sizing letdown line for press surge

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Loss of liquid in high-pressureliquid/vapor separators mayresult in a high-pressure gas flow inthe letdown circuit, causing damageto piping and equipment. Here is

how to design the system to avoiddamage should a pressurized gasflow occur.

42 www.cepmagazine.org November 2001 CEP

Fluids/Solids Handling

any petroleum refinery processes (e.g., distillate hydrotreating,gas sweetening) as well as petrochemical processes (e.g.,methanol synthesis) employ liquid/vapor separators operating athigh pressures. The loss of the liquid level in such equipment

may cause sudden injection of high-pressure gas into the letdown circuit down-stream of the control valve.

Under such conditions, the gas expands at the valve exit, but due to the limitedvolume available, a pressure buildup occurs before the liquid is pushed away by thegas. The inertia of the liquid and its delay in increasing its velocity, which limit thevolume available to the gas for expansion, are likely to cause a sudden pressuresurge in the piping circuit immediately downstream of the control valve. The prob-lem faced by the design engineer is to evaluate the extent of the pressure rise, andto establish adequate mechanical design conditions for the various elements of thecircuit. A relief device may be required to limit the maximum pressure rise duringtransient conditions.

We studied this problem and performed simulations as a means to develop asafe design basis. The study assessed the main consequences of the injection of high-pressure gas into the letdown circuit, and looked at the fluid dynamics in-volved, such that safety provisions would be adequate.

The study results indicated:• Immediately upon loss of level, gas is injected in the low-pressure letdown

circuit, causing a sudden pressure rise, and consequently a water-hammer-typetransient.

• A pressure wave propagates along the line from the control valve to thefirst downstream vessel, pressurizing the whole circuit.

• The liquid is displaced at a high velocity by the gas. Consequently, strongacceleration forces involving severe thrusts on supports develop at any changeof direction.

• The stresses due to these acceleration forces are added to those from the pres-sure increase, and may cause tube-rupture, if not considered in the design.

• The pressure rise is more pronounced for systems in which only a small vol-ume of gas is released by the liquid flashing in the control valve. A large volume of

Size Letdown

Lines for Pressure Surges

M

Gianni Anci,

EPSI



CEP November 2001 www.cepmagazine.org 43

gas attenuates the surge and reduces the speed of propagationof the pressure wave.

A calculation method is now presented for the design.

This method offers a reasonably conservative estimate of thepressure rise during the transient, and permits a safe defini-tion of the required maximum allowable working pressure(MAWP) for the piping.

Design recommendations

The results of the simulations indicate the need to consid-er the phenomena in the hydraulic and structural design of the letdown circuit, and suggest a number of provisions that

can effectively avoid some of the potential risks. The follow-ing precautions are recommended:

1. Preferably use the same rating and design conditions

for the letdown line downstream of the control valve as forthe line upstream, connecting the valve with the high-pressure separator.

2. Locate the control valve as close as possible to theexpansion vessel. This minimizes the length of the letdownline downstream of the valve, and consequently reduces themass of product that suffers the acceleration and developsthe pressure surge.

3. Limit oversizing of the control valve to minimumpractical requirements.

4. Consider having the manual bypass to the control valveclosed and sealed if a bypass is installed.

5. If any equipment is installed in the downstream circuit

and has a MAWP lower than the upstream separator’s operat-ing pressure (or lower than the estimated peak-surge pres-sure), consider installing a quick-acting safety relief device(e.g., a rupture disk).

6. The relief device should be installed preferably imme-diately downstream of the control valve, but, in any case, up-stream of the equipment to be protected.

7. Take special care in designing the supports of thedownstream line, with due consideration to the thrust oc-curring at any change of direction, as with elbows or teesthat are connected to the high-velocity fluid line or in theroute of the gas/liquid interface (associated with a suddendensity change).

Method of analysis

The model is based on a method normally used for water-hammer pressure-surge calculations, adapted to account forthe boundary conditions corresponding to the gas injection inthe upstream section when level loss occurs in the separator.A comprehensive general treatment of water hammer and re-lated problems is presented in Wylie et al. (1).

A number of simplifying assumptions were made in de-veloping the model to avoid excessive complexity and com-putational difficulty, yet maintain sufficient accuracy in thecalculated values of pressure buildup, fluid velocity and ac-celeration — all required for a sound mechanical design of

the pipeline and relevant supports.

