Method of anti-surge protection for a dynamic compressor using a surge parameter

Abstract

A method of surge protection for a dynamic compressor that has a corresponding compressor map. A control system continually calculates an equivalent polytropic head parameter in order to define a surge limit line. The system then calculates a control parameter and determines the distance the control parameter to the surge limit line wherein the control parameter is dynamic to changes in gas compressibility and invariant to changes in suction conditions and gas compressibility. As a result of the distance of the control parameter to the surge limit line, the surge valve of a dynamic compressor is actuated to prevent surge.

Claims

1. A method of surge protection for a dynamic compressor, comprising the steps of: continually calculating a surge parameter with a control system; continually calculating an operating parameter with the control system; defining with the control system a surge limit line based upon the calculated surge parameter on a compressor map; continually calculating a surge control parameter with the control system by dividing the calculated operating parameter by the calculated surge parameter; actuating a surge valve based upon a distance, continually calculated by the control system, the calculated control parameter is from the surge limit line; continually calculating with the control system a polytropic exponent; and continually calculating a compressibility of gas at flow conditions.

2. The method of claim 1 wherein the polytropic exponent is calculated by the control system using the equation: $n=\frac{1}{1-\frac{\log \left[\frac{Z_d}{Z_s}\frac{T_d}{T_s}\right]}{\log \left[\frac{P_d}{P_s}\right]}}$ where n is a polytropic exponent, Z.sub.d is gas compressibility at discharge, Z.sub.s is gas compressibility at suction, T.sub.d is temperature at discharge, T.sub.s is temperature at suction P.sub.d is pressure at discharge, and P.sub.s is pressure at suction.

3. The method of claim 1 further comprising the step of continually calculating an equivalent polytropic head with the control system using the equation: $h_{\mathrm{eq}}=c_2\left[\frac{\left[R_c^{\frac{n-1}{n}}-1\right]}{\left[\frac{n-1}{n}\right]}\right]*\frac{1}{n}=\frac{h_r}{n}$ where h.sub.eq is an equivalent polytropic head, c.sub.2 is a scaling constant, R.sub.c is a pressure ratio across the compressor, n is a polytropic exponent, and h.sub.r is an equivalent reduced head.

4. The method of claim 1 wherein the calculated surge parameter is a function of an equivalent polytropic head.

5. The method of claim 1 wherein the calculated operating parameter is determined by the equation $C\frac{P_o}{P_s}\frac{1}{n}=\frac{q_r^2}{n}=q_{\mathrm{eq}}^2.Math.o$ where c is a constant P.sub.o is a differential pressure across flow measuring device, P.sub.s is pressure at suction, n is a polytropic exponent, q.sub.r.sup.2 is an equivalent reduced flow, and q.sup.2.sub.eq|op is an equivalent flow parameter at an operating condition.

6. The method of claim 1 wherein the distance the control parameter (R) is from the surge limit line is determined based on the control parameter (R) and is a function of [((q.sup.2.sub.eq|op)/f(h.sub.eq))l] where q.sup.2.sub.eq|op is an equivalent flow parameter at an operating condition and f(h.sub.eq) is a function of the equivalent polytropic head parameter.

7. The method of claim 6 wherein when the distance the control parameter (R) is from the surge limit line is greater than 0 then the compressor is operating to the right of the surge limit line and when the distance the control parameter (R) is from the surge limit line is less than or equal to 0 then the compressor is operating to the left of the surge limit line.

8. The method of claim 1, further comprising the step of continually calculating a distance the control parameter (R) is from a surge control line.

9. The method of claim 8, wherein the surge control line is determined based on the control parameter (R) and is a function of [((q.sup.2.sub.eq|op)/f(h.sub.eq))SM]1 where q.sup.2.sub.eq|op is the equivalent flow parameter at an operating condition, f(h.sub.eq) is a function of the equivalent polytropic head parameter defining the surge limit line and SM is the safety margin defining the surge control line.

10. The method of claim 9 wherein when the distance a control parameter (R) is from the surge control line is equal to or greater than 0 the surge valve is closed and when the distance the control parameter (R) from the surge control line is less than 0 the surge valve is opened.

11. A method of surge protection for a dynamic compressor, comprising the steps of: continually calculating a surge parameter with a control system; continually calculating an operating parameter with the control system; defining with the control system a surge limit line based upon the calculated surge parameter on a compressor map; continually calculating a surge control parameter with the control system by dividing the calculated operating parameter by the calculated surge parameter; actuating a surge valve based upon a distance, continually calculated by the control system, the calculated control parameter is from the surge limit line; and continually calculating with the control system a polytropic exponent.

