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April 2008 Full contents
Distillation column relief loads—Part 1 Compare conventional calculation methodology with dynamic simulation
P. L. Nezami, Jacobs Engineering, Houston, Texas Comments? Write:
[email protected] Estimating the relief rates for distillation columns is by far the most complex relief load calculation. The dynamic nature of distillation columns and compositional changes along the column height make it very difficult to accurately establish relief loads for various contingencies. Additionally, the inability of regular (steady-state) process simulation software to predict column behavior in a nonsteady-state condition forces design engineers to create analytical methods that by nature are conservative. This could result not only in oversized relief valves but also in unnecessarily large and costly flare systems, which in turn can jeopardize project viability. The enormous differences between distillation systems, such as column controls, types of condensers and reboilers, heating and cooling media, pumparounds and side reboilers, etc., make it impossible to create a universal method for all distillation columns. The suggested techniques are at best a series of general guidelines and criteria, set forth to provide directions to evaluate each individual case. Common methods. The two most prevalent shortcut techniques, which may or may not be conservative and generally used to estimate order of magnitude relief rates, are: Flash drum approach. This could be used to estimate the relief rate in a loss of cooling/condensing scenario. In this method, the feed stream is flashed at relieving pressure with additional heat input equal to the reboiler duty. Gross overhead vapor. This is usually used to establish a basis for the flare and flare header design at early stages in the projects, and it is the simplest way to roughly estimate relief loads. Although this method seems to be conservative for most cases, it has been argued that it could result in undersized relief valves.1 For better results, one must analyze relief scenarios in detail on a case-by-case basis. The most comprehensive conventional method is to estimate relief loads based on mass and energy imbalance (accumulation) in an upset condition. The bases and assumptions for this method are: 1. At relieving conditions, feeds, products and reflux compositions, as well as top-tray liquid and bottoms compositions, are unchanged. 2. The column trays are at vapor/liquid equilibrium at relief pressure. 3. Except for the feeds, all streams leaving and entering the column are at vapor/liquid
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equilibrium at relieving pressure. 4. Vapors may not be accumulated in the column (after the column reaches the relief pressure) and must leave the system via a relief valve. Liquids could accumulate in the system by the rise or fall of liquid levels. 5. Liquids can absorb heat whether they leave or stay in the system. 6. Credit may be taken for product sensible heat absorption when the feed enters the column below its bubble point at the relieving pressure. 7. The energy imbalance resulting from an upset is converted to mass (vapor) using top-tray liquid latent heat of vaporization. 8. The vapor distillate control valve, if applicable, stays at its position. Credit may be taken for vapor distillate unless its path is blocked. 9. The vapor portions of the feed streams, flashed adiabatically at relief pressure, directly contributes to the relief rate. 10. Credit may be taken for reboiler temperature pinch, if light materials do not reach the column bottom. 11. Any safety margin used in the actual design must be considered in the relief rate calculations. 12. The properties of the vaporized top-tray liquid at bubble point and relief pressure are used to size the relief valve. The relief rate can be defined as: W = WR + W F – WV – WC – WH where:
(1)
W = Relief rate WR = Reboiler and side reboiler load contributions WF = Feed vapor phase contributions WV = Vapor distillate credit WC = Condenser and pumparound credits WH = Liquids enthalpy imbalance.
Dynamic simulation. Nevertheless, the best available technique for distillation column relief rate calculation is dynamic simulation. Dynamic models use a set of mass and energy conservation equations that account for changes occurring over time. Unlike steady-state simulation, these equations include an additional accumulation term that is differentiated with respect to time. The accumulation rate of mass is: Mass flow into system – Mass flow out of system
(2)
And the accumulation rate of total energy is: Flow of total energy into system – Flow of total energy out of system + Heat added to system across the boundary + Heat generated by reaction – Work done by system on surroundings
(3)
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The inclusion of the accumulation term in the mass and energy conservation equations allows the dynamic model to rigorously calculate composition changes at each stage and to modify vapor/liquid equilibrium over time. It also allows integrations of column flowrates, pressures and temperatures with respect to time. The results lead to a much more accurate relief rate. Case study. A comparison between the results of the conventional method with those of the dynamic simulation for a typical distillation column in a loss of condenser scenario will be presented. Fig. 1 shows the flow diagram of the distillation column system under evaluation.