Assumptions

The model assumes that:• The loss of liquid level and the injection of gas in the

pipeline downstream of the control valve occur starting fromsteady-state conditions, corresponding to the operating liquidflowrate (for a conservative design, use the maximum operat-ing liquid flowrate in the circuit).

• The fluid motion in the pipeline is considered one-dimensional; space integration is performed only along the x-axis.

• The fluid in the pipeline is homogeneous. In reality, de-

Nomenclature

a = speed of the pressure wave in the liquid, m/s

C V, liq = liquid-service valve flow-coefficient, dimensionless

C V, gas = gas-service valve flow-coefficient, dimensionless

D = internal pipe dia., m

E = Young’s modulus of the pipe material, kg/m2

f = friction factor, dimensionless

F k = gas-specific-heat ratio factor (air = 1), dimensionless

F P = piping geometry factor (reducer correction), dimensionless

g = acceleration of gravity, m/s2

H = piezometric head, m

k = ratio of specific heats, dimensionless

K eff = effective bulk modulus of fluid, kgf /m2

K gas = bulk modulus of the gas phase, kgf /m2

K liq = bulk modulus of the liquid phase, kgf /m2

L = pipe total length, m

M = gas molecular weightPa = pressure assumed for first secant pole, bar

Pb = pressure assumed for second secant pole, bar

Pc = pressure causing critical flow, bar

P1 = upstream pressure, bar

P2 = downstream pressure, bar

Psep = pressure in upstream separator, bar

∆P = pressure drop, bar

s = pipe thickness, m

t = time, s

T 1 = absolute inlet temperature, K

V = liquid velocity in the pipe, m/s

W = mass flowrate, kg/h

x = distance along the pipe, m

X p = pressure drop ratio, ∆P / ∆P1

Y = gas expansion factor, dimensionless

Z = compressibility factor, dimensionless

X T = pressure drop ratio factor, dimensionless

Subscripts

A,B. P = points in Figure 1

Greek letters

γ = specific gravity of liquid, dimensionless

ε = volumetric fraction of gas in fluid, dimensionless

λ = dimensionless multiplier for combining Eqs. 4 and 5

ρgas = gas density, kg/m3

ρliq = liquid density, kg/m3

ρmix = mixture average density, kg/m3



pending upon the type of fluid and the operating pressures,flashing can occur in the liquid being let down from high tolow pressure. The presence of gas bubbles or even a second

phase reduces the apparent overall or “effective” value of thebulk modulus and the speed of propagation of the pressurewave in the fluid, thus reducing the severity of the pressuresurge for single-phase conditions. This is accounted for byadopting suitably corrected bulk properties for the fluid. Thisapproach was experimentally verified to provide accurate re-sults for volumetric fractions of gases in the liquid up to 3%(2).

• The fluid injected from the upstream separator duringthe transient consists of gas only: entrained liquid, if any, isconsidered to contribute a negligible fraction to the total vol-ume upstream of the gas/liquid interface.

• The inertia effect and the friction losses of the gas are

considered negligible; the pressure in the volume (pipe seg-ment) occupied by the gas is considered uniform.

• The gas pressure follows the ideal gas law.• Neither heat nor mass transfer occurs at the gas/liquid

interface.• The pressure upstream of the valve in the gas/liquid sep-

arator remains constant throughout the computation period.• The gas injection rate is calculated for a constant open-

ing of the control valve (i.e., assuming the valve coefficientcorresponds to steady-state operation at liquid design rate).

• The compression of the gas in the gas-filled portion of the pipeline is isothermal.

The model considers the injection of gas into the pipeline

through the control valve, with the gas occupying the vol-ume of pipe between the valve and the previous fluid inter-face (possibly a liquid with dispersed gas). The gas/fluid in-terface moves along the pipe, depending on the initial(steady-state) conditions of the liquid, and on the evolutionof the pressure at the interface. The pressure buildup in theline accelerates the fluid, which offers resistance due to iner-tia and friction.

The pressure on the gas/fluid interface is calculated usingthe valve’s flowrate equation and mass balance, applying theperfect gas law; it converges on the equilibrium pressure byusing the secant method. The transient pressure and velocityvariations in the fluid are calculated by the equation of mo-

tion and the equation of continuity, following the classicalmethod used in water-hammer analysis.

