas feed stock. 
     The expander in each compressor-expander set is constructed with variable geometry, often adjustable nozzles. The position of the adjustable nozzles is the manipulated variable used to maintain the total nitrogen mass flow rate at a desired set point. The rotational, or angular, speed of the compressor-expander set varies based on the refrigeration load. 
     While the adjustable nozzles of the plurality of expanders are collectively manipulated to maintain the total mass flow rate, each individual compressor-expander set may be operated at a rotational speed providing a desired operating condition of the compressor. In particular, it is usually undesirable for one compressor to be operating on its surge control line while another compressor is operating away from its surge control line. It is almost always less efficient for one compressor to require recycle to avoid surge when another is not recycling compared to increasing the low-flow compressor&#39;s flow rate so no recycle is needed while decreasing the high-flow compressor&#39;s flow rate as long as that reduction does not result in recycle. 
     Therefore, the instant invention calls for manipulation of the expanders&#39; adjustable nozzles to cause the operating points of the compressors to reach their surge control lines simultaneously. Once recycle begins, recycle flow rate or recycle valve opening may be used to balance the operation of the compressors. 
     The compressor in each compressor-expander set is outfitted with a recycle or antisurge valve. When the recycle valve is opened, gas is permitted to travel from the high pressure discharge side of the compressor to the low pressure suction side through the valve, thus increasing the flow rate through the compressor. The recycle valve is used as the manipulated variable by an antisurge control system to avoid operation in the compressor&#39;s unstable surge region. 
     For most centrifugal compressors over most of the operating range, increased flow rate corresponds to increased power required to drive the compressor. Accordingly, when the recycle valve is opened, the power needed to drive the compressors increases. Even when increased flow rate results in reduced power requirement, such as is common for axial compressors, opening the recycle valve results in a change (a decrease) in power required. Therefore, the recycle valve can be used to predictably vary the rotational speed of the compressor-expander set, even while the expander mass flow rate is maintained at a constant value. 
     A novel use of the compressor&#39;s recycle valve is that of critical speed zone avoidance. If a compressor-expander set enters one of its critical speed zones, the automatic control system will open the compressor&#39;s recycle valve to increase the compressor&#39;s flow rate, usually slowing the rotational speed of the compressor-expander set out of its critical speed zone. 
     An additional object of this invention is the use of a feed-forward signal to signal the nitrogen recycle compressor&#39;s control system of a compressor-expander set trip. 
     That is, if a compressor-expander goes into shutdown expectedly or unexpectedly, the nitrogen recycle compressor may be driven toward surge. By signaling the nitrogen recycle compressor&#39;s control system to open the nitrogen recycle compressor&#39;s recycle valve, surge of the nitrogen recycle compressor can be avoided. 
     The novel features which are believed to be characteristic of this invention, both as to its organization and method of operation together with further objectives and advantages thereto, will be better understood from the following description considered in connection with the accompanying drawings in which a presently preferred embodiment of the invention is illustrated by way of example. It is to be expressly understood however, that the drawings are for the purpose of illustration and description only and not intended as a definition of the limits of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         FIG. 1  is a simplified schematic of a portion of a LNG refrigeration system; 
         FIG. 2   a  is a detail schematic of the gas refrigeration cycle; 
         FIG. 2   b  shows a temperature-entropy diagram for the gas refrigeration cycle; 
         FIG. 3  is a detail schematic of the gas refrigeration cycle with instrumentation used in the LNG process; 
         FIG. 4  is a schematic of a LNG refrigeration system comprising a plurality of gas refrigeration compressor-expander sets, each communicating with its own heat exchanger; 
         FIG. 5  is a schematic of a LNG refrigeration system comprising a plurality of gas refrigeration compressor-expander sets, all communicating with a common heat exchanger; 
         FIG. 6   a  is a flow diagram representing a mass flow control system; 
         FIG. 6   b  is a flow diagram representing load sharing and load balancing control; 
         FIG. 7   a  is a flow diagram for critical speed avoidance; 
         FIG. 7   b  is a detail flow diagram of a shutdown sequence; 
         FIG. 8  is a schematic of a preferred gas refrigeration system for subcooling liquid natural gas; 
         FIG. 9  is a compressor performance map for the main compressor in pressure ratio versus flow coordinates; 
         FIG. 10  is a compressor performance map for the main compressor in power versus flow coordinates; 
         FIG. 11  is a compressor performance map for the balance compressor in pressure ratio versus flow coordinates; and 
         FIG. 12  is a compressor performance map for the balance compressor in power versus flow coordinates. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to  FIG. 1 , feed stock  100 , for this example, natural gas, is first dehydrated (not shown) and the heavy components removed (not shown). A relatively high temperature cooling loop  105  (or plurality of loops) such as a propane refrigeration loop, is used to lower the temperature of the gaseous feedstock  100  in a high temperature heat exchanger  110 . 
