Coker A.K. Fortran Programs for Chemical Process Design, Analysis, and Simulation

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Instrument Sizing 377

Table 5-6A

Applicability of Recommended Vent Sizing Methods

Leung's Method

1. The overpressures are limited in

the range 0-50% of absolute set

pressure, i.e., 0 < AP _< 0.5Ps

2. The method includes the mass

unit vent flow capacity per unit area,

G. This allows the user to select any

applicable vent capacity calculation

method.

3. The heat evolution rate per unit

mass, the vent capacity per unit area,

physical properties (e.g., latent heat of

fluid, specific heat and vapor/liquid

specific volumes) are constant.

4. A hand calculation method that

can be used to take account of two-

phase relief when the materials in

the vessel are "natural" surface

active foamers.

5. The methods use drift-flux level-

swell calculation models to take

account of more vapor being in the

inlet stream to relief device than the

average for the vessel.

6. Methods are given for the bubbly

and churn-turbulent flow regimes

within the vessel.

Fauske's Method

The overpressures are limited in the

range of 10-30% of absolute set

pressure, i.e., 0 < AP < 0.3P S. It

assumes that flow is turbulent and

that the vapor behaves as an ideal gas.

The method incorporates the

equilibrium rate model for vent flow

capacity when friction is negligible.

In addition, a correction factor is

used for longer vent lines of constant

diameter and with negligible static

head change.

It allows for total vapor-liquid

disengagement of fluids that are not

"natural" surface active foamers.

To account for disengagement, the

vessel void fraction at disengage-

ment should be evaluated (i.e., the

point at which the vent flow would

cease to be two-phase and start to be

vapor only).

The method is potentially unsafe if

early disengagement (before the

pressure would otherwise have

turned over during two-phase

venting) occurs.

The criterion for safe use to take

account of disengagement is

GAhfg vf

V Vfg(l _ (XD)2 "

However, when disengagement is

not accounted for, then ot D - 1.0, and

the above equation is not required.

378 Fortran Programs for Chemical Process Design

F 2 - flow reduction factor for turbulent flow

G- mass flux through the relief

G~ - mass vent capacity per unit area, kg/mZs

g~ - dimensional gravitational constant, 1.0 kg m/N s 2

hfg - latent heat, J/kg

AH v - heat of vaporization of the fluid, J/kg

k- isentropic coefficient

M - mass of liquid in vessel, kg

M o - initial mass of liquid in vessel, kg

m~- mass of the sample in the RSST, kg

Pm-

maximum allowable pressure during venting, bar

PMAP-

maximum allowable vessel pressure, psia

P~ - relief set pressure, psia

P~ - pressure in the upstream vessel, N/m2abs

AP - overpressure, bar

AP~ - difference between the (reduced) set pressure and the maxi-

mum pressure allowable, N/m 2

AP 2 - pressure difference, N/m 2

dP/dt - maximum rate of pressure rise in the test vessel, bar/s

dP/dt - measured maximum rate of pressure rise in the RSTT, lb/in 2

min

Qg- volumetric gas generation rate of temperature and pressure

in reactor during relief, m3/s

Qgl- maximum rate of gas generation, m3/s

q~ - self-heat rate, W/kg

q - rate of heat production (W/kg) at the relief set pressure, or an

average value between the relief set pressure and the maxi-

mum permitted pressure if this is more than 120% of the re-

lief set pressure

T - temperature corresponding to relief actuation, K

T s - absolute saturation temperature of the fluid at the set pres-

sure, K

AT - temperature rise corresponding to the overpressure, K

AT~- temperature difference between that at the maximum pres-

sure allowable, and that at the redefined set pressure, k.

Atv - venting time

(dT/dt)~- rate of temperature rise corresponding to the relief set pres-

sure, K/s

V - reactor volume, m 3

= total vessel volume, m 3

Vfg - difference between vapor and liquid specific volume, m3/kg

Instrument Sizing 379

vf = liquid specific volume, m3/kg.

V G = specific volume of gas, m3/kg.

V L - specific volume of liquid, m3/kg.

