This invention relates generally to a method and apparatus for antisurge control of turbocompressors having complex and changing surge limit lines. More specifically, it relates to a method for using a function of multiple variables to describe (with high accuracy) a surge limit line under the influence of varying process conditions.
Antisurge controllers are designed to incorporate an approximation to compressors"" surge limit lines. This approximation is referred to as the antisurge controller""s surge reference line. A turbocompressor""s surge limit line, in many cases, has a complex and changing shape which directly corresponds to a number of process variables with changing values; for example, guide vane position, rotational speed, isentropic exponent, and the molecular weight of the gas. This relates particularly to multistage centrifugal and axial turbocompressors equipped with adjustable inlet or diffuser guide vanes, or both.
Compensating for these complex and changing shapes consists of employing an antisurge controller to alter the surge reference line in accordance with the above mentioned process variables. However, existing antisurge controllers do not incorporate sufficient capability to fully compensate for the surge limit line""s ongoing changes. This drawback results in narrowing the area of the zone (on the compressor map) in which the turbocompressor can operate with the antisurge valve closed, thereby significantly decreasing the efficiency of the turbocompressor""s operation.
A purpose of this invention is to improve upon the prior art by providing efficient antisurge control of a turbocompressor with a surge limit line whose complex shape and location are functions of one or more process variables of a turbocompressor operation condition. This proposed control method includes describing the surge limit line with an analytic function of multiple (m) variables, ƒn(x1, x2, . . . , xmxe2x88x921, xm), that provides the following relation at the surge limit line:                               S          s                =                                                            f                n                            ⁡                              (                                                      x                    1                                    ,                                      x                    2                                    ,                  …                  ⁢                                      xe2x80x83                                    ,                                      x                                          m                      -                      1                                                        ,                                      x                    m                                                  )                                                    Δ              ⁢                              xe2x80x83                            ⁢                                                p                  o                                /                p                                              =          1                                    (        1        )            
where Ss is a proximity-to-surge parameter; variables x1, x2, . . . , xmxe2x88x921, xm-1, xm (where 1 less than m)are parameters which affect the surge limit line""s shape and location; xcex94p0 is the differential pressure across a flow measuring device; andp is an absolute pressure. Organized in this way, the analytic function describes, with high accuracy, the complex shape and location of the surge limit line under the influence of changing conditions. This method is unlike that mentioned in the prior art, which employs the standard present-day approach for constructing the surge parameter, Ss, using independent functions, such as ƒ1(x1) and ƒ2(x2):                                           S            s                    =                                                                      f                  1                                ⁡                                  (                                      x                    1                                    )                                                            Δ                ⁢                                  xe2x80x83                                ⁢                                                      p                    o                                    /                                      p                    s                                                                        ⁢                                          f                2                            ⁡                              (                                  x                  2                                )                                                    ,        …        ⁢                  xe2x80x83                ,                              f                          m              -              1                                ⁡                      (                          x                              m                -                1                                      )                          ,                                            f              m                        ⁡                          (                              x                m                            )                                =          1                                    (        2        )            
The emphasis of the new technique is especially directed to multistage centrifugal and axial turbocompressors operating with variable rotational speed or variable gas parameters (or both), and equipped with adjustable inlet or diffuser guide vanes (or both); although the method is not limited to this type of turbocompressor. Compensating for the complex and changing shape of a turbocompressor""s surge limit line can be difficult and imprecise when using existing antisurge control methods. A typical present-day antisurge controller defines the surge parameter, Ss, as a measure of the relative location of a turbocompressor""s operating point and its surge limit line, or as proximity-to-surge:                                           S            s                    =                                                    f                1                            ⁡                              (                                  R                  c                                )                                                    Δ              ⁢                              xe2x80x83                            ⁢                                                p                  o                                /                p                                                    ⁢                  
                ⁢                  where                ⁢                  
                ⁢                                                                                                  f                    1                                    ⁡                                      (                                          R                      c                                        )                                                  =                                                      Δ                    ⁢                                          xe2x80x83                                        ⁢                                                                  p                        o                                            /                      p                                        ⁢                                          xe2x80x83                                        ⁢                    when                    ⁢                                          xe2x80x83                                        ⁢                                          S                      s                                                        =                                      1                    ⁢                                          xe2x80x83                                        ⁢                                          on the surge limit line                                                                                                                                                                                    R                    c                                    =                                      pressure ratio                                                  ,                                  xe2x80x83                                ⁢                                                      p                    d                                    /                                      p                    s                                                                                                                                            p                  d                                =                                  absolute pressure at discharge                                                                                                                          p                  s                                =                                  absolute pressure in suction                                                                                                        p                =                                  absolute pressure                                                                                                                          Δ                  ⁢                                      xe2x80x83                                    ⁢                                      p                    o                                                  =                                  differential pressure from a flow measurement device                                                                                        (        3        )            
When it is necessary to compensate for influences on the surge limit line because of changes in other process variables, the influence coefficients that correlate with these variables are introduced into Eq. (3). For example, if the shape and the location of the surge limit line depend on inlet and diffuser guide-vane positions, then the appropriate coefficients of influence on the position of the inlet guide vanes (xcex1) and the position of the diffuser guide vanes (xcex2) are incorporated into Eq. (3) as follows:                               S          s                =                                                            f                1                            ⁡                              (                                  R                  c                                )                                                    Δ              ⁢                              xe2x80x83                            ⁢                                                p                  o                                /                p                                              ⁢                                    f              2                        ⁡                          (              β              )                                ⁢                                    f              3                        ⁡                          (              α              )                                                          (        4        )            
where ƒ2(xcex2) and ƒ3(xcex1) are the coefficients of influence of the positions of the guide vanes. When ƒ2(xcex2)=ƒ3(xcex1)=1 (or some arbitrary, constant value), Eq. (4) precisely describes the limit line; but when ƒ2(xcex2)xe2x89xa01 and ƒ3(xcex1)xe2x89xa01, the precision level significantly declines. The cause of a discrepancy between the xe2x80x9crealxe2x80x9d new shape and location of the surge reference line and the expression of Eq. (4), is that the coefficients ƒ2(xcex2) and ƒ3(xcex1) can only scale the function ƒ1(Rc) which may not be congruent with the compressor""s actual surge limit line. Consequently, it becomes necessary to limit the turbocompressor""s operating zone where the antisurge valve can be kept closed which substantially decreases the economic efficiency of the turbocompressor""s operation.
More effectual control can be achieved by the proposed method, which describes the surge reference line with an analytic function, Eq. (1). This function can be built as a superposition of functions of less than m variables. Particularly, this function can be built as a superposition of polynomial functions in which the coefficients and power of each is determined by the shape and location of the surge limit line. Formed in this way, the analytic function matches, with high accuracy, a surge limit line under the influence of changing process conditions, unlike the standard present-day approach used to construct a surge parameter.
A significant example of the proposed method involves a petrochemical process supported by a large compressor equipped with inlet and diffuser guide vanes. In order to continue the process without surge when one of two guide vanes fails, the last position of the failed guide vane must be identified, thereby allowing the antisurge controller to utilize the correct surge reference line.