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Scaling Up Safely: Making Smarter Decisionsabout Rate Dependency
Zubin Kumana, P.E., Venkata Badam,P.E.,
and Achilles Arnaez, P.E.
7600 W. Tidwell Rd., Ste. 600 | Houston, TX 770400(713) 802-2647 | SmithBurgess.com
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Scaling Up Safely: Making Smarter Decisions about Rate Dependency
Zubin Kumana, P.E. Smith & Burgess LLC
7600 W. Tidwell Rd, Ste 600 Houston TX 77040
Venkata Badam, P.E. Smith & Burgess LLC
Achilles Arnaez Smith & Burgess LLC
Smith & Burgess LLC grants AIChE permission for itself and its designated agents to reproduce, sell, or distribute this paper. Copyright to this paper is retained by Smith & Burgess LLC, from whom permission to reproduce must be obtained by any other party. All information deemed reliable but may not be applicable to any given installation.
Any risk assessment or safety analysis should be independently verified by a qualified engineer. © 2016, Smith & Burgess, LLC
Prepared for Presentation at American Institute of Chemical Engineers
2016 Spring Meeting 12th Global Congress on Process Safety
Houston, Texas April 11-13, 2016
AIChE shall not be responsible for statements or opinions contained in papers or printed in its publications
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Scaling Up Safely: Making Smarter Decisions about Rate Dependency
Zubin Kumana, P.E. Smith & Burgess LLC
7600 W. Tidwell Rd, Ste 600 Houston TX 77040
Venkata Badam, P.E. Smith & Burgess LLC
Achilles Arnaez Smith & Burgess LLC
Keywords: Process Safety, Safe Design, and Venting and Emergency Relief
Abstract
Over the lifetime of a facility, it is almost a certainty that the throughput of a process will be increased, often repeatedly. Rate-dependency is frequently used as a way to identify pressure relief system sizing that would be affected by the scaling up of process throughput. This paper will define rate-dependency as it relates to pressure relief systems and describe the various ways in which rate-dependent classifications may be affected by the mechanical and thermodynamic constraints of the process and equipment. In addition, examples of when the "rate-dependent" designation may no longer apply due to common assumptions and methodological choices will be provided.
1 Introduction
In the refining and chemical processing industries, increasing throughput through a processing unit is often considered as a means of maximizing value with existing capital or minimal additional investment. Often, the throughput will be increased many times over the lifetime of the facility. The pressure relief system for a process is designed in part based on the throughput of the unit; therefore, the change in the throughput may affect the adequacy of the pressure relief system design.
Verifying the design of the process unit’s pressure relief system for these increased rates is typically done by identifying overpressure scenarios as either rate-dependent or rate-independent. A rate-dependent overpressure scenario is one whose required relief rate varies with changes in process throughput. A common example is a blocked outlet scenario on a separator. With higher
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the process throughput, the quantity of mass that must be relieved to limit the pressure to the allowable accumulation is expected to increase.
Conversely, rate-independence refers to overpressure scenarios whose required relief rate is independent of process throughput. A common example is exterior fire, where the required relief rate depends on the heat of vaporization of the liquid mixture inside the vessel, the density of the vapor and liquid phases, and the wetted area of the vessel the fluid is residing in. Changing the feed rate to the vessel is not expected to result in a change to the required relief area for the exterior fire scenario. In some circles, these scenarios may also be termed “equipment-dependent”. While the equipment and piping remains constant, the required relief rate remains constant. However, as rate scale-up increases, the equipment and piping may be changed to accommodate the additional capacity.
Figure 1: Rate-dependent scenarios increase in required relief rate (and therefore area) with process flow rate increase, while equipment-dependent scenarios are effectively constant until a change to equipment is required.
