Calculating column relief loads Conventional, steady-state and dynamic simulation techniques are compared in a study of relief loads for failure modes applied to a distillation column Haribabu Chittibabu, Amudha Valli and Vineet Khanna Bechtel india PVE Ltd Dipanjan Bhattacharya Bechtel Corporation
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mergency relief in the process industries aims to protect equipment, the environment and operating personnel from abnormal conditions. Appropriate estimation of relief loads under extreme conditions is important for the correct sizing of relief valves and flare headers, and for the selection of disposal media. In addition, during debottlenecking or revamping of process units, adding a new relief valve and modifying the relief system can be very costly and, in terms of construction, difficult to implement. Estimating accurate relief loads for distillation columns under various conditions is more complex
because of compositional changes along the column height. The conventional method of estimating relief load (unbalanced heat method) is normally conservative and leads to bigger relief valves and flare headers, but it is the approach most widely practised. With increasing computing speed and software reliability, process simulation is increasingly used as an important tool for estimating relief load and properties. Steadystate simulation can also be used to estimate the relief load within limitations and can overcome some of the assumptions envisaged in the conventional method. Dynamic simulation provides an alternative
method for determining relief load under abnormal conditions. This article considers different methods for estimating relief load for a distillation column — a debutaniser in this case — and discusses the strengths and weaknesses of each method. There are many emergency cases that apply to a distillation column, and estimation of the maximum possible relief load requires an understanding of plant behaviour and identification of the worst case.
Case study: a debutaniser
The debutaniser column separates liquified petroleum gas (LPG) components from light naphtha.
PDC
To flare, R
PC
135°F 174 psia
Pset = 214 psia
Off gas CWS
CWR
FC LC LC
Debutaniser
196000 lb/hr
Reflux pump
Feed, F 673700 lb/hr, 301°F
TC
Feed pump
FC
Reflux drum
Sour water Distillate, sour LPG, D
FC
58120 lb/hr, 104°F
Reboiler
LC
412°F
Steam Condensate
391°F FC
391°F 178 psia Product pump
CWS
CWR
Bottom, naphtha product, B 615600 lb/hr, 391°F
Figure 1 Distillation column (debutaniser)
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The overhead includes a cooling water total condenser, reflux drum and off-gas valve, which is normally closed. The debutaniser operates at 174 psia and relief is set at 214 psia. The debutaniser bottom is heated by a thermosyphon reboiler utilising medium-pressure steam. Figure 1 shows a flow diagram of the debutaniser under evaluation. Major relief conditions or plant situations identified for the debutaniser are loss of reflux, loss of feed and site-wide power failure.
R
QC
Reflux drum
Top tray Excess heat
D, hD
F, hF
Debutaniser
Qunbalanced = F hF - B hB - D hD + QR - QC - (F - B - D) hL R = Qunbalanced (excess) / λ
QR
B, hB
Conventional method
The conventional approach Figure 2 Distillation column: unbalanced heat envelope is also known as the unbalanced heat method, column is available in various literwhere a mass and energy balance is ature1 and hence is not covered in developed under relief conditions, detail here. based on the scenario under considThere are several assumptions in eration, to determine if there is any determining relief loads: unbalanced or excess heat. The • Feed, products, reflux and top unbalanced heat is divided by the tray liquid compositions are unallatent heat of vapourisation of the tered during the relief condition top tray liquid to give the relief • Feed, product, reflux and stripload: ping medium will continue at the normal rate unless the hydraulics at Relief load = Qunbalanced (excess) / λ the relieving condition determine otherwise The conventional method for • Enthalpy is balanced on the top determining the relief load of a tray and all unbalanced heat will
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Relief valve opens
Reflux stops
Reflux drum fills
reach and act upon the top tray liquid • There is enough top tray liquid available to generate vapour during upset conditions. To determine Qunbalanced, the first step is to develop a sketch around the affected system (see Figure 2) and perform a mass and energy balance in line with the upset condition:
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where F = Debutaniser or column feed rate at relief hF = Specific enthalpy of feed at relief B = Debutaniser or column bottom rate at relief hB = Specific enthalpy of bottom at relief D = Debutaniser distillate rate at relief hD = Specific enthalpy of distillate at relief QR = Reboiler heat input at relief QC = Condenser duty at relief (generally, the design duty can be considered) hL = Specific enthalpy of top tray liquid λ = Latent heat of vapourisation of top tray liquid R = Relief load Credit may be taken for reboiler pinch. At relieving pressure, the column temperature rises and the reboiler temperature difference may fall, leading to lower heat input to the column. This is reboiler pinch.2 Assume that the volume of the sump is sufficient to maintain a constant reboiler circulation rate and to re-rate the reboiler to obtain duty at relief condition. If there was a significant reduction in the reboiler duty at relief, the lighter components would begin travelling towards the bottom, causing the duty to rise again. Many designers re-rate the reboiler with feed composition instead of bottoms composition in these circumstances, to maintain a more conservative/ realistic reboiler duty at relief.