Fig. 1
Flow diagram for the distillation system.
In a loss of condenser scenario, the reflux drum liquid level drops causing the level control valve to close. Reflux continues at a constant rate until the drum runs dry. The feed continues at a constant rate since its pressure, upstream of the control valve, is higher than the relief pressure. With no liquid distillate product, the only place for light materials in the feed is the column bottoms; hence, no credit could be taken for reboiler temperature pinch. On flow control, the steam control valve opens wide and the reboiler chest pressure equalizes with the steam header pressure (a zero pressure drop is assumed across the control valve). Clean reboiler duty is used for both calculations. Conventional method. Table 1 is the summary of the stream properties and column parameters at normal and upset conditions. Stream properties in upset conditions were obtained by performing the following flash calculations on the basis of normal stream compositions:
Feed—adiabatic flash at relief pressure Vapor distillate—dew-point flash at relief pressure Liquid distillate—bubble-point flash at relief pressure Decant water—bubble-point flash at relief pressure Bottoms product—bubble-point flash at relief pressure.
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Based on the calculation results listed in Table 1: WR = 403,980 lb/hr WF = 0 lb/hr The vapor distillate pressure control valve at its normal position (normal Cv) can pass 9,128 lb/hr of the column overhead vapor at relieving pressure. WV = 9,128 lb/hr WC = 0 lb/hr WH = 179,992 lb/hr The relief rate would be the sum of the above calculated values:
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W = 214,860 lb/hr Dynamic simulation. A dynamic model was developed for the column. Fig. 2 shows the simulation flow diagram for it. The following parameters were set to generate the initial values of dynamic simulation variables:
The reboiler UA was set to clean UA value for a zero fouling factor on both sides. The reboiler chest pressure was adjusted to obtain normal reboiler duty. This emulates pressure drop across the steam control valve at steady-state conditions. The reflux drum and column bottom sump dimensions were set to actual values to simulate liquid level variations in a dynamic mode. The condenser was set to constant medium temperature mode.
Fig. 2
Dynamic simulation flowsheet.
The initial setting of dynamic parameters, such as reflux drum and column bottom sump dimensions, reboiler heating medium temperature, column tray hydraulics, etc., are part of the required data in steady-state simulation. The parameter values will be carried over to the dynamic simulation as initial variable values when the steady-state simulation is exported to the dynamic model In the dynamic model, the condenser failure was initiated after 10 min. of normal (steady-state) run. At the same time, the reboiler heating medium temperature was set to the steam header temperature to simulate a zero pressure drop across the steam control valve. The simulation was run for two hours, and the results were captured and recorded (Figs. 3–8).
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Fig. 3
Column overhead pressure for simulated run.
Fig. 4
Simulated stream flowrates.
Fig. 5
Temperature variations during the simulation.
Fig. 6
Reflux drum and bottom sump liquid levels during simulation.
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Fig. 7
Condenser and reboiler duties for dynamic model.
Fig. 8
Column relief rates for simulation.
Here are some highlights of the simulation results:
The overhead pressure starts to rise right after the upset was introduced. It peaks at 165 psig 12 min. later. Liquid distillate stops 5 min. after the condenser fails (this interval depends on the level controller parameters: proportional gain, integral time, derivative time, process variable and output ranges). The 5-min. duration, in this example, is based on the simulation's PID controller default parameters. Reflux continues for another 25 min. at normal flow rate, then practically stops. This is when the reflux drum dries out. The relief valve starts relieving 5 min. after the upset, exactly when liquid distillate completely stops. The relief rate peaks at about 161,200 lb/hr 12 min. after the upset and keeps at almost a steady rate for 16 min.. Then it drops for about 7 min. to 8 min. and reaches a new steady rate of about 122,000 lb/hr very close to the normal liquid distillate rate. The overhead temperature starts to increase at upset and, after about 6 min. to 8 min., it reaches a temporary stable condition. It stays steady so long as the relief rate is at its peak. As the relief rate drops, the overhead temperature rises again to its new maximum and stays constant through the rest of the simulation time. The vapor distillate rate increases to double the normal flowrate immediately after the upset. Its mass flowrate keeps rising slowly due to the change of overhead molecular weight and reaches its maximum value at the end of the simulation time. The vapor distillate rate is very comparable to the one calculated in the conventional method. Reboiler duty spikes to its maximum, right when the upset is initiated. It drops immediately and keeps flat through the 25 min. of maximum relief rate; then it drops again, this time, to its minimum steady level. The column reaches a new steady-state condition approximately 30 min. after the upset with a constant relief rate of 122,000 lb/hr.