1.1 How Rate Dependency is used in Pressure Relief System Design
The common practice in pressure relief system design is to select a unit process basis that the user believes represents both the actual operation of the process as well as the worst case for the relief system design – specifically, the case that will result in the largest required areas and piping diameters. Since process units can have a range of operating modes and rates, selection of these cases tends to favor the following:
• Modes of operation with lighter feed, as this can result in more vaporization and therefore larger vapor and two-phase relief loads
• Higher process throughput rates; often the peak rate achieved, or some percentage above the peak rate
Requ
ired
Relie
f Rat
e
Process Flow Rate
Rate-Dependent v. Equipment-Dependent Scenarios
Rate
Equipment
Dependency
Change to Equipment Required
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The conscientious user might separately specify a worst-case heavy liquid relief load basis in order to properly design the liquid handling capabilities of the disposal system.
As the pressure relief system design is completed, the engineer performing the design will typically identify overpressure scenarios as rate-dependent as the analysis proceeds. This designation is then used when the throughput rate is modified in the future. This allows engineers to minimize the amount of recalculation that needs to be performed, by only performing new calculations for the overpressure scenarios that are dependent on rates; the scenarios that had been identified as rate-independent are believed to be static and are left unchanged.
A generalized expression for pressure relief device sizing is given in API Std 520 Part I (9th ed.) Annex B, equation B.5, rearranged to solve for required area [1]:
𝐴𝐴 = 𝑊𝑊𝐺𝐺∏[𝐾𝐾] (Eq. 1)
Where
G is the theoretical mass flux through the nozzle
W is the mass flow through the PRV
A is the effective discharge area
Π[K] is the product of all applicable correction factors
The scale-up of the pressure relief system design is typically done using the assumption that the only change is to the flow rates through the unit; variables such as fluid composition, operating pressures and temperatures are assumed to remain constant. This effectively limits the relationship between the throughput rate and the relief system required areas to a linear one; as the fluid mass flux is considered constant, and the applicable correction factors are generally constant (exceptions are always possible based on Reynolds’ number and actual backpressure resulting from flow), the values of A and W are directly proportional.
For the evaluation of the pressure relief system design, this has led to the following widespread practice:
1. The user takes the heat and material balance at the previous throughput rate 2. The user obtains a list of calculations that had been identified as rate-dependent 3. The user takes the percentage increase in flow and factors this value into the required
relief rates 4. The user re-evaluates the pressure relief device requirements vs. capacity (along with
other associated concerns where relevant, e.g. pressure losses if calculated at required relief rates)
This process rarely involves revalidating the process unit simulation to confirm the heat and material balance. Typically this practice has been followed for small changes to throughput rates. However, once the procedure has been implemented, the potential exists for repeated applications
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to increase the degree of deviation from a validated baseline even further. This poses a danger, as excessive extrapolation and repeated application of the scale-up process without carefully considered heat and material balance revalidation can quickly lead to larger and larger deviations, and the potential for undersizing the pressure relief system.
This paper focuses on rate scale-ups that do not involve any change to the as-built system. The rate scale-ups considered are therefore limited to the maximum throughput that the existing equipment can support. Debottlenecking the equipment in the process unit (rotating equipment, exchanger heat transfer area, and pipe sizing) may be required to accommodate further rate scale-up. As a capital project, this effort typically includes development of a new project baseline heat and material balance along with a review of the pressure relief system design.
2 Proper Identification of Rate-Dependency
2.1 How to Identify Rate-Dependency
Smarter decision-making with regard to rate dependency begins with understanding the ways that the traditional definition of rate-dependency may be invalidated by subsequent modeling choices in the determination of the required relief rate.