Loss of reflux •
Figure 3 Loss of reflux: flow vs time
•
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Reflux stops immediately The reflux drum and
the
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column sump level, and finally reaches zero • The column overhead vapour rate decreases, the reflux drum level drops, and the distillate rate decreases to maintain the condenser level and finally becomes zero. Therefore: OO O O O O
Peak pressure
2ELIEFPRESSURE PSIA
Qunbalanced = F hF - B hB - D hD + QR - QC - (F - B - D) hL
2ELIEFPRESSURE 2ELIEFVALVESETPRESSURE 2ELIEFVALVEACCUMULATED PRESSURE
Site-wide power failure (SWPF) •
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Figure 4 Loss of reflux: relief pressure vs time
Reflux drum fills
All electrical equipment fails, therefore the feed pump, the debutaniser bottom pumps and the reflux pumps stop • Assuming all cooling water pumps are electrically driven, the condensing duty is also immediately lost • Steam is assumed to flow continuously to the reboiler. Therefore: O O
O
O
OO
Qunbalanced = F hF - B hB - D hD + QR - QC - (F - B - D) hL (OLDUPLEVEL
Dynamic simulation of relief conditions
2EBOILERSUMP 2EFLUXDRUM #OLUMNSUMP
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Figure 5 Loss of reflux: holdup level vs time
condenser flood, restricting the O O O overhead vapour path and pressu- Q = F h B h D h + Q Q (F B D) hL unbalanced F B D R C rising the column • The feed is pumped and sufficient head is available to maintain Loss of feed the feed flow rate at relief • Feed stops immediately condition • After some time, when the • Bottom product continues at the column level drops, the bottom same rate. Therefore: product decreases to maintain the Relief load calculated by conventional method Upset condition Relief load, lb/hr Temperature, °F Molecular weight Loss of reflux 124 980 164 49.28 Loss of feed 43 650 164 49.28 Site-wide power failure 342 796 164 49.28
Table 1
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Chemical plants and refineries are never truly at a steady state and this is the case during relief. The transient behaviour of a column is best studied by means of dynamic simulation, which has gained in importance since the 1990s and has been used increasingly successfully as the reliability of simulation software has increased. The equations for material, energy and composition balances include an additional accumulation term, which is differentiated with respect to time. The inclusion of an accumulation term enables the dynamic model to rigorously calculate compositional changes at each stage and to modify vapour/liquid equilibrium over time. Unlike steady-state simulation, dynamic simulation works within a Pressure-Flow (P-F) network with two basic equations: resistance and volume balance. The resistance equation defines flow between pressure hold-ups, and the volume balance equation defines material balance at pressure hold-ups. For the case under consideration, the accuracy of dynamic simulation
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Pinched reboiler duty
-OLECULARWEIGHT
$UTY "45HR
2EBOILERDUTY #OLUMNSUMP MOLECULARWEIGHT
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Figure 6 Loss of reflux: reboiler duty and molecular weight vs time
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Feed stops
Relief valve open
Relief valve close
Bottom & distillate flow zero
Relief flow
Loss of reflux condition
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Figure 7 Loss of feed: flow vs time
Peak pressure
2ELIEFPRESSURE PSIA
The reflux pump is stopped in five minutes (see Figure 3). The level in the reflux drum starts to increase (see Figure 5). The overhead vapour from the column continues to flow through the condenser and fill the reflux drum. After 17 minutes, the reflux drum floods and the flow to the condenser is blocked; the column pressure starts to increase (see Figure 4). When the column reaches the set pressure, after about 21 minutes, the relief valve starts to open. Note that the pressure did not reach the maximum accumulated pressure for the given orifice area of the relief valve. Initially, the level in the column bottom sump decreases as the reflux is stopped, and the bottoms product level control valve closes to maintain the column sump level. The feed continues at a constant rate, since its pressure upstream of
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provides extra inputs compared with steady-state simulation: • Dimensions, especially volumes, for all static equipment; column bottom and reflux drum levels are set to normal to simulate hold-ups • A vendor curve for pressure flow relationships for rotating equipment • Specific conductance for control valves (Cv value) for pressure flow relationships, and an actuator mode and rate for valve actuator dynamics • Detailed exchanger thermal design for calculation of pressure drop and heat transfer coefficient. If detailed design is not available, a resistance term for the pressure flow relationship and overall UA can be specified • Actual tray information such as diameter, flow path, distributor details, weir length and height are required for column hydraulic performance • Controller for determining control actions during transitions. Credit is not taken for the control action, which reduces the relief load; for example, the column bottom temperature controller reduces the steam flow rate when the column bottom temperature rises at the relief condition.