W = required relief rate, kg/s

x = mass fraction of vapor at inlet

cz = void fraction in vessel

~D - vessel void fraction corresponding to complete vapor disen-

gagement

~o = initial free board volume

9 = density, kg/m 3

9f = liquid density, kg/m 3

Pr =

density of the reactants, kg/m 3

PROBLEMS AND SOLUTIONS

Problem 5.1

Orifice Sizing for Liquid Flow

Calculate the size of an orifice for the bore of a flange-tapped orifice

required to measure 12.84 ft3/min of gasoline in a 2-inch schedule 80 pipe.

Design data:

Internal pipe diameter (I.D.) = 1.939 inches

Normal differential pressure = 64 in H20

Flowing temperature = 80.5~

Density of gasoline = 42.26 lb/ft 3

Viscosity of gasoline = 0.6 cP

Assuming the coefficient of discharge C D - 0.62

F a - 1.0

Orifice Sizing for Gas Flow

Determine the size of an orifice to give a full-scale reading of 20 in.

H20

for 0.25 lb/s flow of gas through a 4-inch (I.D = 4.026) schedule 40

pipe. The upstream gas density is 0.075 lb/ft 3, viscosity of the gas is

0.0219 cP, the specific heat ratio, k, is 1.4, and the upstream pressure is

14.7 psi.

Solutions

The computer program PROG51 calculates the orifice size for liquid

and gas services. Tables 5-7 and 5-8 show the input data and results of

the liquid and gas orifice calculations. For the liquid service of gasoline,

380

Fortran Programs for Chemical Process Design

Table 5-7

Orifice Sizing for Liquid Flow: Program Inputs and Outputs

DATA51.DAT

LIQUID

INCH-H20

1.939 64.0

42.26 12.84 0.6

ORIFICE SIZING FOR LIQUID FLOW

TYPE OF FLOW:

TYPE OF PRESSURE DROP:

INTERNAL PIPE DIAMETER,

inch:

ORIFICE PRESSURE DROP, inch-H20:

ORIFICE PRESSURE DROP,

psi:

LIQUID DENSITY, ib/ft^3:

LIQUID VISCOSITY, cP:

LIQUID VOLUMETRIC RATE, ft^3/min.:

LIQUID MASS RATE, ib/sec.:

ORIFICE SIZE,

inch:

REYNOLDS NUMBER:

LIQUID

INCH-H20

1.939

64.000

2.308

42.260

.6000

12.840

9.044

1.501

176582.

Table 5-8

Orifice Sizing for Gas Flow: Program Inputs and Outputs

DATA51.DAT

GAS

INCH-H20

4.026 14.7

1.4 0.075

0.0219

20.0 0.25

ORIFICE SIZING FOR GAS FLOWS

TYPE OF FLOW:

TYPE OF PRESSURE DROP:

INSIDE PIPE DIAMETER,

inch:

UPSTREAM PRESSURE,

psia.:

ORIFICE PRESSURE DROP, INCH-H20:

ORIFICE PRESSURE DROP,

psi.:

SPECIFIC HEAT RATIO (k=Cp/Cv):

UPSTREAM FLUID DENSITY, ib/ft^3:

GAS VIscOsITY, cP:

GAS FLOW RATE, ft^3/min.:

GAS MASS RATE, ib/sec.:

EXPANSION FACTOR:

ORIFICE DIAMETER,

inch:

FULL SCALE GAS FLOWRATE, ib/sec.:

REYNOLDS NUMBER:

GAS

INCH-H20

4.026

14.700

20.000

.721

1.4000

.075

.0219

200.000

.250

.0409

1.811

.25O

64410.

the orifice diameter at the liquid flow rate of 12.84 ft3/min and pipe

diameter of 1.939 in. is 1.501 in. For the gas flow rate of 0.25 lb/s and

pipe internal diameter of 4.026 in., the orifice size is 1.811 in.

