dynamic depressuring

On the Modeling of Vessel Depressuring Using HYSYS 1.1 Dynamics

INTRODUCTION

The need to model vessel depressuring can be seen in the design and operation of vessels at very low temperatures during emergency shut down (ESD), where the use of special design materials maybe required. Specifically, we consider the instant the maximum allowable working pressure of a vessel is exceeded as defined in Sections 3.15.3 and 3.19.1 API 521 (1) under emergency conditions.

In this work, a model of a single depressuring vessel and its relief device is presented under adiabatic conditions. A comparison of the results obtained is made to HYSIM Depressuring Utility, an accepted method of solution for top blowdown depressuring analysis (2).

THEORY

For a closed system, consider the first law of thermodynamics,

(1) Energy transfer from the surroundings into a system = Energy accumulation in the system

(2) The change in internal energy of a closed system is described by the state function,

where,

U internal energy of a system

H enthalpy of a system

PV work done by a system

In the following model development we account for heat effects of a vessel wall on its bulk fluid. As well, we consider the expansion of the fluid in the vessel resulting in work done by the system (fluid) on the vessel walls. Although work energy is generally excluded in energy balance equations, this cannot be done here because of the need for accurate wall temperature predictions.

BRIEF PROBLEM DESCRIPTION

Consider a single insulated vessel with a two phase fluid initially present in the vessel at the instant of emergency shut down (ESD). The vessel is de-inventoried through a relief device and the influence of piping is not considered. The vessel and valve details are given in Appendix A.

HYSIM SIMUALTION SETUP

(See Appendix A)

Page 1 of 16On the Modeling of Vessel Depressuring Using HYSYS 1.1

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HYSYS SIMUALTION SETUP

Vessel Energy Balance

In general we have for a HYSYS dynamic vessel,

(3) Energy Flow Into Vessel - Energy Flow Out of Vessel = rate of change of energy in a vessel

so that we get,

(4)

Now consider the depressuring of a vessel where the feed flow is cutoff. Also, a block valve prevents the flow of liquids downstream and the vessel contents are vented through a relief device located downstream of the vessel. We need to modify the energy balance eq. (4) to account for:

1. wall effects 2. work of the expanding fluid on the vessel wall

We then write,

(5) Energy Flow Out of Vessel + Wall Effects + PV Work of Expanding Fluid = rate of change of energy of fluid in vessel

Assuming thermodynamic equilibrium at each time step,

(6)

Using the gas law with compressibility z, we can write,

(7)

As was done by Montgomery (3), substitute the third term in eq. (6) with,

(8)

we then get,

(9)

where R is 1.986 ft-lb/Btu.

Using a spreadsheet and transfer function to delay r by one time-step, solve the derivative d(rT)/dt numerically. Add work energy (PV) term to vessel Q (energy input). The HYSYS spreadsheet calculations are,



Energy Balance for the Vessel Wall

As was done by Key and Henley (4), model vessel wall temperature changes by noting vessel energy input Q can be modified using a spreadsheet, then account for rate of change of wall temperature numerically. Use a transfer function to delay the wall temperature by one time step for numerical solution of the derivative dTwall /dt. Therefore for the wall we can write,

(10) Energy transfer from wall = rate of change of energy in the wall

(11)

Add UA(Twall-Tbulk) to Q. The spreadsheet calculations look like,

Modeling the Relief Device

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The flow rate through a relieving device can be described by equations for supersonic or subsonic flow. However, the valve rate is generally both supersonic and subsonic, especially when multiple vessel depressuring is considered and the resulting backpressure effects vary significantly.

Typically, the Masonellan formula for choked flow best describes the actual valve rate because of its ability to correct for backpressure. Here we use the Masonellan formula, however any equation which adequately describes the actual valve rate can be used. The Masonellan equation is,

(12)

Backpressure correction is given by,

(13)

and,

(14)

If Y>1.5, Yf is set to 1.0. Here Yf becomes important as the system pressure approaches the downstream pressure. Cf is dependant on the valve type.

There are two ways to model the Masonellan equation in a HYSYS flowsheet model:

1. As was done by Tassone and Duque (5), equate the Masonellan formula eq. (11) for choked flow to HYSYS rate equation (6) given by,

(15)

and find Cmax,

(16)

In essence we size the existing HYSYS control valve for maximum flow under choking conditions. The valve is kept wide open (100%) and here the downstream pressure is set to 1 atm. The valve rate is now a function of upstream pressure only. This approach gives good results, is the easiest to setup and allows the user (if he chooses) to design a pressure relief valve (PRV) performance curve using a P-only controller.