     The feedstock  100  then enters a main heat exchanger  115 , where the remainder of the sensible heat is removed, and at least some of the latent heat is also removed from the feedstock  100 . The feedstock  100  is further cooled in a subcooling heat exchanger  120  where the temperature of the feedstock  100  is lowered below the saturation temperature. At this point, with very little additional processing, the pressure of the liquid natural gas is dropped and the LNG stream is directed to storage. 
     The refrigeration loop providing the low temperature stream in the main heat exchanger  115  is often a mixed refrigerant (MR) refrigeration system. Two stages of compression  125  in series, each compression stage  125  with its own driver  130  are shown in the schematic of  FIG. 1 . Typical drivers  130  include gas turbines and steam turbines. Although typical, the depicted arrangement is not universal. Heat is rejected to the ambient (air or water) by two ambient MR heat exchangers  135 . Cooling of the MR to a lower temperature occurs in the high temperature heat exchanger  110 . 
     The cold MR stream is passed through the main heat exchanger  115  where heat is transferred from the feedstock  100  stream to the MR stream. 
     Cascaded with the MR refrigeration loop is at least one gas refrigeration loop  140 . The refrigerant in a typical gas refrigeration loop  140  for LNG production is pure nitrogen (N 2 ). A nitrogen recycle compressor  145  is driven by a driver  150 , such as a gas turbine. The rotational speed of the nitrogen recycle compressor  145  is typically variable. Referring now to  FIGS. 2   a  and  2   b , as well as  FIG. 1 , the nitrogen recycle compressor  145  brings the pressure of the nitrogen refrigerant from its lowest pressure [state (1)] to an intermediate pressure [state (2)], where heat is rejected from the nitrogen stream to the ambient in a first nitrogen ambient heat exchanger  155 . The pressure, p, tends to drop from state (2) to state (3), through the first nitrogen ambient heat exchanger  155  as seen in  FIG. 2   b  where the dotted curves represent constant pressure curves. Additionally, the temperature, T, decreases and entropy, s, is transferred out of the nitrogen stream with the heat. 
     From the outlet [state (3)] of the first nitrogen ambient heat exchanger  155 , the nitrogen refrigerant passes through the compressor  160  in the compressor-expander set  165 , where the pressure of the nitrogen stream is increased to its greatest value [state (4)]. 
     The nitrogen stream then passes through a second nitrogen ambient heat exchanger  170  [state (4) to state (5)]. Here the pressure again drops slightly, the temperature, T, decreases, and entropy, s, is transferred out of the stream with the heat, all depicted in  FIG. 2   b . More heat and entropy are transferred out of the nitrogen in a regenerative heat exchanger  175 . The heat transferred out of the stream from state (5) to state (6) enters the relatively lower temperature stream from state (8) to state (1). Note, again, in  FIG. 2   b , the temperature, T, pressure, p, and entropy, s, all decrease in the regenerative heat exchanger  175  from state (5) to state (6). 
     The nitrogen stream is expanded from state (6) to state (7) in the expander  180  of the compressor-expander set  165 . As shown, the expander  180  is outfitted with adjustable nozzles  210 . At the discharge of the expander  180  [state (7)], the temperature reaches its lowest value, as clearly seen in  FIG. 2   b.    
     The subcooling heat exchanger  120  is encountered next, where the nitrogen stream passes from state (7) to state (8), gaining heat and entropy from the feedstock  100  stream. The temperature, T, of the nitrogen stream increases from state (7) to state (8), while the pressure, p, decreases due to friction. 
     Due to the relatively low temperature, T, of the nitrogen stream at state (8), the stream can be used in the regenerative heat exchanger  175  to reduce the temperature of the nitrogen stream from state (5) to state (6). The nitrogen stream entering the regenerative heat exchanger at state (8) exits at state (1). The process from state (8) to state (1) involves an increase in heat, entropy, s, and temperature, T, and a decrease in pressure, p. 