A general rule of thumb often passed around among novices in pressure relief system design is that overpressure scenario required relief rates that result from equations are rate-independent, and required relief rates that come from a heat and material balance (HMB) are rate-dependent. However, while it may be generally true for many facilities, there are aspects that are commonly overlooked in this approach, and some engineers may take subsequent steps in the required relief rate calculation that can change the classification. These additional steps are often taken as a means to “sharpen the pencil” when the initial determination of the required relief rate results in an undersized pressure relief device. These may include such actions as:
• Taking credit for an outlet that would not be blocked as a result of the scenario (including secondary causes like controller action and shut off systems)
• Reducing heat transfer into the system due to elevated bubble point temperatures • Limiting flow rates based on the hydraulic limits of the piping, including valves and fittings • Limiting flow rates to the maximum capacity of rotating equipment that can deliver the stated
pressure at the point of relief
For example, if determining the required relief rate in the event of a blocked liquid outlet on an exchanger by taking the normal feed rate as the required relief rate is found to result in a required relief area greater than the currently installed relief area, the engineer may review the inputs and determine that when discharging against the relief pressure, the capacity of the feed pump is reduced below the normal feed rate, potentially making the existing installed relief area adequate. In this example, the overpressure scenario has changed from rate-dependent to equipment-dependent.
Table 1 shows common sources for determining the required relief rate for an overpressure scenario, and potential additional modeling choices that can change the classification.
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Table 1. Examples of Dependency and Factors That May Change Classification†
Overpressure Scenario
Rate Commonly Derived From
Dependency for Common Derivation
Factors that may change Classification
Closed outlets HMB/Simulation, Exchanger duty
Rate-Dependent Limited by pump/compressor, valve, or pipe capacity
Reflux failure HMB/Simulation, Exchanger duty
Rate-Dependent
Cooling failure HMB/Simulation, Exchanger duty
Rate-Dependent
Overfilling HMB Rate-Dependent Limited by pump or valve capacity
Inadvertent opening of manual valve
Line capacity Equipment-Dependent Credit taken for volume outflow
Failure open of inlet control valve
Valve capacity Equipment-Dependent Credit taken for normal minimum flow or outflow
Check valve failure Valve or line capacity Equipment-Dependent Abnormal heat input Valve or exchanger
capacity, HMB/Simulation
Rate-Dependent
Exterior fire Fluid properties, Vessel area
Equipment-Dependent
Hydraulic expansion (pipe)
Fluid properties, Pipe area
Equipment-Dependent
Hydraulic expansion (exchanger)
Fluid properties, Exchanger duty
Equipment-Dependent Exchanger duty driven by hot side flow rate
Tube rupture Exchanger properties, fluid properties
Equipment-Dependent
Tube leak Exchanger properties, fluid properties
Equipment-Dependent
Plate weld failure Exchanger properties, fluid properties
Equipment-Dependent
Column power failure (Complex)
HMB/Simulation, Exchanger duty
Rate-Dependent
Column power failure (Simple*)
Fluid properties, reboiler duty
Rate-Dependent
Loss of Absorbent HMB/Simulation Rate-Dependent *Simple column failure includes overpressure scenarios where the required relief rate can be determined as a function of the reboiler duty and heat of vaporization of the residing fluid. †Not a comprehensive list
3 Rate-Dependent Factors Influencing Pressure Relief System Design
Although the common practice is to size the pressure relief system as a linear function of process flow rate, the reality is more complex, as other factors that are themselves influenced by process flow rate can also impact the pressure relief system design, primarily through their impact on pressure relief device sizing. These factors can impact the pressure relief device sizing by causing additional deviations in relief rate calculations for rate-dependent overpressure scenarios (i.e., non-
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linear relations), as well as creating changes in required relief rates for overpressure scenarios previously categorized as equipment-dependent.
A quick review of three factors influencing pressure relief device sizing will aid in understanding the limits of scaling up the pressure relief system design basis: composition, operating conditions, and heat exchanger duties. Note that this list is intended for illustrative purposes of the effects and is not an all-inclusive list; there are other factors that can influence the design of the pressure relief system that may change during a process rate scale-up.
3.1 Composition
3.1.1 Composition and Pressure Relief System Design
Fluid composition impacts the pressure relief device sizing in two significant ways.