2ELIEFVALVESETPRESSURE 2ELIEFPRESSURE 2ELIFVALVE ACCUMULATEDPRESSURE
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Figure 8 Loss of feed: relief pressure vs time
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Reboiler sump level drops
(OLDUPLEVEL
Column sump level drops
2EBOILERSUMP 2EFLUXDRUM #OLUMNSUMP
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Figure 9 Loss of feed: holdup level vs time
2EBOILERDUTY #ONDENSERDUTY #OLUMNSUMP MOLECULARWEIGHT
$UTY "45HR
Pinched reboiler duty
Condenser duty
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Figure 10 Loss of feed: reboiler duty and molecular weight vs time
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Site-wide power failure
Relief valve open
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Figure 11 Site-wide power failure: flow vs time
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the control valve is higher than the relief pressure. Figure 6 shows the reboiler duty and column sump molecular weight during this relief condition. As soon as the reflux is stopped, the molecular weight in the column sump increases, leading to an increase in the boiling temperature of the column bottoms, finally resulting in reduced reboiler duty. After 17 minutes, when the path for the overhead vapour was blocked (condenser flooded), lighter components started to fill the column sump and reboiler duty again started to increase. After 21 minutes, when the relief valve started to open, reboiler duty settled, based on the column sump composition at relief condition.
Loss of feed condition
The feed pump stops after five minutes (see Figure 7). After 10 minutes, the column sump level drops (see Figure 9) and the bottom flow is reduced to maintain the column sump level. As the column overhead vapour starts to decrease (see Figure 7), the reflux drum level decreases and the distillate flow reduces to maintain the reflux drum level. After 20 minutes, when distillate and bottoms stop completely, only the vapour generated by the reboiler is condensed by the condenser. Figure 10 shows the pinched reboiler duty, condenser duty and column sump molecular weight. During loss of feed, the column sump molecular weight increases, resulting in reduced reboiler duty. Since the top reflux is maintained at normal flow, the lighter components start migrating towards the bottom. The column profile starts becoming lighter and the temperature profile starts lowering. This also results in the lower molecular weight of the column overhead vapour. After about 11 minutes, the condenser is not able to fully condense the overhead vapour due to its lower molecular weight, resulting in a rise in column pressure (see Figure 8). When the column reaches the set pressure, after about 23 minutes, the relief valve starts to open. Note that the
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pinched reboiler duty at this time is higher because of the lower molecular weight in the column sump. After about 35 minutes, all noncondensable or lighter components exit the column, reboiler duty reduces again to about 42% of normal, and the column stabilises at total reflux mode.
2ELIEFPRESSURE PSIA
Site-wide power failure condition
Summary Loss of reflux condition
Figure 15 shows a comparison of relief load values obtained for loss
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2ELIEFVALVESETPRESSURE 2ELIEFPRESSURE 2ELIFVALVE ACCUMULATEDPRESSURE
4IME MIN
Figure 12 Site-wide power failure: relief pressure vs time
Column sump level increases
(OLDUPLEVEL
2EBOILERSUMP 2EFLUXDRUM #OLUMNSUMP
4IME MIN
Figure 13 Site-wide power failure: hold-up level vs time
-OLECULARWEIGHT 2EBOILERDUTY #ONDENSERDUTY
Increasing column sump molecular weight
Reboiler duty decreases
-OLECULARWEIGHT
$UTY "45HR
Assume that site-wide power failure occurs after five minutes (see Figure 11). During the power failure, the feed pump, column bottom pump, reflux pump and cooling water pump stop, and their respective flows become zero immediately. The column sump level increases immediately as the tray inventories are dumped to the bottom (see Figure 13). As the flows of feed, distillate, bottoms and cooling water are cut, the vapours generated by the reboiler cause the column pressure to increase (see Figure 12). After 11 minutes, the relief valve opens. Initially, there is mass transfer between the vapours from the reboiler and the residual liquid on the trays; progressively, as the trays dry up, the temperature and molecular weight of the overhead (relieving) vapour increase. The bottoms progressively become heavier, resulting in a continuous decrease in the reboiler duty (see Figure 14). As the pinched reboiler duty carries on decreasing, the relief valve will eventually close. During power failure, the relief load is relatively low compared with the loss of feed condition because the pinched reboiler duty is much less due to the high molecular weight in the column. During loss of feed, continuing reflux makes the column relatively lighter. The time taken to pressure up the column is much higher in the loss of feed scenario because the condenser is available, compared to the loss of power condition, where condensing duty was lost immediately.