     In  FIG. 3 , details of a control system are included, along with the refrigeration equipment shown in  FIGS. 1 and 2   a . Recycle, or antisurge, valves  300 ,  305  are provided for the nitrogen recycle compressor  145  and the compressor  160  of the compressor-expander set  165 , respectively. The recycle valves  300 ,  305  are used to vary the flow rate of the nitrogen through these compressors  145 ,  165 . Surge avoidance in the nitrogen recycle compressor  145  is effected by the manipulation of the first recycle valve  300 . In the compressor of the compressor-expander set, antisurge control is effected through the manipulation of the second recycle valve  305 . 
     In a typical LNG process, measured data are displayed, used for alarms, and for automatic control. Some of the transmitters used for the recycle compressor  145  include: a flow transmitter, FT 1   310 , a suction pressure transmitter, PT 1   315 , a discharge pressure transmitter, PT 2   320 , and a rotational speed transmitter, SE 1   480 . The flow transmitter, FT 1   310  is shown on the suction side of the recycle compressor  145  in  FIG. 3 , but the present invention is not limited thereto. 
     Signals from the recycle compressor flow transmitter, FT 1   310 , suction pressure transmitter, PT 1   315 , and discharge pressure transmitter, PT 2   320  are read into an antisurge control system, A/S PID  01   330 , where an automatic control algorithm, preferably a Proportional, Integral, Differential (PID) algorithm, is used to keep the recycle compressor from surging. The recycle compressor recycle valve  300  is manipulated by the antisurge control system, A/S PID  01   330 . 
     Some of the transmitters used for the compressor  160  of the compressor-expander set  165  include: a flow transmitter, FT 2   330 , a suction pressure transmitter, FT 3   335 , a discharge pressure transmitter, FT 4   340 , and a rotational speed transmitter, SE 2   345 . 
     The flow transmitter, FT 2   330  is shown on the discharge side of the compressor  160  in  FIG. 3 , but the present invention is not limited thereto. 
     Signals from the compressor-expander set compressor flow transmitter, FT 2   330 , suction pressure transmitter, PT 3   335 , discharge pressure transmitter, PT 4   340  are read into a second antisurge control system, A/S PID  02   350 , where an automatic control algorithm is used to keep the recycle compressor from surging. The compressor-expander set compressor recycle valve  305  is manipulated by the antisurge control system, A/S PID  02   350 . 
     Note that redundant transmitters are not shown in  FIG. 3 . However, redundant transmitters are common in LNG processes. 
     A single compressor-expander set  165  is shown in each of  FIGS. 1 ,  2   a  and  3 . Usually, however, multiple compressor-expander sets  165  are provided and often arranged in parallel, serviced by a single nitrogen recycle compressor  145  as shown in  FIGS. 4 and 5 . In  FIGS. 4 and 5 , four (4) compressor-expander sets  165 ,  410 ,  420 ,  430 , are shown operating in parallel with one another. In  FIG. 4  each compressor-expander set  165 ,  410 ,  420 ,  430  is associated with its own subcooling heat exchanger  120 . The plurality of subcooling heat exchangers  120  are arranged in series on the LNG side, thus energy is removed from the product  100  consecutively in each of the subcooling heat exchangers  120 . All the compressor-expander sets  165 ,  410 ,  420 ,  430  share a single subcooling heat exchanger  120  in  FIG. 5 . The present invention is not limited to either of these subcooling heat exchanger arrangements. 
     The sum of the mass flow rates of the nitrogen in all the compressor-expander sets  165 ,  410 ,  420 ,  430  is determined using the signals received from the flow transmitter, FT 3   440 , the pressure transmitter, PT 5   450 , and the temperature transmitter, TT 1   460 . 
     The nitrogen is always superheated at the position of these transmitters, so the pressure and temperature are independent thermodynamic properties. Hence, the density, ρ, of the nitrogen gas may be evaluated as ρ=ρ(p,T) and the mass flow rate, {dot over (m)}, is obtained by:
 
 {dot over (m)}=ρQ=A√{square root over (ρΔp)} 
 
where A is a constant associated with a differential pressure flow meter and Δp is the signal received from the flow transmitter  440 . The resulting mass flow rate, {dot over (m)}, is used in an automatic control algorithm such as a PID loop as shown in  FIG. 6   a.  