1. Firstly, it can directly impact the determination of the required relief rate; for example, fire calculations use the latent heat of vaporization for a mixture, and depending on the particular modeling choices selected (e.g. inclusion of sensible heat, vaporization interval selected) may include further dependencies on heat capacity, bubble point temperature, vapor to liquid volume ratio, and other variables. Orifice flow calculations (such as are found in tube rupture calculations) depend on the density or molecular weight, compressibility, and specific heat ratio for the fluid.
2. Secondly, the composition of the fluid mixture directly impacts the relationship between the pressure of the fluid and the specific volume of the fluid, which governs the determination of the critical mass flux across the relief device nozzle (G in equation 1).
3.1.2 How Scaling Up the Process Can Affect Composition
It has been commonly observed that the compositional data in a heat and material balance is rarely adjusted when a scale-up of the unit throughput is performed. This assumption can be invalidated by any of the following effects:
1. Changes in the operating pressure and temperature – Changes in operating temperature and pressure can have an impact on the composition by affecting the separation of the vapor and liquid phases within the process equipment. Increasing the operating pressure can raise the bubble point temperature of the fluid mixture, requiring additional heat to achieve the same separation point. Decreasing the operating pressure can reduce the bubble point temperature of the fluid mixture, possibly resulting in more vapor flashing off, with a higher molecular weight.
2. Limitations on feed sources – In order to maximize the throughput for the specific process unit, feeds from multiple sources may be required. If the process unit has excess capacity but insufficient feed is available from on-site units, feed may be supplemented from offsite or from tankage. These feeds may have variations in compositions, and as the new feed is added, the blend ratio can change. For example, a gas oil hydrotreating unit (GOHT) may have additional capacity, but due to changes in product demand the crude column system may be producing a higher proportion of lighter products. To take advantage of the slack
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in the GOHT, additional gas oil may be imported, resulting in a change in composition of the feed.
3.2 Operating Conditions
3.2.1 Operating Conditions and Pressure Relief System Design
The operating conditions within equipment in the process unit can directly impact the pressure relief device sizing primarily through the temperature’s effect on the fluid conditions (for overpressure scenarios that model the required relief rate using its operating temperature). Temperature also influences the maximum mass flux across the pressure relief device. Since the relief device is sized at the relief pressure, there is no similar direct effect of operating pressure.
More significantly, changes in the normal operating temperature and pressure can affect the required relief rate calculations for overpressure scenarios that require these values as inputs, such as modeling flow across an orifice, flow through piping or valves, or where separation processes are occurring. For example, inadvertent opening of a valve into a separator may involve flow of the fluid mixture across a valve and series of pipe fittings, followed by a separation where the vapor is expected to overpressure the downstream vessel, while the liquid will slowly fill the vessel. The change in overall vapor quality can both affect the required rate to be relieved while the vessel is filling as well as affect the available time for operator intervention – in some cases making the required relief rate better, and in other cases making it worse. Another example is the potential for changes in composition, temperature, or pressure to change the net positive suction head available (NPSHA) for pumps, requiring adjustments to liquid levels in order to maintain proper pump operation, thereby affecting equipment-dependent overpressure scenarios.
It is even conceivable that such a change may alter the applicability of an overpressure scenario, where the existing operating conditions are already near the threshold of applicability – from either direction. Changing the operating pressure may affect the suction pressure of a pump or compressor, thereby altering the deliverable pressure to a downstream system, whose determination of applicability for a control valve failure or inadvertent opening of a manual valve overpressure scenario may depend on the comparison of this pressure to the downstream system maximum allowable working pressure.
Changes to operating conditions can also affect the specification of the pressure relief device. Operating pressures that were previously at the limit of the acceptable range that may now exceed the operating limits of the pressure relief device may require alternative relief device specification (e.g., if the operating pressure exceeds 90% of the PRV set pressure, this may require replacing a conventional PRV with a pilot operated PRV). Significant changes to operating temperature may also affect the set pressure of the pressure relief device. For a spring loaded valve, a new cold differential set pressure may be required.