The integration of the differential equations is performedby the method of characteristics, with finite-difference ap-proximations in time and space. Piping components arecharacterized by mathematically formulating appropriateboundary conditions describing the corresponding flowproperties. For simplicity, no inline valves or other compo-nents are considered, as a simple pipe appears to be general-ly adequate and sufficient to characterize most letdown cir-cuits. If more complex components or equipment are pre-sent, specific boundary conditions or mathematical modelsshould be adopted.

Fluid properties

The model uses average properties for the fluid (liquidcontaining dispersed gas):

The mean fluid density is evaluated with Eq. 1:

ρmix = ε ρgas + (1 - ε) ρliq (1)

The speed of propagation of sound in the fluid, is evaluat-ed by using:

(2)

and is influenced by the fraction of gas in the gas/liquid mix-ture, and by the elastic properties of the pipe. An effectivebulk modulus is defined by:

K eff = 1/[(1 - ε)/ K liq + ε / K gas + d / Es] (3)

At low temperatures and moderate pressures, the gas-phase bulk modulus may be approximated by the local gasabsolute pressure.

Basic equations

The basic equations in water-hammer analysis are theequations of motion and continuity. By considering an ele-ment of fluid in a pipe, the equation of motion may be ex-pressed by Eq. 4, while the equation of continuity may be ex-pressed by Eq. 5:

(4)

(5)

Equations 4 and 5 contain the two unknowns V and H . Wecan consider a linear combination of the two equations, in theform of Eq. 6, that can be rearranged in the form of Eq. 7.

Eq. 4 + λ Eq. 5 = 0 (6)

λ is a dimensionless multiplier used for the linear combi-

nation of the two equations. The linear combination permitstransforming the partial-derivative equations into total-deriva-tive ones, and enables solving them under some conditions.

(7)

If Eq. 8 and 9 are satisfied, then the first bracket of Eq. 7would be the total derivative, dH / dt , and the second bracketwould be the total derivative, dV / dt , as in Eqs. 10 and 11:

∂ H ∂ x

V + λg +∂ H ∂t

+ λ ∂V ∂ x

V + a 2

gλ+ ∂V

∂t +

λ fV V

2 D= 0

a 2

g∂V ∂ x

+ ∂ H ∂t

+ V ∂ H ∂ x

= 0

g∂ H ∂ x + V ∂V ∂ x + ∂V ∂t + fV V

2 D = 0

a = K eff / ρ mix





(8)

(9)

(10)

(11)

Equations 8 and 9 must be equivalent, which implies thatEq. 12 is also valid:

(12)

Solving for λ, we obtain λ = ± (a / g). Thus, these two real,

distinct values of λ convert the two partial differential equa-tions into two total differential equations, subject to the re-strictions of Eqs. 8 and 9.

Substituting for λ, we obtain Eqs. 13, 14, 15 and 16. Sincein water-hammer calculations the value of V is small com-pared with a, it may be dropped.

(13)

(14)

(15)

(16)

The significance of these equations may be interpreted bysome considerations in the x-t plane (Figure 1). In this plane,the curve labeled as C+ is a plot of Eq. 14, while C- is a plotof Eq. 16. Equation 13 is valid only along the C+ characteris-tic, while Eq. 15 is valid only along the C- characteristic.Equations 13 and 15 contain two unknowns for any point onthe characteristic, but at the intersection of the two curves C+

and C-, at Point P, the values of the unknowns must satisfyboth equations. So, the two equations may be solved for thetwo unknowns to yield the values of head, H , and velocity, V .

At this point Eqs. 14 and 16 may be solved for x and t .

Consequently, the solution is carried out along the character-istics, starting from known conditions, by finding new inter-sections, so that velocity and head values are calculated forthe next time-step.

Finite differences

For the purpose of calculation, the pipe is considered to bemade of N equally spaced segments, of length ∆ x. Head, H ,and fluid velocity, V , are initially known for each of thesesections from steady-state analysis. In the computation, Eqs.14 and 16 are used to determine the resulting time-step, and,hence, the mesh size in the grid system. Along the character-istic curves, the time increment, ∆t , is related to the space in-

crement, ∆ x, by: ∆t = ∆ x / a.By using a first-order approximation in the integration

along the C+ and C- characteristics, Eqs. 13 and 16 be-come Eq. 17 along the C+ characteristic, and Eq. 18 alongthe C- characteristic:

(17)

(18)

Adding Eqs. 17 and 18 eliminates H P , while subtractingeliminates V P , resulting in Eqs. 19 and 20, respectively:

(19)

(20)

