SURGE LINE CALCULATION OF A CENTRIFUGAL COMPRESSOR – SINGLE STAGE

Surge point is a point on the compressor operating curve where a condition of minimum flow and maximum pressure exists. It is determined on operating curve at which compressor is operating at particular operating RPM of the compressor.

Surge line is the locus of all the surge points at various operating RPM of the compressor.

 

Surge limit line and surge control line

 

Surge limit line (SLL)

As mentioned above, the surge line also defined as surge limit line (SLL). If operating point in compressor map goes to the left of SLL, then surge occurs.

Surge control line (SCL)

For the safe and stable operation of the compressor, the operating margin is provided on the surge limit line and a line is plotted relative to it. This line is called surge control line (SCL).

Normally the margin is approximately 10% of the flow and it will be as per OEM design value.

Simply SCL (Surge Control line) = SLL (Surge limit line) + 10% of the flow.

The main purpose of surge control line is it adds some margin to the surge region and this margin allow the surge control system to respond and prevent compressor from surge.

Boost line or Recycle trip line (RTL)

If back pressure is too high then the operating parameter tends to cross RTL and could lead to compressor surge. So when compressor operating point reaches RTL, controller gives the larger step opening command or multiple opening steps command to the ASV to avoid surge.

This will cause high process disturbances. There are advanced control systems which uses relatively smaller steps based on the deviation before operating point reaches to SCL.

Deviation

The distance between compressor operating point and SCL is deviation or surge parameter.

Based on the value of deviation, the operating region can be determined as stable zone or nearer to surge.

Deviation	Operating region of the compressor	Risk level
Negative	Between SLL and SCL	Alert or Alarm
Zero	On SCL	Alert or Alarm
Positive	Right of SCL (Stable and safe zone)	Normal

 

Calculation of surge control line

As discussed earlier, from the surge test, we get the surge points from the surge test as (F1,P1), (F2,P2) & (F3,P3). [if we consider surge test is performed for 3 RPMs]

Gain & Bias are the two parameters to be incorporated in the surge controller system and these values are calculated from the basic line equation.

Initially these values are calculated by considering the operating point falls on the surge control line and adapting deviation as Zero.

The representation of the basic line equation Y=mX+b is shown in the following figure.

 

 Here, in this context, the basic mathematical line equation is represented as follows.

Deviation = [(Flow * Gain) + Bias – Discharge Pressure]

Where, Y = Discharge pressure

                X = Flow

                m (Slope) = Gain

                b (Y intercept) = Bias

Hence

 Deviation = mX+b-Y .......................... (Surge control line equation)

As said above, gain and bias values are calculated initially by considering deviation as Zero.

Then the above equation becomes

                0 = mX+b-Y

                m = (Y-b) / X

Gain (m) = Y axis / X axis

                = (P3-P1) / (F3-F1) or (P2-P1) / (F2-F1) or (P3-P2) / (F3-F2)

                = G (say)

Bias (b) = Y-mX

                = P – (Gain * F) [Here P & F can be taken as P1 or P2 or P3 & F1 or F2 or F3]

                = B (say)

Hence the obtained gain and bias values are incorporated in the surge control system and surge control line equation becomes as follows.

Deviation = [(Flow * G) + B – Discharge Pressure].

As per the above table and based upon the value of deviation, the zone of the compressor can be determined whether it is stable or not and surge controller acts based upon the deviation value to make the compressor in stable operating region with the help of ASV.