3.2.2 How Scaling Up the Process Can Affect Operating Conditions
The operating conditions can be impacted in the following ways during a scale-up:
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1. The mechanical characteristics of rotary equipment – For example, for a given installed impeller diameter, as the flow rate is increased, the operating point of the rotating equipment must move out on the pump performance curve, resulting in a lower delivered pressure. (This can be countered by changing out the pump impeller, but that is outside the scope of this paper).
2. Piping hydraulic limitations – As flowrate is increased, the pressure drop is expected to increase. With changes in the pressure drop between equipment, the operating pressure profile may be affected. For flow in the turbulent region, for the same diameter of piping, the pressure drop normally follows a trend of
𝐹𝐹1𝐹𝐹2
𝑣𝑣1𝑣𝑣2
= 𝑄𝑄1𝑄𝑄2
= �𝛥𝛥𝛥𝛥1𝛥𝛥𝛥𝛥2
(Eq. 2)
Where
F is the mass flow rate
v is the specific volume of the fluid
Q is the volumetric flow rate of the fluid
ΔP is the pressure drop through the pipe
3. Heat transfer – As flowrates change, when running up against the limits of the heat transfer equipment, changes in temperature and mass quality may result. For example, applying the same duty to a fluid entering at a higher feed rate will soak up more sensible heat and result in a smaller vapor fraction exiting the equipment.
3.3 Heat Exchanger Duties
3.3.1 Heat Exchanger Duties and Pressure Relief System Design
Heat exchanger duties can potentially cause deviations in the relief device sizing basis if the process duties are used as inputs in determining the required relief rates. Note that some users choose to use the design duties of the exchangers in lieu of the process duties. This may mitigate the impact of scale-up (up to the point where new heat transfer equipment is required). Common examples of overpressure scenarios impacted by this factor are blocked outlets on heat exchangers, thermal expansion, and simplified column calculations (i.e. boil-up).
The other route through which heat exchanger duties can impact the pressure relief system sizing is by impacting the operating conditions of the process (see section 3.2.1).
3.3.2 How Scaling Up the Process Can Affect Heat Exchanger Duties
Scaling up the process flow rate through an exchanger can significantly impact the exchanger heat duty if it is limited by flow instead of limited by heat transfer area and overall heat transfer coefficient (“UA-limited”). For the same heat exchanger, the flow pattern correction factor FT is expected to be constant. In these cases an increase in process fluid flow can result in increased duty, up to the point where the exchanger UA becomes limiting. Note that for forced convection, since the Nusselt number is a function of the Reynolds number, the value for the overall heat
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transfer coefficient U is not constant; rather, it is itself a weak function of flow rate (as well as composition and operating conditions). If the exchanger duty is limited by UA, then the exchanger heat transfer duty can be still changed by differences in log mean temperature difference (ΔTlm). The temperatures changes may come about as described in section 3.2.2.
3.4 Extent of Deviations and Overall Impact on Pressure Relief System Design
The above discussions have focused on how rate scale-ups can impact the pressure relief system design in ways beyond the typically assumed linear relationship between mass flow rate and required relief area, as well as impacting scenarios that might otherwise not be classified as rate-dependent. While it can be expected that minor changes in flowrate would have a correspondingly minor impact on composition, temperature and pressure, and heat exchanger duties, and therefore a minor impact on the pressure relief system design, it is important to recognize that the extent of deviation from linear behavior can increase with the extent of the process throughput scale-up. Additionally, repeatedly performing scale-ups on a previously scaled-up process, without revalidating the heat and material balance, can lead to the same result in a less obvious manner.
4 Examples
4.1.1 Examples of Compositional Impact on Pressure Relief System Design
For equipment and systems where relief rate is determined by calculating a rate of vaporization, the relief rate typically increases as the proportion of lighter components within the feed increases. Even where the relief rate is not determined by calculating a rate of vaporization, a lighter feed may not change the required relief rate mass flowrate but might instead decrease the relief device capacity, on a mass basis. For example, crude units can be operated with significant variations in the crude slate. These changes in feed composition could cause different effects for relief device design within the crude unit, even with no change in overall unit throughput.