H P = 0.5[ H A + H B + a / g V A – V B

– af ∆t /2gD V A V A – V B V B ]

V P = 0.5[ V A + V B + g / a H A – H B

– f ∆t /2 D V A V A + V B V B ]

ga H P – H B + V P – V B +

f V B V B

2 D∆t = 0

ga H P – H A + V P – V A +

f V A V A

2 D∆t = 0

dxdt

= V – a ≅ –a

–ga dH dt + dV dt +

fV V

2 D = 0

dxdt

= V + a ≅ a

ga

dH dt

+ dV dt

+ fV V

2 D= 0

V + λg = V + a 2

λg

dV dt

= ∂V ∂ x

dxdt

+ ∂V ∂t

dH dt = ∂ H ∂ x dxdt + ∂ H ∂t

dxdt

= V + a 2

λg

dxdt

= V + λg


∆x ∆x ∆t

∆t

∆t

∆t

A C

C-C+

P

B

∆x

x

∆x ∆x

s Figure 1. Characteristic curves in space-time region.

∆t

A C

P

R S B

∆x

RC = AC *a ∆t

∆x

s Figure 2. Interpolation scheme used in solving equations.



From an analysis of these equations, it can be seen that theterms of the right-hand sides are constants and known valuesfrom the previous time-step. The solution is then carried outat the intersections of the characteristic curves, as shown in

Figure 1. The solution can be carried out only in a limited re-gion, unless information is given for external conditions as afunction of time for x = 0 and for x = L (at the initial and ter-minal sections of the pipeline). Once the piezometric head(pressure expressed as height of liquid column) and the fluidvelocity values are known for a given time-step, the proce-dure is repeated for the next step, until the required time peri-od is covered.

In standard water-hammer analysis two simplifying as-sumptions are often made:

1. The bulk properties of the fluid are considered constantthroughout the pipe length.

2. The time-step is taken as the time interval required by a

sound wave to travel the length of the space step (∆t = ∆ x / a).This avoids the need for interpolation, since the space-timegrid points are always on the characteristic curves.

In reality in our case, the pressure surge will causechanges in the density and the bulk modulus of the dis-persed gas phase, thus causing a variation in the speed of propagation of the pressure wave. It is therefore necessaryto introduce local fluid properties (density and bulk modu-lus) to evaluate the wave speed, and to select a fixed inte-gration time-step not linked to the wave propagation speed(which varies as the surge propagates along the line). Inter-polation of the fluid velocity and head values have been in-troduced in the model, with the interpolation scheme illus-

trated in Figure 2.The head in Points R and S is interpolated from the values

calculated in A, C, B using Eqs. 21 and 22:

(21)

(22)

The sonic velocity, a, is calculated based on the pressureprofile determined at the previous step. A similar procedure isfollowed for the interpolation of the fluid velocity profile.

H (S) = H (C) + H (B) – H (C) a∆t ∆ x

H (R) = H (C) + H (A) – H (C) a∆t ∆ x



0

0

5

10

15

20

25

14 28 42

2.0 s

0.2 s

1.0 s

1.4 s

0.6 s3.0 s

4.0 s

56 70 84 98

Pipe Length, m

P r e s s u r e ,

b a r g

s Figure 4. Pressure profiles along the pipe length.

1 2 3 4 5 6

Distance, m

7 8

Gas Liquid

9 10

Separator

s Figure 3. Interface model for separator and downstream piping.

0

0

5

10

15

20

25

14 28 42

2.0 s

0.2 s

1.0 s

1.4 s

0.6 s

3.0 s

4.0 s

56 70 84 98

Pipe Length, m

F l l u i d V e l o c i t y ,

m / s

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

120 24 36 48 60

Pipe Length, m

T i m

e s ,

s

s Figure 6. Position of the interface during the event.

s Figure 5. Velocity profiles along the pipe length.



Boundary conditions

Boundary conditions here refers to those conditions at theend section of a pipe segment. At either end of a pipeline,

only one of the two equations, C+ or C-, is available, in thetwo unknowns, H P and V P (head and velocity). For a left-hand boundary, the C- curve holds, and for a right-handboundary, the C+ curve is valid. An auxiliary equation isneeded for each case that specifies H P and V P, or some rela-tionship between the two, so that the equations can be solvedfor the two unknowns.