 
     Referring to  FIG. 6   a , the raw signals from the transmitters  440 ,  450 ,  460  may need to be scaled and an offset accommodated as shown in blocks  610  to obtain actual values of pressure differential, Δp, pressure, p, and temperature, T. 
     The pressure, p, and temperature, T, values are used in the function block  620  for calculating the density, ρ, of the nitrogen as a function of pressure, p, and temperature, T. 
     A first product block  630  is used to calculate the product of the pressure differential, Δp, and density, ρ. Then the square root of the product is found in the square root block  640 . 
     A second product block  650  resolves the product of the square root of the product of the pressure differential, Δp, and density, ρ and the constant, A  660 . The result of the second product block  650  is the calculated mass flow rate, {dot over (m)}, of the nitrogen. The mass flow rate, {dot over (m)}, is used as the process variable in the mass flow rate PID loop  670 . The set point  680  is preferably provided by a supervisory or optimizing control system, but also may be entered by an operator or field engineer. The output of the mass flow rate PID loop  670  is directed to the adjustable nozzles  210  of one or more of the expanders  180  in the compressor-expander sets  165 ,  410 ,  420 ,  430 . 
     In  FIG. 6   b , the transmitters associated with the main compressor: flow transmitter, FT 2   330 , suction pressure transmitter PT 3 ,  335 , and discharge pressure transmitter PT 4 ,  340  may need to be scaled and an offset accommodated as shown in blocks  610  to obtain actual values of pressure differential, Δp, suction pressure, p s , and discharge pressure, p d . 
     In a first division block  615 , the pressure differential, Δp, and the suction pressure, p s , are combined to produce a dimensionless flow parameter denoted here as q 2 . In a second division block  625 , the discharge pressure, p d , and the suction pressure, p s , are combined to produce a dimensionless pressure ratio denoted here as R c . 
     The values of q 2  and R c  are combined to produce a measure of proximity to a surge control line, S s , in a function block  635 . 
     An identical process is carried out, using sensors and transmitters associated with the balance compressor, to calculate a measure of proximity to a surge control line, S s , for the balance compressor as indicated by the S s,balance  block  645 . The two values of proximity to the surge control line, S s,main , and S s,balance  are used in the respective antisurge control systems to protect these two compressors from surge. These same values may be used by a load sharing and balancing control system, whereby the rotational speeds of the respective compressors are manipulated via the expander adjustable nozzles  210 . The overall performance of the combined system is controlled by the mass flow rate PID loop  670 , which maintains the mass flow rate at its set point. 
     A flow diagram outlining the critical speed avoidance algorithm is shown in  FIG. 7   a . A rotational speed transmitter  470  is provided to each of the compressor-expander sets  165 ,  410 ,  420 ,  430 . The critical speed avoidance control system receives a rotational speed signal, N, from the rotational speed transmitter  470 . A test is made in a first comparator block  705  to determine if the rotational speed signal, N, resides between the low boundary CS 1  and the high boundary CS 2  of the critical speed zone, and therefore indicates critical speed avoidance is needed. If the result of the first comparator block  705  is false, a timer is set to t=0 in timer set block  710  and the rotational speed, N, continues to be monitored. 
     The first instance the result of the first comparator block  705  is true, the timer is initiated  715 . Any time the result of the first comparator block  705  is true, the time reported by the timer is compared to a predetermined maximum time, t max , the compressor-expander set  410  will be permitted to operate in the critical speed zone. This operation is carried out in block  720 . If the maximum time, t max , time has been exceeded, the control system will initiate an orderly shutdown of the compressor expander set  410  as shown in shutdown block  725 . As long as the maximum time limit, t max , has not been exceeded, a determination is made in a second comparator block  730  whether the compressor-expander set  410  rotational speed, N, is less than the minimum operational speed—and is therefore in startup mode. If the result of the second comparator block  730  is true, the recycle valve  305  associated with the compressor  160  in the compressor-expander set  410  is ramped closed  735  at a predetermined ramp rate  740  until either of the results of the first comparator block  705  or the second comparator block  730  is false. It should be noted that, typically, the recycle valve  305  is held open on startup. 