Peak pressure
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Figure 14 Site-wide power failure: reboiler duty and molecular weight vs time
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Conventional method
2ELIEFLOAD LBHR
Steady-state simulation
Dynamic simulation
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Figure 15 Loss of reflux: relief load vs time
Relief load calculated by dynamic simulation Upset condition Relief load, lb/hr Temperature, °F Molecular weight Loss of reflux 90 800 310 62.5 Loss of feed 93 500 117 44.2 Site-wide power failure 29 250 290 76
Table 2
of reflux. According to the conventional method, the predicted relief load is higher than the value obtained by dynamic simulation. In the conventional method, the
assumption is that all of the unbalanced heat will vapourise the top tray liquid, which has a lower specific enthalpy. The molecular weight and temperature are lower
2ELIEFLOAD LBHR
Conventional method
Dynamic simulation
Figure 16 Loss of feed: relief load vs time
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4IME MIN
for the top tray at bubble point and relief pressure when compared to dynamic simulation, which simulates reflux failure, resulting in a higher temperature and molecular weight. In a dynamic simulation of loss of reflux, the column almost reaches a new steady-state condition after 25 minutes. The rectifying section of the column goes dry and only the stripping section is involved in mass transfer. This new steady state can also be reasonably simulated using a steady-state simulator (see Steady-state simulation to obtain relief load and properties). There is a marginal difference in the relief load obtained by steadystate simulation and dynamic simulation because, in steady-state simulation, the column pressure has been raised to an accumulation pressure (set pressure +10% or +16% based on the scenario), whereas in dynamic simulation the pressure safety valve starts opening at its set pressure and the pressure does not reach the maximum accumulated pressure for the selected orifice area. Note that the conventional method and steady-state simulation are not time dependent, so the relief load appears constant in comparison with the dynamic simulation relief load.
Loss of feed
Figure 16 shows a comparison of relief load obtained for loss of feed. The relief load calculated by the conventional method is lower than by dynamic simulation. In the conventional method, the condenser duty equals the design duty and the cooling effect is predominant. In dynamic simulation, the condenser duty is not fixed and the hold-up of the individual components in the column determines the behaviour of the condenser. Initially, during loss of feed, the reboiler duty decreases due to pinch and the lighter components subsequently travel to the bottoms and the whole column profile becomes lighter. Eventually, the reboiler duty again starts to raise due to the decrease in molecular weight. This phenomenon cannot be evaluated with the conventional
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Conventional method
2ELIEFLOAD LBHR
Dynamic simulation
4IME MIN
Figure 17 Site-wide power failure: relief load vs time
method, but validates the hypothesis that, if the pinched duty is too low, the designer should re-evaluate the reboiler duty, assuming lighter composition in the column bottoms.
much lower than by the conventional method. In reality, during this condition, after the trays dry up the column simply acts as a boiling pot without mass transfer. The reboiler duty continuously decreases as the contents become heavier with time. According to the conventional approach, reboiler duty and relief rate are calculated at one instant, which is at the start of the emergency (not at the start of
Site-wide power failure
Figure 17 shows a comparison of relief load obtained for site-wide power failure. In dynamic simulation, the relief load obtained is
Steady-state simulation to obtain relief load and properties
To relief
Debutaniser
Off gas
To condenser CWS
Feed
CWR
Reflux drum
Recycle
Reflux
Sour water
Total liquid from column bottom stage (internal stream)
Reflux pump
Distillate
Internal energy stream
Bottom Set Twinned column bottom
To external reboiler Internal energy duty = external reboiler duty
Steam
External reboiler Condensate
Figure 18 Distillation column – steady-state simulation – relief condition
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relief). This results in a conservative estimate. The effect of hold-up volumes and time taken to pressurise is normally ignored. The conventional method is the most conservative and requires less effort during design. Steady-state simulation to determine the relief load has limited applicability. For grassroots designs, the conventional method may be the most appropriate, as detailed design and/or complete vendor information may not be available at the time of the relief system’s design. It also helps to build in inherent design margins for any possible future expansion/ debottlenecking operation, and to minimise changes during the late stages of the project due to any unforeseen design development. Dynamic simulation models the system rigorously and tends to provide more accurate results, taking into account actual system dynamics and configuration. It tries to emulate plant behaviour, which usually results in lower relief loads. Dynamic simulation also provides relief loads based on time, which can be further analysed for optimising the relief system’s design. Dynamic simulation can be particularly useful in unit revamps, to limit the capital cost involved in relief system modifications.