The simulation results are based on hysteresis (opening and closing curves) of a typical relief valve in compressible fluid service. The relief valve hysteresis is presented in Fig. 9.
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Fig. 9
Relief valve hysteresis
The major advantage of dynamic simulation, over the conventional method, is the accuracy of calculated relief rates. The ability of the dynamic model to integrate simulation variables over time and to rigorously calculate various column parameters would result in much more realistic relief load values. Another advantage is engineering man-hours and project schedule time savings. Given that the conventional method requires a separate detailed analysis for each relief case, dynamic simulation can save a great deal of engineering time, since a single dynamic model can be used for all various relief scenarios. The third advantage of a dynamic model is that, for a great majority of the cases, the relief loads calculated by dynamic simulation are smaller than the ones calculated by using the conventional method. This could result in a considerable cost saving, particularly in cases where there are limitations in the flare system capacities. In the example, the difference is greater than 33%, which could even be higher (up to 41%) if, instead of a single large relief valve, two smaller ones were used. With multiple relief valves, the allowable accumulation pressure would increase to 116% of the design pressure and the combined relief loads would peak at 152,600 lb/hr. At the end it is worth mentioning that, if the conventional method relief loads are smaller than the ones calculated by dynamic simulation, one can be certain that the conventional method results would lead to an undersized relief valve. HP LITERATURE CITED 1 Bradford, M. and D. G. Durrett, "Avoiding common mistakes in sizing distillation safety valves," Chemical Engineering, July 9,
1984.
The author Piruz Latifi Nezami is a process engineering section manager with Jacobs Engineering in Houston, Texas. He holds a BS degree in chemical engineering from Sharif University of Technology in Tehran, Iran, and has more than thirty years of experience in the design and engineering of chemical, petrochemical and refining projects.
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Log off or Change user (SARA DAVIS) Subscribe to HP magazine! Advanced search Reader service request HPInformer: the new blog from Hydrocarbon Processing Letters to the editor from our January 2009 issue: The climate change debate rages on
May 2008 Full contents
Distillation column relief loads—Part 2 The conventional method is expanded and a series of guidelines are developed
P. L. Nezami, Jacobs Engineering, Houston, Texas Comments? Write:
[email protected] In the first part of this article, a comparison between the two methods for distillation column relief load calculations was made. In this part, the conventional method will be expanded and a series of guidelines to predict relief loads for distillation columns in upset conditions will be developed. The method presented here is based mainly on the mass and energy imbalance at upset conditions. This method relies heavily on detailed analysis of the contingencies that must be executed on a case-by-case basis. It also is based on several assumptions that simplify the complex behavior of distillation columns and make it possible to determine relief loads through a series of simple calculations and by using regular steady-state process simulation software. Basic assumptions. There are several suppositions that must be made to enable determining relief loads: 1. At relieving conditions, feeds, products and reflux compositions as well as top-tray liquid and bottoms compositions are unchanged. Note that for multi-feed columns this is valid only if all the feed rates, at relief conditions, vary proportionally to the normal rates. This method cannot be used if the said condition is not applicable. 2. The column trays are at vapor/liquid equilibrium at relief pressure. 3. Except for the feeds, all streams entering and leaving the column are at vapor/liquid equilibrium at relieving pressure. 4. Vapors may not be accumulated in the column after reaching relieving pressure and must leave the system via the relief valve. Liquids could accumulate in the system by means of rising and falling liquid levels. 5. The liquid phase of feeds can absorb or release heat whether they leave or stay in the system. 6. Credit may be taken for the difference between liquid feed enthalpies and the enthalpies of the liquid products and accumulated liquids. That is if the total enthalpy of the liquid feeds is less than the total enthalpy of the liquid products and accumulated liquids. The difference must be converted to relief load if the total enthalpy of the liquid products and accumulated liquids is less than the total enthalpy of the liquid feeds (liquids enthalpy imbalance). 7. Energy imbalance, resulting from an upset, is converted to the relief load using top-tray liquid
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latent heat of vaporization, calculated at relieving conditions. 8. The vapor portions of the feed streams, flashed adiabatically at relieving pressure, directly contribute to the relief load. 9. The vapor distillate control valve, if applicable, stays at its position. Credit may be taken for the vapor distillate flowrate unless its path is blocked. 10. Credit may be taken for reboiler temperature pinch, if light materials can not reach the column bottom. 11. Any safety margin used in the design of equipment must be considered in the relief load calculations. 12. The properties of the vaporized top-tray liquid at bubble point and relief pressure are used to size the relief valve. The orifice area of any relief valve in vapor service, using API RP-520 equations, is a function of the relieving fluid temperature, molecular weight and compressibility factor. All of this plus top-tray liquid latent heat of vaporization change with time during a relief event. The orifice area would be at maximum value when the following function is at maximum:
where:
T = Relieving fluid temperature, °R Z = Relieving fluid compressibility factor, dimensionless M = Relieving fluid molecular weight, lb/lb-mol = Latent heat of vaporization, Btu/lb.