12. A method of surge protection for a dynamic compressor, comprising the steps of: continually calculating a surge parameter with a control system; continually calculating an operating parameter with the control system; defining with the control system a surge limit line based upon the calculated surge parameter on a compressor map; continually calculating a surge control parameter with the control system by dividing the calculated operating parameter by the calculated surge parameter; actuating a surge valve based upon a distance, continually calculated by the control system, the calculated control parameter is from the surge limit line; and continually calculating the compressibility of gas at flow conditions.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic diagram of a dynamic compressor;

(2) FIG. 2 is a block diagram of a control system of a dynamic compressor;

(3) FIG. 3 is a schematic diagram of a surge control system of a dynamic compressor; and

(4) FIG. 4 is a graph having equivalent flow squared versus equivalent polytropic head.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

(5) FIG. 1 shows a dynamic compressor 10 that includes a compressor 12 that is driven by a compressor driver 14. The compressor driver is of any type including a motor, gas turbine, steam turbine, expander or the like. The compressor 12 has a gas inlet 16 and a gas outlet 18 wherein gas flows through the compressor 12 to be compressed. An anti-surge or recycle valve 20 is fluidly connected between the gas inlet 16 and gas outlet 18 so that when the anti-surge valve 20 opens a fluid flow path exists to convey gas from the gas outlet 18 to the gas inlet 16. A plurality of sensors 22 including pressure sensors, temperature sensors, flow measurement sensors and the like are placed throughout the dynamic compressor 10 in order to determine processed conditions for the components of the dynamic compressor including the compressor 12, the driver 14, the gas inlet 16, and gas outlet 18 and the anti-surge valve 20. The plurality of sensors 22 are electrically connected to the control system 24 where the control system 24 is in communication with all of the components of the dynamic compressor and controls the opening of the anti-surge valve 20.

(6) FIG. 2 shows a control system 24 used for a dynamic compressor 10. Specifically, a controller 26 such as a Network Master controller is utilized in combination with a load controller 28 that monitors the inlet 16 of the dynamic compressor 10 and a surge controller 30 that monitors and operates the anti-surge valve 20. The arrangement and set up of the control system 24 shown in FIG. 2 is merely an example of a control system 24 for a dynamic compressor 10 and is shown as exemplary. Specifically, other control arrangements that utilize Master controllers, load controllers, and surge controllers in series cascade and parallel cascade can be used without falling outside the scope of the present invention.

(7) FIG. 3 is yet another exemplary embodiment of the control system 24 used with another dynamic compressor 10. In this embodiment the station and load controllers are not used and instead the control system 24 takes readings straight from the plurality of sensors 22 to determine an input to the surge valve 20.

(8) The control system 24 of the present invention, like prior art control systems, determines a compressor map that corresponds to the dynamic compressor 10 as best shown in FIG. 4. In the present invention the compressor map 32 presents a horizontal axis 34 that measures the square of an equivalent flow q.sup.2.sub.eq and has a vertical axis 36 that presents an equivalent polytropic head. On the map 32 is a surge limit line 38 that is calculated by the control system 24 wherein at points to the left of the surge limit line 38, surge within the dynamic compressor 10 typically occurs. Spaced at a predetermined distance that is considered a safety margin 40 is a surge control line 42 wherein when a control parameter reaches a point either on or to the left of the surge control line 42 the control system 24 actuates the anti-surge valve 20 to provide flow through the anti-surge valve 20. Additionally seen on the map 32 are operating control lines 44 that represent additional control lines that are used if the safety margin 40 is desired to be increased to protect against a surge within a compressor.

(9) The compressor map 32 of the present invention is an equivalent compressor map wherein instead of attempting to measure inlet volumetric flow and apply it against polytropic head the present invention calculates a surge control parameter R. The surge parameter R is determined by the control system 24 using the following equation:

(10) $R=\frac{q_{\mathrm{eq}}^2.Math.o}{q_{\mathrm{eq}}^2.Math.\mathrm{surge}}-\mathrm{SM}$
where q.sub.eq.sup.2|op is an operating parameter at flow conditions, q.sub.eq.sup.2|surge is a surge parameter at flow conditions, and SM is a safety margin that is predetermined and entered into the control system to determine a surge control parameter or line.