Problem 5.2

( 1 ) Determine the control valve capacity coefficient, C v, for the follow-

ing liquid flow conditions"

Instrument Sizing 381

Flow- 400 gpm P1- 150 psia

P2-

125 psia SpGr~- 1.0

(2) Calculate the control valve coefficient for gas flow under the fol-

lowing conditions"

Flow - 1200 ft3/h P~ - 550 psia P2 - 150 psia SpGrg - 0.6 T - 100~

(3) Calculate the steam flow through a valve with a capacity coefficient,

C v - 75, under the following conditions"

~ superheat - 0 P~ - 70 psia

P2 -

60 psia

Solutions

The computer program PROG52 calculates the control valve capac-

ity coefficient (Cv) or the maximum flow rate that will pass through the

valve. Table 5-9 shows the input data and results of the control valve calcu-

lations for liquid, gas, and steam conditions. For the liquid service, at a flow

rate of 400 gpm and the control valve pressure drop of 25 psi, the control

valve capacity coefficient (Cv) is 80. The gas service with a flow rate of

1200 ft3/h, and control valve pressure drop of 400 psi gives the control

valve capacity coefficient (Q) of 0.059. For the steam condition of capac-

ity coefficient (Q) = 75, and the control valve pressure drop of 10 psi, the

maximum steam flow rate through the valve is 5511.4 lb/hr.

Problem 5.3

(1) In a biological plant, ammonia is used to control the pH during

fermentation to obtain maximum yield of the product. For this purpose,

liquid ammonia is vaporized by passing steam through a coil in a vapor-

izer. A relief valve from the vaporizer is set at a pressure of 290 psig. If

the relieving rate of ammonia vapor is 620 lb/hr, determine the size of

the relief valve required to relieve ammonia vapor during an emergency.

Design data are:

Ratio of specific heat capacities

(Cp/Cv) -

1.33

Molecular weight of ammonia

Critical Pressure, Pc

Critical Temperature, T c

Constants in Antoine's equation: A

= 17.03

= 111.3 atm

= 405.6 K

- 16.9481

= 2132.5

= -32.98

382 Fortran Programs for Chemical Process Design

Table 5-9

Control Valve Sizing for Liquid, Gas and Steam

Conditions- Program Inputs and Outputs

DATA52.DAT

LIQUID

4OO.0 0.0

150.0 125.0 1.0

GAS

1200.0 0.0

550.0 150.0 0.6 i00.0

STEAM

75.0

70.O 6O.O 0.0

CONTROL VALVE SIZING FOR LIQUID SERVICE

****************************************************************************

FLUID SERVICE: LIQUID

LIQUID FLOWRATE, gpm: 400.00

LIQUID SPECIFIC GRAVITY: 1.000

INLET PRESSURE, psia: 150.000

OUTLET PRESSURE, psia: 125.000

CONTROL VALVE PRESSURE DROP, psi: 25.000

CONTROL VALVE CAPACITY COEFFICIENT: 80.000

CONTROL VALVE SIZING FOR GAS SERVICE

***************************************************************************

FLUID SERVICE: GAS

GAS FLOW RATE, ft^3/hr.: 1200.000

SPECIFIC GRAVITY: .600

INLET PRESSURE, psia: 550.000

OULET PRESSURE, psia: 150.000

CONTROL VALVE PRESSURE DROP, psi: 400.000

INLET TEMPERATURE, oF: i00.000

CONTROL VALVE CAPACITY COEFFICIENT: .059

CONTROL VALVE SIZING FOR STEAM SERVICE

***************************************************************************

FLUID SERVICE: STEAM

CALCULATED

STEAM FLOW RATE, ib/hr.: 5511.352

DEGREE OF SUPERHEAT, oF: .000

INLET PRESSURE, psia: 70.000

OUTLET PRESSURE, psia: 60.000

CONTROL VALVE PRESSURE DROP, psi: i0.000

CONTROL VALVE CAPACITY COEFFICIENT: 75.000

(2) A bellow style pressure relief valve is required to protect a vessel

containing an organic liquid. The required relieving capacity is 310 gpm.

Inlet temperature is 170~ Set pressure is 100 psig. Allowable over-

pressure is 25%. Built-up back pressure is 25 psig. Specific gravity is

1.45 and viscosity is 3,200 cE Determine the orifice size of the valve.