In order to conservatively size a relief valve, one might calculate the maximum value of the function, f, over the boiling range of the top-tray liquid and use corresponding properties, including top-tray liquid latent heat of vaporization, in sizing calculations. Relief load calculation. Based on the above assumptions the relief rate can be defined as:
where:
W = Relief rate WR = Load contribution from reboilers and side-reboilers WF = Feed streams vapor contributions WV = Vapor product credits WC = Condenser and pumparound credits WH = Liquids enthalpy imbalance credit/contribution.
Load contributions from reboilers. Heat input from the reboilers and side-reboilers is converted to relief load using top-tray liquid latent heat of vaporization:
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QR = Reboilers and side-reboilers total duty, Btu/hr = Top-tray liquid latent heat of vaporization, Btu/lb.
Credit is allowed for reboiler temperature pinch if light materials cannot reach the column bottom at relieving conditions. The heat transfer coefficients of the reboilers and side-reboilers, however, must be adjusted to clean (zero fouling factors) values. Feed streams vapor contribution. The vapor portions of the feeds, flashed adiabatically at relief pressure, directly contribute to relief load. The compositions of those vapors, however, are different from that of the relief stream. The [latent] heat contents of the vapor portions of the feeds must be calculated and converted to relief load. The assumption is that as the rising vapor feeds come in contact with tray liquids they are partially condensed while vaporizing some of the tray liquids. This happens all the way to the top tray. The heat content of each vapor feed, which contributes to relief load, is equal to the feed heat-ofvaporization at relief pressure. This heat is simply the difference between dew point and bubble point enthalpies of the vapor feed at relieving pressure.
where:
QFV = Vapor feeds total heat of vaporization, Btu/hr HFVD i = Specific enthalpy of vapor feed i at dew point and relief pressure, Btu/lb HFVB i = Specific enthalpy of vapor feed i at bubble point and relief pressure, Btu/lb FFV i = Flowrate of vapor feed i at relief conditions, lb/hr
The relief load contribution from vapor feeds is equal to the total heat of vaporization of the vapor feeds divided by the top-tray liquid latent heat.
Vapor product credits. If the vapor products and the relieving fluid are of different compositions, the same method used for the vapor feeds should be applied to convert vapor product (latent) heat contents to a relief load credit:
and
where:
Q
PV
= Vapor products total heat of vaporization, Btu/hr
= Specific enthalpy of vapor product at dew point and relief pressure, Btu/lb = Specific enthalpy of vapor product at bubble point and relief pressure, Btu/lb = Flowrate of vapor product
at relief pressure, lb/hr.