(11) The surge parameter q.sub.eq.sup.2|surge is determined by first continuously calculating the compressibility of the gas or gas mixture at flow conditions. As one example, based on the gas or gas mixture type that is entered into the control system 24, and using the sensed pressure and temperature at inlet or suction, and at discharge, the control system 24 determines the gas compressibility at suction Z.sub.s and at discharge Z.sub.d from gas tables. The control system 24 then determines the gas compressibility ratio at flow conditions using the following equation:

(12) $Z=\frac{z_d}{z_s}$

(13) Next, the control system calculates a polytropic exponent n using the following equation:

(14) $n=\frac{1}{1-\frac{\log \left[\frac{Z_d}{Z_s}\frac{T_d}{T_s}\right]}{\log \left[\frac{P_d}{P_s}\right]}}$

(15) The control system then determines the equivalent polytropic head, h.sub.eq using the following equation:

(16) $h_{\mathrm{eq}}=c_2\left[\frac{\left[R_c^{\frac{n-1}{n}}-1\right]}{\left[\frac{n-1}{n}\right]}\right]*\frac{1}{n}=\frac{h_r}{n}$
where c.sub.2 is a defined scaling constant, R.sub.c is the pressure ratio across the compressor (i.e., P.sub.d/P.sub.s) and h.sub.r is the equivalent reduced head.

(17) The control system then determines the surge parameter or surge line based upon a function of the equivalent polytropic head, f(h.sub.eq). The function is either programmed into the control system 24 or input into the control system 24 by a user. The f(h.sub.eq) is of many types and in one example is shown on a table where the x-axis is the calculated h.sub.eq and the y-axis is a calculated equivalent flow q.sub.eq.sup.2 at the corresponding surge point where equivalent flow is determined by known equations such as:

(18) $q_{\mathrm{eq}}^2=\frac{Q^2}{V_c^2}$
where Q is volumetric flow and V.sup.2.sub.c is the sonic velocity of gas at flow conditions.

(19) The control system continually calculates an operating parameter by first determining an equivalent reduced flow, q.sub.r.sup.2, using the equation:

(20) $q_r^2=c_1*\frac{P_o}{P_s}$
where c.sub.1 is a constant based on a type of flow element used and piping geometry, P.sub.o is the differential pressure across flow measuring device, and P.sub.s is pressure at suction.

(21) Next, the control system determines the operating parameter q.sub.r.sup.2|op by dividing the equivalent reduced flow q.sub.r.sup.2 by the calculated polytropic exponent, n, or

(22) $q_{\mathrm{eq}}^2.Math.o=\frac{q_r^2}{n}$
In this manner, since a polytropic exponent n is used to model a gas compression process using Real Gas law equation, changes in gas compressibility at flow conditions are accounted for as per the embodiment of control system 24 shown in FIG. 3. In addition, based on the derived calculations shown for h.sub.eq and q.sub.eq.sup.2 there is no need to know or use the gas constant, molecular weight, or specific heat ratio in deriving a surge control parameter.

(23) To arrive at the surge control parameter, R, the operating parameter is divided by the surge parameter and then the safety margin is subtracted so that when R1.0 anti-surge control valve 20 is closed and when R<1.0 the anti-surge recycle valve 20 is open.

(24) In addition, the control system 24 determines the distance to the surge control line :
=[((q.sub.eq.sup.2|op)/f(h.sub.eq))SM]1=(R1)
so when is 0 the valve is closed and when is <0 the valve is open. Thus the surge controller acts on to actuate the surge valve and prevent surge.

(25) By continuously calculating the compressibility of gas, Z, and the polytropic exponent, n, as opposed to relying on fixed gas compressibility and constants as preached in present art, a much more accurate and dynamic surge control parameter R is determined.

(26) In operation, as the dynamic compressor 10 is operating, the control system 24 continually monitors the dynamic compressor 10. The control system 24 continually calculates an equivalent polytropic head parameter and an equivalent flow parameter in the manners discussed above. A surge limit line 38 is defined on the compressor map 32 as a function of the equivalent polytropic head parameter. The control system 24 continually calculates a distance b that a control parameter R is from the surge limit line 38 wherein the control parameter is dynamic to changes in the gas compressibility. Then, as a result of the distance the control parameter is from the surge limit line the control system 24 actuates the anti-surge valve 20 accordingly.

(27) Thus, provided is a dynamic compressor control system that utilizes an equivalent compressor map 32 to improve upon the state of the art. The equivalent compressor map 32 bases a surge parameter on the polytropic compression process equation and modeling of the dynamic compressor 10 based on flow, pressure, speed (or inlet guide vane), compressibility and temperatures of the dynamic compressor 10. The equivalent polytropic head parameter and equivalent flow parameter are based on the dynamic similitude theory, a mach number determination using sonic velocity of gas at flowing conditions and gas compressibility.

(28) When determining control parameter (R), the parameter is dynamic to changes in compressor load, both in the increasing and decreasing direction. Therefore, presented is a control parameter that has high dynamic sensitivity along with invariance of the surge equivalent parameter due to changes in suction pressure, temperature, gas composition, rotation speed or inlet guide vane geometry. Thus, at the very least all of the stated objectives have been met.

(29) It will be appreciated by those skilled in the art that other various modifications could be made to the device without departing from the spirit and scope of this invention. All such modifications and changes fall within the scope of the claims and are intended to be covered thereby.