Interface model

The interface model establishes the boundary conditionsat the interface where the gas is injected in the line owing tothe loss of liquid level in the upstream separator, and the liq-uid mass flowing along the pipe (Figure 3). The model evalu-

ates the pressure at the gas/liquid interface, while consideringthat the gas phase behaves as a perfect gas. If desired, correc-tions for gas compressibility can be introduced. The pressureis supposed to be uniform in the whole gas volume down-stream of the control valve. Its variation over time is evaluat-ed by calculating the total gas moles that have entered thepipeline from the loss of the liquid level, and the total volumeavailable for the gas due to the displacement of the interfaceup to the time-step being considered.

The calculation starts from steady-state conditions, so theinitial velocity of the interface is the bulk velocity of the liq-uid in normal operation. The model is the same as wouldapply for an upstream reservoir with pressure variation, only

the boundary conditions apply to a mobile section, the inter-face. The location of the interface is calculated at each time-step, and the boundary conditions are applied at the pipe’slongitudinal section that corresponds to the distance traveledby the interface from the start of the integration up to the cur-rent time-step. The boundary conditions are applied to thesubsequent section only after the interface has moved for thefull ∆ x length.

Pressure (head) and flowrate (velocity) are calculated forthe liquid along the pipeline. The pressure is assumed to beequal to the gas pressure at interface, and is the same for allsections of the pipeline that lay upstream of the current posi-tion of the interface. As the position of the interface moves,

the volume available for the gas increases. The gas pressureis calculated based on the total gas moles in the pipeline up tothe current time-step, and on the current volume.

Gas rateThe rate of gas entering the pipeline is calculated based on

the normal operating pressure in the separator, the normal gascharacteristics (molecular weight, compressibility factor, spe-cific heat ratio), and the operating pressure downstream of the control valve. This pressure is initially assumed to be thesteady-state value; subsequently, the pressure is calculated ateach time-step. It is assumed that the loss of liquid level inthe separator occurs with the control valve blocked in under

normal operating conditions. This implies that the valvemaintains a constant flow coefficient, C V , corresponding tothe one required to attain the design liquid flowrate at the

normal (steady-state) ∆P.Equations 23 to 26 (as reported in the sizing manual of a

major control valve supplier (3)) are used to characterize theflow through the control valve. Since the pressure piping ge-ometry factor, F P, appears in both equations, it can be as-sumed to be equal to unity without affecting the accuracy of the calculation. The critical pressure ratio may be estimatedfor a real gas by Eq. 27:

(23)

(24)

Y = 1 –[ x /(3F k X T )] (25)

F k = k /1.40 (26)

(27)

The flow will remain critical and will only depend upon

the upstream pressure, as long as the ratio between thedownstream and the upstream pressures stays lower than theabove value. The gas entering the pipeline at each time-stepis calculated by computing the gas flowrate through thevalve with the steady-state valve C V , the normal operatingupstream pressure (separator pressure), and the downstreampressure calculated for the gas space at the previous step.The initial pressure is assumed to be the steady-state operat-ing pressure downstream of the control valve in liquid ser-vice operation. The operating valve coefficient, C V , is com-puted on the basis of the selected steady-state liquidflowrate, and the valve is considered to maintain the samecoefficient throughout operation. This coefficient is used at

each step to compute the gas flowrate.The volume of pipeline made available for the gas during

the time step ∆t is calculated as the product of the liquidflowrate at the interface (m3 /s) times the duration of the time-step(s). This volume is added to the total volume displacedby the gas in the previous steps, and the pressure is calculatedby applying the ideal gas law to the total gas moles occupy-ing the volume. At each integration step, the pressure down-stream of the valve is calculated by converging on the gasflowrate via the secant method. The pressure values (poles)assumed to initialize the computation, Pa and Pb, are selectedas the extreme values of the possible range: Pa = Psep (pres-sure downstream of the valve equal to the upstream separator

Pc / P1 = 2k + 1

k k – 1

= X T

C V , gas =W

94.8F PPV Y T 1 Z

X P M

C V , liq = W

27.3F P P1 – P2 γ




pressure, which implies zero flow across the valve) and Pb =0 (pressure downstream of the valve equal to zero, which im-plies maximum flow across the valve). At each step, the pre-viously calculated value of the pressure is taken as a new se-cant pole, substituting the previous pole (P = Psep in the ini-tial step), until the values calculated in two subsequent cycles

are within a given tolerance (fixed at a relative error of 10–4

).