•
Simulate the distillation column into three sections: column, column overhead system and reboiler system • The column can also be simulated as a reboiled column (column with a reboiler) with theoretical stages and normal operating pressure ■ Define a reflux stream and feed it to the top tray ■ Define the feed stream and assign an appropriate feed location. Give a normal pressure drop across the column ■ Fix the normal reboiler duty to the energy stream and normal boilup ratio (as a specification) ■ Converge the column • The column overhead system includes a pressure safety valve (PSV), cooling water condenser and reflux drum
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■ Split the overhead vapour from the column “to relief” and “to condenser”, and set the “relief flow” rate to zero ■ Simulate the condenser as a shell and tube exchanger with cooling water on the tube side and overhead vapour totally condensed. Simulate the reflux drum, reflux pump, distillate product and reflux ■ The reflux from the reflux pump should be same as the defined reflux stream to the top tray, so connect them through a recycle block • The reboiler system should be simulated as a separate shell and tube heat exchanger (external reboiler) in order to study reboiler pinch at relieving conditions ■ Create an internal stream of the total liquid from the bottom stage in the column. The internal stream minus the column bottoms is the feed to the external reboiler, so split the internal stream to the external reboiler and twinned column bottoms. Set the column bottoms flow rate to the twinned column bottoms stream ■ Specify the normal UA to the external reboiler ■ Specify the hot side of the external reboiler. For the case under consideration, the hot-side inlet is steam at its saturation condition and the hot-side outlet is total condensate • Increase the column pressure to relief pressure (PSV set pressure + allowable accumulation). Since the bottom pressure is higher (relief
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pressure + normal ∆P), the bubble point of the column bottom increases. The temperature difference across the external reboiler reduces, leading to lower external reboiler duty (pinch). The calculated duty of the external reboiler should be equal to the energy stream attached to the column (internal energy stream). Iterate the column internal energy stream so that it matches the external reboiler duty. Even though the LMTD tends to increase in the condenser, many designers tend to restrict the maximum condenser duty to design duty due to uncertainties in the calculation. For this exercise, the condenser duty is limited to the design duty only. Now the column is at relieving pressure, giving an idea of the reduced reboiler duty and the amount of overhead vapour. The next step is to simulate the cause of overpressure to the maximum convergence of the column. For loss of reflux, increase the flow “to relief”, so that flow to the condenser is reduced and, ultimately, the flow to the reflux is reduced. Simultaneously reduce the distillate flow step-wise as the reflux pump is stopped. At the same time, keep iterating the column internal energy stream so that it matches the external reboiler duty. Ultimately, when the reflux and distillate are zero, all the overhead vapour from the column is the relieving flow. The above methodology can also be extended to other emergencies,
where it is expected that the relieving scenario could approach the steady-state condition. References 1 Sengupta M, Staats F Y, A new approach to relief valve load calculations, May 1978. 2 Rahimi Mofrad S, Tower pressure relief calculation, Hydrocarbon Processing, Sep 2008. Haribabu Chittibabu is an Engineering Specialist in the Advanced Simulation and Analysis group at Bechtel India. He has a bachelor’s degree in chemical engineering from University of Madras and a master’s in petroleum refining and petrochemicals from Anna University, India. Email:
[email protected] Amudha Valli is an Engineering Specialist in the Advanced Simulation and Analysis group at Bechtel, India. She has a bachelor’s degree in chemical engineering from Coimbatore Institute of Technology, India, and a master’s in chemical engineering from Anna University, India. Email:
[email protected] Vineet Khanna is Project Engineering Manager with Bechtel India. He has a bachelor’s degree in chemical engineering from the Indian Institute of Technology, Delhi, India. Email:
[email protected] Dipanjan Bhattacharya is an Engineering Specialist in the Advanced Simulation and Analysis group at Bechtel, Houston. He has a bachelor’s degree in chemical engineering from Jadavpur University, India, and master’s in chemical engineering from University of Oklahoma. Email:
[email protected]
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PTQ Q2 2010 65