Condenser and pumparound credits. Similar to the reboilers and side-reboilers, the condenser and pumparound duties are converted to relief load credit using the top-tray liquid latent heat of
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vaporization:
where:
QC = Condensers and pumparounds total duty, Btu/hr
Although the temperature difference (LMTD) in the condensers and pumparounds tends to increase during relief, it is hard to justify additional credit for the increased duties of the condensers and pumparound exchangers. Liquids enthalpy imbalance. The assumption that the product compositions stay unchanged at relieving conditions logically concludes that the feeds, if continued, will partition into the same product compositions as in normal conditions. The products will be formed in the column whether they leave or accumulate in the system. Since the compositions of the products are the same as the normal compositions, the product rates at relief should be proportional to the normal product rates. The heat absorbed or released by the feeds to form products (at their liquid phase) is the enthalpy imbalance and is equal to the sum of the enthalpies of liquid products and accumulated liquids minus the sum of the liquid feed enthalpies at relieving conditions. Credit may be taken for the liquids enthalpy imbalance if the sum of the feed enthalpies is smaller than the sum of the product and liquid accumulation enthalpies. If the reverse is true, the enthalpy difference must be converted into and added to the relief load. It is important to understand that the liquids enthalpy imbalance is the heat required (with a positive or a negative sign) to form products at their liquid bubble point status. Note that the relief load calculations are based on the heat input to the system and the latent heat of vaporization, which is the heat required changing bubble point liquids to dew point vapors. In short, liquid feeds form bubble point liquid products (using liquids enthalpy imbalance) and bubble point liquid products form relief load or vapor products (using latent heat of vaporization). It is important to ensure that while all the input and output heats are accounted for, they are not double dipped in the calculations. The basis for enthalpy imbalance, however, must be a balanced mass and applies only to the liquid portions of the feeds. The vapor phase is directly converted to relief load as previously explained. The method used to calculate the mass of liquid bubble point products and accumulations is: 1. The total rate of all feeds (liquids plus vapors) at relieving conditions is distributed to product streams, proportional to the normal product rates. Obviously, if the feed rates are not changed the results would be the same as normal product flowrates. 2. The products are sorted by specific enthalpies in a descending order. A rate equal to the sum of vapor portions of all feeds at relieving conditions is subtracted from the product rates, starting with product 1 (highest specific enthalpy) and moving to the next product subtracting the balance of the vapor feed rates. The results are the adjusted liquid product rates the sum of which should be equal to the total rate of the liquid portions of the feeds. The adjusted rates and the liquid feed rates are the mass basis for the liquids enthalpy imbalance calculation. Note that the adjusted [product] rates are independent of the actual liquid product rates at relieving conditions. Once again, the assumption is that liquids can accumulate in the column by the rise or fall of the liquid level. 3. The liquids enthalpy imbalance is simply the sum of the enthalpies of the adjusted products minus the sum of the enthalpies of liquid feeds:
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and
where:
QH = Liquids enthalpy imbalance, Btu/hr = Specific enthalpy of liquid product at bubble point and relief pressure, Btu/lb = Adjusted flowrate of the liquid product lb/hr HFLi = Specific enthalpy of the liquid phase of the feed i at relief pressure, Btu/lb FFLi = Flowrate of the liquid phase of the feed i at relief conditions, lb/hr
A numerical example. A typical distillation column is evaluated for a condenser failure scenario. The column parameters, feed properties and product properties are summarized in Table 1.
Contingency analysis. The reflux drum liquid level drops quickly. Both reflux and liquid distillate product streams will be lost regardless of either being on level or flow control. The difference is timing and sequence. The one on level control stops first, and pretty quickly. The feed is on flow control and its rate stays constant. The vapor distillate product control valve stays at its position (constant Cv). At relieving pressure, it can pass 135,500 lb/hr (an extra 12%) vapor product. With no liquid distillate product, the lights in the feed could get to the column bottom; therefore, no credit may be taken for the reboiler temperature pinch. Load calculations: Load contribution from reboilers and side-reboilers:
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Feed streams vapor contribution:
Vapor product credits:
Condenser and pumparound credits:
Liquids enthalpy imbalance:
The liquid product specific enthalpies and adjusted rates as well as the sum of the product total enthalpies,
, are summarized in Table 2. HP
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The author Piruz Latifi Nezami is a process engineering section manager with Jacobs Engineering in Houston, Texas. He holds a BS degree in chemical engineering from Sharif University of Technology in Tehran, Iran, and has more than 30 years of experience in the design and engineering of chemical, petrochemical and refining projects.
Return to top Copyright © 2009 Hydrocarbon Processing Copyright © 2009 Gulf Publishing Company
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