Ariel Calculation Method

Definitions
Ace - area of crank-end piston, in2
Ahe - area of head-end piston, in2
Arod - area of piston rod, in2
Ac - adjusted equivalent cylinder area, in2
Av - adjusted equivalent valve area per corner, in2
Avc - area of valve and cylinder combined, in2
BHP - total frame brake horsepower
Cb - cylinder bore, in
CE - crank-end
CHP - total cylinder horsepower
CHP/MM - cylinder HP/MMSCFD at 14.4 psia & Tsl
CL - cylinder clearance, fraction
EM - mechanical efficiency, fraction
FHP - frame friction horsepower
GVd - gas velocity at discharge, fpm
GVs - gas velocity at suction, fpm
HE - head-end
(HP) - designation for high pressure cylinder or stage
IHP/MM - indicated HP/MMSCFD at 14.4 psia & Tsl
“k” - ratio of specific heats
(LP) - designation for low pressure cylinder or stage
MCp - Molal heat capacity, BTU/LB MOL °R  
MMSCFD - million standard cubic feet per day , 14.7 psia & 60 °F
MW - molecular weight
Patm - atmospheric pressure, psia
PD - total piston displacement, (HE + CE), cfm
Pdflg - flange discharge pressure, psia
Pdi - internal discharge pressure, psia
Pdl - line discharge pressure, psia
PLd - discharge pressure loss, %
PLs - suction pressure loss, %
Psflg - flange suction pressure, psia
Psi - internal suction pressure, psia
Psl - line suction pressure, psia
Q - cylinder capacity, (HE + CE), MMCFD at 14.4 psia and Tsl
Rflg - flange to flange pressure ratio
Ri - initial pressure ratio
Rint - internal pressure ratio
RLc - Internal compression gas rod load, lbs
RLt - Internal tension gas rod load, lbs
SG - specific gravity
Tdf - final discharge temperature, °R
Tdi - initial discharge temperature, °R
Tsi - initial suction temperature, °R
Tsl - line suction temperature,°R
Tsph - preheated suction temperature, °R
VE - volumetric efficiency, fraction
VEa - average volumetric efficiency,
Za - average compressibility,
Zd - discharge compressibility at Pdflg and Tdf
Zsph - suction compressibility at Psflg and Tsph
Zstd - base compressibility, at 14.7 psia & 60 °F
Calculation Procedure:

    1.  Knowing MW, SG or gas analysis, calculate “k” value.

    2.   Determine pressure drop between line and first stage cylinder suction flange, and between last stage cylinder discharge flange and line, calculate flange pressures:

    Psflg = Psl - suction drop
    Pdflg = Pdl + discharge drop

    3.   The following pressure drops are recommended for:  

    a) intake scrubber, piping and bottles

b) interstage piping, cooling section, scrubber and bottles

    c) bottles, piping, discharge cooling and scrubber

Flange Pressure

Pressure Loss

Not To Exceed

35 psia and below

5%

1 psi

36 psia to 250 psia

3%

5 psi

251 psia to 1000 psia

2%

10 psi

1001 psia and above

1%

 

4.

    5.

6. Tsph = Tsl + [(0.02 + (0.002 x Cb)) x (Tdi - Tsl)]

    7. Determine suction or discharge compressibility.
    8.
    9.
    10.
    11.
    12.
    13.
    14.
    15.
    16. Calculate rod loads using internal pressures. Calculated rod load must stay within the limits as defined in the specification or the nameplate for each model. Maximum load is defined as the sum of the compression and tension rod loads for double acting or tandem cylinders. Limits on compression and tension loads are outlined in the specifications or the nameplate for each model. Double acting cylinders may be operated single acting on crank-end by removing head-end suction valves or by using head end suction valve unloaders. Single acting cylinders must have reversal of rod load and must not exceed tension rod load limits.

Double Acting Cylinders

    RLc = Ahe x Pdi - Ace x Psi - Arod x Patm
    RLt = Ace x Pdi - Ahe x Psi + Arod x Patm

Single Acting Crank-End Cylinders

    RLc = Ahe x Pdihe - Ace x Psi - Arod x Patm
    RLt = Ace x Pdi - Ahe x Psihe + Arod x Patm

Tandem Cylinders - (High Pressure Cylinder Outboard)

    RLc = Ahe(HP) x Pdi(HP) +[Ahe((LP) - Ahe(HP)] x Psflg(LP) - Ace(LP) x Psi(LP) - Arod x Patm
    RLt = Ace(LP) x Pdi(LP) - [Ahe(LP) - Ahe(HP)] x Psflg(LP) - Ahe(HP) x Psi(HP) + Arod x Patm

Tandem Cylinders - (High Pressure Cylinder Inboard)

    RLc = Ahe(LP) x Pdi(LP) - [Ahe(LP) - Ahe(HP)] x Psflg(LP) - Ace(HP) x Psi(HP) - Arod x Patm
    RLt = Ace(HP) x Pdi(HP) + [Ahe(LP) - Ahe(HP)] x Psflg(LP) - Ahe(LP) x Psi(LP) + Arod x Patm

17. Find IHP/MM using the following formula:


    18. EM = 0.95

19.

20. CHP = CHP/MM x Q

    21. BHP = CHP + FHP Values for FHP at rated rpm are:

    Frame

    Frictional Horse Power

    2 Throw

    4 Throw

    6 Throw

    JGS/1

    0

     

     

    JGM/1-JGI/1

    2

     

     

    JGM/2

    3

     

     

    JGP/1

    5

     

     

    JGP/2

    10

     

     

    JGN/1

    2

     

     

    JGN/2

    3

     

     

    JG

    3

    6

     

    JGQ/1

    5

     

     

    JGQ/2

    6

     

     

    JGA

    6

    12

    18

    JGW-JGR

    5

    10

     

    JGJ

    6

    12

    18

    JGH

    7

    14

     

    JGE

    10

    20

    30

    JGK

    12

    24

    36

    JGT

    10

    20

    30

    JGD

    19

    38

    57

    JGC

    19

    38

    57

    JGZ

    23

    46

    69

    JGU

    23

    46

    69

    KBB

     

    76

    114

    KBV

     

    76

    114

     
     
    FHP varies in direct proportion to compressor rpm.
    22.

23.

    24. To convert from pounds/hour (when required) :
    25.
 

Ariel Corporation Application Manual

28 December 2008