The sizing scenarios for crude column systems commonly include partial power failures that result in continuing crude feed and heat input from the fired heater, with loss of all overhead and pumparound cooling, among other effects (such as backflow and desalter water carryover). In these scenarios, the relief stream is based on the lighter portion of the crude feed, which typically consists of the offgas, liquefied petroleum gas (LPG), naphthas, kerosene, and/or diesel, etc., depending on the heating capability of the feed heater relative to the feed. Therefore, a change in crude slate that increases the proportion of naphtha cuts in the crude while decreasing the proportion of atmospheric gas oil (AGO) cuts can result in a direct increase on the relief rate of the crude column, whereas a change that only changes the heavier portions of the crude feed may not have a significant effect on the crude column. Note that composition changes that do not affect the crude column may affect another system, such as the vacuum column.
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4.1.2 Examples of Changes in Operating Conditions on Pressure Relief System Design
Tank
Crude Pumps
Desalter
Furnace
Water and Demulsifier
Crude-Pre-Flash Drum
Pre-Flash Vapor to Crude Column
Crude Column Charge
Water to Benzene Stripper
PreheatExchanger
Train
PreheatExchanger
Train
Crude/Vacuum Column Products/Pump Arounds
Crude/Vacuum Column Products/
Pump Arounds
Vacuum Column Residue
PSV-1
Figure 2: Crude Feed Pre-heating System Process Flow Diagram
The process flow diagram in Figure 2 represents the feed pre-heating section of a Crude Column system. Feed from tankage is pre-heated in a series of exchangers against hot fluid from Crude/Vacuum Column products and pump arounds; the crude feed is then treated for salt content in the Desalter before sending to the Crude Pre-Flash Drum. The Crude Pre-Flash Drum operates significantly lower than the Desalter, allowing the crude to flash. The flashed vapor is directly sent to Crude Column, while the liquid from the drum is sent through another train of exchangers, the furnace, and then to the Crude Column.
a. Effect of Operating Pressure Change on Composition
PSV-1 on the Flashed Crude pre-exchangers is sized for Blocked Outlet, and this case is usually selected as rate-dependent. However, a change in operating pressure of the Crude Pre-Flash Drum, with or without the throughput change, affects the composition of flashed liquid and vapor at the Crude Pre-Flash Drum, because the bubble point of the crude stream components is directly related to the operating pressure. In this case, as the fluid composition is changed, an assumption of a linear relationship between changes in throughput and required area may not be accurate.
b. Effect of Operating Temperature Change on Composition
Similarly, a change in the throughput may result in change in product rates, Crude Column product/pumparound rates and Vacuum Column product/pumparound rates, which could result in change in the heat input at the Crude Preheat exchangers. Similar to pressure, a change in Pre-Flash Drum inlet temperature, may affect the composition of Crude Pre-Flash Drum liquid and vapors, and the rate dependent assumption may no longer apply for Blocked Outlet case for PSV-1.
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5 Conclusion
The economic driver for maximizing the production from process units is ever-present. However, it is vitally important to ensure that the techniques used to evaluate the pressure relief system design are appropriate and suitable to the task. Awareness of the assumptions inherent in rate-dependent classifications, and the potential to invalidate this classification with further “pencil-sharpening”, is a starting point. Understanding the ways in which process throughput scale-ups can impact other factors in determining the design of the pressure relief system, such as affecting the fluid composition, operating conditions, and heat exchanger duties, and their impact on required relief rate determination or even scenario applicability, helps to illuminate potential problem areas when evaluating a process throughput scale-up, and informs the decision on whether a revalidation of the heat and material balance is appropriate. Altogether, these considerations should enable engineers to make smarter decisions about rate-dependency and ensure safer operation during process throughput scale-ups.
6 References
[1] American Petroleum Institute, API Standard 520: Sizing, Selection, and Installation ofPressure-relieving Devices Part I – Sizing and Selection, 9th edition, July 2014.