Example and insights gained

A typical example is presented that evaluates the pressureprofiles in the letdown line for a raw condensate letdown cir-cuit from a methanol synthesis loop. Typical conditions se-lected are reported in Table 1. Figures 4 and 5 show the pres-sure and velocity profiles in the letdown piping circuits, eval-uated at different times after the gas breakthrough. Figure 6traces the position of the interface as a function of time, dur-ing the displacement of the initial fluid by the injected gas.Parameters for these three figures are 3% flash and 60 m 3 /h.

The study was performed for various different gas vol-

ume-fractions in the liquid downstream of the control valve(as calculated at steady-state conditions, before gas break-through and surge occurrence), and different initial flow con-ditions. The influence of these parameters on the peak valueof the pressure is summarized in Table 2. The following gen-eral conclusions can be drawn:

• The calculated pressure and velocity profiles at varioustime intervals confirm the intuitive expectations: the presenceof a larger gas fraction dampens the pressure surge, and re-duces the speed of propagation of the pressure front. Also,the maximum fluid velocity is reduced with respect to lowergas fractions.

• The maximum pressure generally is reached immediate-

ly upon loss of level, and propagates with a step profile atsonic speed along the pipe. When the whole pipe is pressur-ized, a gradual variation, caused by friction losses, is estab-lished between the interface front and the pipe outlet. Theprofile becomes steeper as the fluid is accelerated by thepushing action of the gas.

• Only for large, initial gas-volume-fractions does thepressure slightly increase during propagation. This can be ex-plained as due to a slowdown of the interface displacementspeed due to the increase of fluid density caused by compres-sion of the gas fraction.

• The flow velocity of the fluid, after the propagation of the pressure wave from the interface to the pipe outlet, in-creases gradually, with a bulk motion of the fluid in the pipe,and reaches its maximum value when the interface reachesthe pipe outlet. The total displacement of the fluid occurs in afew seconds as the fluid velocity reaches high values.

• Maximum caution in design appears to be required incases such as high-pressure gas solvent treating, due to the

high density of the liquid and the relatively low amount of gasbeing released by the solvent in the letdown process. Thesefactors tend to involve higher pressures and larger thrusts onsupports, due to larger changes in density at the interface.

Computer program

A listing of a BASIC computer program is available onthe author’s web page at http://web.tiscali.it/Ancihome. CEP



GIANNI ANCI is a founder and managing director of EPSI, a process

consulting company in Rome, Italy (E-mail: [email protected]). He has

nearly 30 years of experience in process synthesis, design and

engineering. He is the author of Italian Patent No. 1276517, “Simultaneous

Production of Aviation Jet Fuel and Low Sulphur Gasoil by Hydrotreatment.”

His current commitments are with Technip Italy as process and engineering

manager in project management support contracts in Argentina for LNG

recovery at Compañia MEGA and in a methanol plant for Repsol-YPF. He is a

graduate of Rome Univ., Italy, and a chartered professional engineer.

Literature Cited

1. Wylie E. B., et al., “Fluid Transients in Systems,” Prentice Hall, En-

glewood Cliffs, NJ (1993)

2. Swaffield & Boldy, website: www.iteract.cam.ac.uk/wh/SWAFFIELD3. “Control Valve Sizing and Selection Handbook,” Masoneilan Co., Bul-

letin OZ 1000 (June 1994) (now Dresser Flow Control, Avon, MA).

Table 2. Influence of parameters on maximum peak pressure.

Maximum Pressure Developed in Letdown Circuit, barg

% Gas volume downstream control valve

0.5% 3% 15%

20 m3 /h 18.15 13.94 10.43

60 m3 /h 28.75 21.76 16.69

100 m3 /h 35.90 27.56 20.82

Initial liquidflowrate

Table 1. Data for methanol example.

Parameter Value

High-pressure separator pressure, barg 80

Low-pressure flash vessel pressure, barg 5

Liquid density, kg/m3 800Liquid viscosity, cP 0.6

Liquid bulk modulus, kg/m2 2 E+07

Volume fraction of gas downstream control valve 0.005–0.15

Liquid flowrate before loss of level, m3 /h 20–100

Gas molecular weight 4

Gas specific-heat ratio 1.4

Pipe characteristics

Dia., mm 154

Thickness, mm 7

Material Carbon steel

Roughness, mm 0.05

Modulus of elasticity, kg/m2 2 E+10

Total length downstream valve, m 100

sizing letdown line for press surge

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