The correction factors are:

K v-l.0 K w-0.925 K d-0.65

Instrument Sizing 383

(3) Calculate the required area for the relief valve for a horizontal, non-

insulated storage tank exposed to fire and containing liquid vinyl chlo-

ride monomer. The tank dimensions are shown in Figure 5-14, with the

design pressure of 100 psig. Discharge from the relief valve will be

vented to a gas holder operating at 0.5 psig. A 20% accumulation is

assumed over the design pressure. Average inventory of the tank con-

tents will equal 75% of the vessel's inside diameter.

Solutions

The computer program PROG53 sizes relief valves for vapor, steam,

liquid, air, and fire conditions. Tables 5-10 and 5-11 show the input data

and results of the vapor and liquid services. The results of the relief

valve sizing of an ammonia vaporizer at the relieving rate of 620 lb/hr

and a set pressure of 290 psig, indicate that the calculated orifice area is

0.030 in 2. The nearest standard orifice size is D with an orifice area of

0.110 in 2. The relief valve calculations for the organic liquid at the

relieving rate of 310 gpm and a set pressure of 100 psig give the calcu-

lated orifice area of 2.233 in 2. The nearest standard orifice size is L,

with an orifice area of 2.853 in 2.

[ .... 20ft : :[

Valve

Vent to

gas holder

Uninsulated

tank

10ft. Grade

Figure 5-14. A horizontal, non-insulated storage tank.

Table 5-10

Relief Valve Sizing for Vapor Service" Program Inputs and Outputs

DATA53.DAT

VAPOR

620.0 290.0

i0.0 133.4

0.84 17.03

1.31

VAPOR RELIEF VALVE SIZING

BASIS OF SELECTION:

REQUIRED VAPOR RATE, ib/hr.:

VALVE SET PRESSURE, psig:

PERCENTAGE IN OVERPRESSURE, (%):

UPSTREAM FLUID TEMPERATURE, DEG. F:

COMPRESSIBILITY FACTOR:

MOLECULAR WEIGHT OF VAPOR:

RATIO OF SPECIFIC HEATS OF FLUID:

GAS CONSTANT DETERMINED BY RATIO OF Cp/Cv:

CALCULATED VALVE ORIFICE AREA, in^2:

NEAREST STANDARD ORIFICE AREA, in^2:

NEAREST STANDARD ORIFICE SIZE:

PREFERRED VALVE BODY SIZE: (IN-OUT) inches:

MAXIMUM VAPOR FLOWRATE WITH STD. ORIFICE, Ib/hr.:

REACTION FORCE, ib:

VAPOR

620.

290.000

i0.000

133.400

.8400

17.030

1.310

347.913

.030

.ii0

1-2

2302.

28.

Table 5-11

Relief Valve Sizing for Liquid Service" Program Inputs and Outputs

DATA53.DAT

LIQUID

310.0 i00.0

25.0 1.45

3200.0 1.0

0.925 0.65

RELIEF VALVE SIZING FOR LIQUID

BASIS OF SELECTION:

LIQUID FLOWRATE, US gpm:

VALVE SET PRESSURE, psig:

BACK PRESSURE ON VALVE, psig:

FLUID SPECIFIC GRAVITY:

FLUID VISCOSITY,

cP:

VISCOSITY CORRECTION FACTOR,

Kv:

BACKPRESSURE CORRECTION FACTOR, Kw:

EFFECTIVE COEFFICIENT OF DISCHARGE, Kd:

CALCULATED VALVE ORIFICE AREA, in^2:

NEAREST STANDARD ORIFICE AREA, in^2:

NEAREST STANDARD ORIFICE SIZE:

PREFERRED VALVE BODY SIZE, (IN-OUT)

inches:

MAXIMUM LIQUID FLOWRATE WITH STD. ORIFICE, gpm:

VISCOSITY CORRECTION FACTOR:

REYNOLDS NUMBER:

CALCULATED VALVE ORIFICE AREA, in^2:

NEAREST STANDARD ORIFICE AREA, in^2:

NEAREST STANDARD ORIFICE SIZE:

PREFERRED VALVE BODY SIZE, (IN-OUT)

inches:

MAXIMUM LIQUID FLOWRATE WITH STD. ORIFICE, gpm:

LIQUID

310.

i00.000

25.O0O

1.450

3200.0000

1.0000

.9250

.650

1.772

1.838

3-4

322.