2. Using a control valve for relief device as was done by Cassata et al. (7) and a PI-controller, at each time step, calculate the valve rate using the Masonellan formula in a spreadsheet and use this rate as a new setpoint SP (cascaded) for flow controller. This approach gives the best results. Here, we overwrite the existing HYSYS control valve equation eq. (14) with our own and regulate the flow through the control valve based on the rate determined by the Masonellan rate formula. Results presented here correspond to method 2. The spreadsheet



below shows the parameters and formulae used for these calculations,

RESULTS

Comparison to HYSIM 2.61 Depressuring Utility

HYSIM 2.61 depressuring utility is generally considered to an accepted method of solution for depressuring analysis (2) and was used in this study to compare HYSYS results.

Figs 1-6 show the temperature, pressure and vent rate profiles obtained from HYSYS and HYSIM simulators. As can be seen, the trends or qualitative behavior of the results for the two simulators compare favorably. Fig. 7 shows the heat transfer from wall to bulk fluid using HYSYS and is compared to Table 1, results from HYSIM. Here, as above, agreement between the two simulators is good throughout the entire depressuring period.

Metal Wall Temperature

As given in API 521 Section 3.15.3, when the maximum allowable working pressure (MAW) is exceeded, a relieving device is operated to ensure overpressure protection. During emergency or planned pressure let-down, the relief device is opened to fail-open position. During this period the fluid temperature becomes very cold causing a corresponding drop in the wall temperature. Because the possibility for vessel rupture, the design engineer maybe faced with using special and sometimes costly design materials. In other design situations, such as revamp, again the design engineer is faced with having to replace pieces of equipment. The accurate prediction and modeling of wall temperatures is important and may result in improved materials design specifications.

Here we examine the effect of the heat transfer coefficient U on the wall temperature. From Figs 8-15, it can be seen, by increasing the heat transfer coefficient from 100 to 5000 Btu/hr-ft2-F, the overall bulk fluid temperature is warmer and the wall temperature colder. Thus, a colder fluid



temperature doesnt necessarily mean a colder wall temperature and when one considers a closed system with fixed initial energy content, in a given period, wall temperatures are then determined by the energy transfer from the wall to the fluid or the rate at which the wall heats the fluid. Moreover it is observed, in each case, the wall temperature does not change significantly, even for large U, although the fluid temperature does. For design purposes, very cold fluid temperatures encountered during depressuring may not mean the use of special materials in the design of pressure vessels.

REFERENCES:

1. API 521 Guide for Pressure-Relieving and Depressuring Systems, Part I Design, 4th Edition, 1976.

2. Szczepanski, R., "Simulation Programs for Blowdown of Pressure Vessels," IChemE SONG Meeting 12 April 1994.

3. Montgomery G., "How to Predict Temperatures during Gas Depressuring," Hydrocarbon Processing, pp. 85-88, April 1995.

4. Key C. and D. Henley, "Multiple Vessel Depressuring Using HYSYS," presented at 1996 Hyprotech International Technology Conference.

5. Tassone V. and C. Duque, "On the Modeling of Tower Relief Dynamics Using HYSYS," presented at 1996 Hyprotech International Technology Conference.

6. Franks, R.G.E., "Mathematical Modeling in Chemical Engineering," Wiley, New York, 1967.

7. Cassata, J. R., S. Dasgupta and S. L. Gandhi, "Part 1 Modeling of Tower Relief Dynamics," Hydrocarbon Processing, pp. 71-76, October 1993.

APPENDIX A

Simulation Details:

Reference Case: HYSIM Users Guide p. 9-76, Adiabatic Mode example.

The contents of vessel at t=0s is:

Stream TANK2 Temp F 75 Press psia 600 Methane mole_frac 0.1779 Ethane mole_frac 0.1983 Propane mole_frac 0.1925 i-Butane mole_frac 0.1351 n-Butane mole_frac 0.1492 i-Pentane mole_frac 0.0719 n-Pentane mole_frac 0.0750 (temp and press given in manual is in Error)

Operation:

Vessel Volume 1.6e3 ft3 Liquid Volume 1.3e3 ft3 Depressuring Time 1200s (20 min)

Heat Flux:



Wetted area 500 ft2 Vessel Mass Cp 25 Btu/lb-f U_Overall 0.001 Btu/hr-ft2-F

PSV Valve:

C1=38.61, C2=0.5, Cv=50, Cf=1.0 (Masonellan eq.), Pback=14.7 psia

For HYSIM Simulation

Final Pressure 14.7 psia Isentropic efficiency 50% Press steps 50

Fig 1.

Fig 2., U=0.001 Btu/hr-ft2-F, isentropic eff.= 0.5

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Fig 3.

Fig 4.

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Fig 5.

Fig 6.

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Fig 7.

Fig 8. U=100 Btu/hr-ft2-F, isentropic eff.= 0.5

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Fig 9. U=100 Btu/hr-ft2-F

Fig 10. U=500 Btu/hr-ft2-F, isentropic eff.=0.5

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Fig 12. U=1000 Btu/hr-ft2-F, isentropic eff. =0.5

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Fig 14. U=5000 Btu/hr-ft2-F, isentropic eff. =0.5

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HYSYS PFD

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