     If the result of the second comparator block  730  is false when the result of the first comparator block  705  is true, it is concluded the compressor-expander set  410  rotational speed, N, is within the normal operating range. In this case, the recycle valve  305  is ramped open  745  at a predetermined ramp rate  750  until the result of the first comparator block  705  is false. 
     The shutdown block  725  is expanded in a representative shutdown procedure in  FIG. 7   b . Such a procedure is used regardless of the reason for the shutdown. As those of ordinary skill in this art are well aware, a shutdown may be planned in advance, or it may be an emergency shutdown due to a sensed condition demanding immediate shutdown. 
     Referring now to  FIG. 7   b , to keep the nitrogen recycle compressor  145  from surging upon a trip of one of the compressor-expander sets  165 ,  410 ,  420 ,  430 , a feedforward signal is provided to the nitrogen recycle compressor&#39;s control system, A/S PID  01 ,  330 . 
     This step is shown in feedforward block  755 . The nitrogen recycle compressor&#39;s control system  330  will act to increase the opening of the nitrogen recycle compressor&#39;s antisurge valve  300 , as shown in the resultant block  760 , when it receives this feedforward signal. The increase in opening may be a predetermined, fixed amount, or the increase may be calculated based on operating parameters of the nitrogen recycle compressor  145  and/or the tripped compressor-expander set  165 ,  410 ,  420 ,  430 . 
     Other steps in the shutdown procedure, not necessarily in the order in which they will be carried out include: opening the compressor-expander set compressor  160 ,  810 ,  820  recycle valve as shown in the recycle block  765 ; closing the expander adjustable nozzles  210  as indicated in the nozzle block  770 ; closing the expander shutdown valve  850  or  860  as illustrated in the shutdown valve bock  775 ; and alarming the operator of the shutdown  780 . The order in which these steps are carried out depends on the system, rates of actuation, and personal preference. 
     In  FIG. 8 , a preferred piping system is illustrated. In this piping arrangement, the compressors  810 ,  820  within the main and balance compressor-expander sets, respectively, are plumbed in parallel. The expanders  830 ,  840 , on the other hand, are not in parallel with one another. Rather, the main expander  830  feeds the subcooling heat exchanger  120 , while the exhaust from the balance expander  840  is combined with the discharge of the subcooling heat exchanger  120 , and the entire flow is used as the cold fluid in the regenerator  175 . This piping arrangement is presented to provide a full disclosure of the systems on which the present invention may be used. However, the method and apparatus of the instant invention is unaffected by the known piping variations shown in  FIGS. 1 ,  2   a ,  3 - 5 , and  8 . 
     Expander shutdown valves  850 ,  860  are provided for shutting down the main and balance compressor-expander sets. 
     Performance maps for the main compressor  810  are shown in  FIGS. 9 and 10 . Performance maps for the balance compressor  820  are shown in  FIGS. 11 and 12 . As those skilled in this art know, for a given rotational speed, N, the shaft power required by a centrifugal compressor  160 ,  810 ,  820  often has a positive slope as shown in  FIGS. 10 and 12 . Frequently, as especially seen in  FIG. 12 , at high flow rates, the shaft power curve for a constant rotational speed, N, may have a negative slope. Either way, the shaft power required by the centrifugal compressors  160 ,  810 ,  820  changes with flow rate. Therefore, the shaft power varies with the opening of the recycle valve  305 . The speed is governed by the equation: 
                       1   2     ⁢   I   ⁢       ⅆ     N   2         ⅆ   t         =         W   .       i   ⁢           ⁢   n       -       W   .     out               (   1   )               
where I is the moment of inertia for the compressor-expander set  410 , N is the rotational speed of the compressor-expander set  410 , {dot over (W)} in  is the shaft power supplied to the compressor  160 ,  810 ,  820 , and {dot over (W)} out  is the shaft power required by the compressor  160 ,  810 ,  820 . Opening the recycle valve  305  changes {dot over (W)} out , and hence the rotational speed, N. Therefore, changing the opening of the recycle valve  305  may be used to move the rotational speed, N, of the compressor-expander set  410  out of a critical speed zone.
 
     The above embodiment is the preferred embodiment, but this invention is not limited thereto. It is, therefore, apparent that many modifications and variations of the present invention are possible in light of the above teachings. It is, therefore, to be understood that within the scope of the appended claims, the invention may be practiced otherwise than as specifically described.