.794

290.

2.233

2.853

3-4 or 4-6

396.

384

Instrument Sizing 385

Fire Relief Valve Sizing

The wetted surface for the vessel equals the wetted area of the two

heads plus that of the cylindrical section. Thus:

Aw _- 27t(yD~ + D2L//;

where y = the fraction of the vessel's internal diameter (ID) that is equiva-

lent to average liquid inventory.

D~ = diameter of circular blank from which head is shaped (D 1 will

depend on the type of head).

D 2 = y times the ID of the tank.

L = tangent-to-tangent length of the cylindrical section.

Dl= llft

Therefore, the wetted surface area is"

A w -

2rt[(0.75)(11)] 2

+ rt(0.75)(10)(20)

A w - 578.15ft 2

The relieving temperature at the set pressure plus 20% accumulation

plus 14.7 psia = 135~ At this temperature, the latent heat of vaporiza-

tion is 116 Btu/lb. Molecular weight of vinyl chloride, M w = 62.5. Ratio

of specific heat capacities, k = 1.17. The critical properties of vinyl

chloride are:

Pc - 809 psia

T c - 313.7~

Pr -

P/Pc - 134.7/809 - 0.165

T r - T/T c - (135 + 460)/(313.7 + 460) - 0.77

From a compressibility factor chart, Z = 0.86. The rate of heat input due

to fire and flow rate of the vapor release can be determined by Equa-

tions 5-53 and 5-45. Table 5-12 gives the input data and results of vinyl

chloride monomer. The results show that the calculated relief valve ori-

fice area is 2.172 in 2. The nearest standard orifice size is L, with an

orifice area of 2.853 in 2.

386

Fortran Programs for Chemical Process Design

Table 5-12

Relief Valve Sizing for Fire Service- Program Inputs and Outputs

DATA53.DAT

FIRE

1.0 578.15

116.0 100.0

20.0 135.0

0.86 62.5

1.17

FIRE RELIEF VALVE SIZING

BASIS OF SELECTION:

ENVIRONMENTAL FACTOR:

WETTED SURFACE AREA OF VESSEL, ft^2:

LATENT HEAT OF VAPORIZATION, Btu/ib:

VALVE SET PRESSURE,

psig:

PERCENTAGE OF OVERPRESSURE, (%):

FLUID TEMPERATURE, DEG. F:

FLUID COMPRESSIBILITY FACTOR:

FLUID MOLECULAR WEIGHT:

RATIO OF SPECIFIC HEATS OF FLUID:

GAS CONSTANT DETERMINED BY RATIO OF Cp/Cv:

VAPOR RELIEF FLOW RATE, ib/h.:

CALCULATED VALVE ORIFICE AREA, in^2:

NEAREST STANDARD ORIFICE AREA, in^2:

NEAREST STANDARD ORIFICE SIZE:

PREFERRED VALVE BODY SIZE, (IN-OUT)

inches:

MAXIMUM VAPOR FLOWRATE WITH STD. ORIFICE

ib/hr.:

REACTION FORCE,

ib:

FIRE

1.000

578.150

116.000

I00.000

20.000

135.000

.860

62.500

1.170

334.173

33315.

2.172

2.853

3-4 or 4-6

43760.

271.

Problem 5.4

Determine the vent size for a vapor pressure system using the follow-

ing data and physical properties.

Reactor Parameters

Volume, V - 10 m 3

Mass, M - 8,000 kg

Vent opening pressure- 15 bara

= 217.5 psia

Temperature at set pressure T~- 170~

= 443.15K

Overpressure allowed above operating pressure- 10%

= 1 bar (105 Pa)

Material Properties

Specific heat, Cp- 3000 J/kg.K

Slope of vapor pressure and temperature curve dP/dT - 20,000 Pa/K