CAPITULO II DISCREPANCIA FISCAL
2.3. Ingreso y erogaciones
where ΔTA is the temperature difference between the two streams at end A, and ΔTB is the temperature difference be-tween the two streams at end B. In this case, the LMTD will have a limit of 0, so it will need a UA with an infinite limit.
The second aspect to consider for any real equipment is the pressure drop that will be consumed on the hot and cold sides as the respective streams flow through the heat exchanger.
It is normal for the process engineer to designate how much pressure drop will be allocated to a particular exchanger. For example, in turbulent flow inside tubes, the local heat transfer coefficient varies approximately with the mass velocity raised to the power 0.8. The pressure drop varies approximately with the mass velocity squared. This means that, if pressure drop is kept low, the heat transfer coefficient will be very low, and a large surface area will be needed for the heat exchanger. A realistic pressure drop must be estimated at this stage to en-able the design of the heat exchanger later without having to rework the process design.
A more realistic way to model the exchanger is to assume that one side of the exchanger is between 90°C and 25°C, with the other side heating up from 20°C to 85°C. Both sides have a pressure drop of 0.5 bar (FIG. 2).
This type of idealized approach is often used to model an exchanger where a process stream is heated by utility steam in a heat exchanger. Pure fluids, like steam, condense isother-mally at constant pressure. If isothermal condensation is pres-ent, then EQ. 3 can be applied to good effect; however, in real-ity, any pressure drop on the steam side will result in a lower saturation temperature, and then the exit temperature will be lower than the inlet temperature.
The main issue with this approach is that it is easy for the process engineer to specify conditions that later make it diffi-cult to achieve a practical exchanger design. This hampers ef-fective collaboration between process engineers and thermal design specialists, resulting in additional cycles of engineering to refine the overall process and equipment designs.
One way to promote better collaboration between disci-plines and achieve better designs quickly is to use a rigorous exchanger modeling tool within the process simulation to achieve a preliminary design. This approach enables the pro-cess engineer to get a better first approximation for evaluating the feasibility of the process, and to give the thermal specialist a useful starting point for full design optimization. Where this technique is employed, it has been shown to reduce project schedules and eliminate costly rework.
Revamp studies. The second type of project where rigorous heat exchanger modeling can improve the engineering work-flow is a revamp. Typically, revamp projects have two main aspects. First, there is a check that the actual proposed equip-ment in the process is accurately simulating the plant perfor-mance data. Secondly, “what if ” options can be explored for process and capital improvements, with different equipment geometries and stream sequencings validated against the re-vamp’s performance objective.
Modeling an existing exchanger can be easy if plant data is available. The process simulator allows the specification of process conditions for the exchanger. This, in turn, allows simple modeling of an exchanger based on EQ. 3, and it en-ables the simulator to estimate the exchanger duty. The inher-ent assumption is that UA will remain constant. The pressure drop will not be recalculated by the simulator, so any variation will need to be estimated with a manual calculation. As men-tioned earlier, for single-phase turbulent flow inside tubes, the local heat transfer coefficient will vary according to:
␣ = f(m0.8) (5)
where ␣ is the local tube-side heat transfer coefficient, and m is the mass velocity in the tubes. This indicates that, as the flow of either stream in an exchanger is varied, the simple modeling of the simulator will result in an error in the estimated duty of an exchanger. Change in steam properties will also be unac-counted for in this simple modeling approach.
In the following example, the first exchanger downstream of the desalter in a crude preheat train is subject to examina-tion in a revamp study where the overall aim is to recover more pumparound energy and increase the throughput of the refinery (FIG. 3). The first step is to model the existing exchanger. The crude on the tube side of this exchanger is fo-cused on in TABLE 1.
FIG. 2. Heat exchanger model showing one side heating up and one side cooling down.
FIG. 3. Revamp study of an exchanger in a crude preheat train.
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Heat Transfer Developments
The first two columns are the values of the pressure drop and the temperature changes on the tube side of the exchang-er. The last two columns represent the difference between the simple UA modeling and the rigorous modeling approaches.
In the first set of process conditions, the rigorous model and UA model values are close. This is expected, since the UA mod-el is based on the result of the rigorous calculation performed during the design stage. However, when the process conditions change, the UA model and rigorous model diverge, with the relative difference increasing from less than 1% to more than 3% for the temperature drop, and from less than 2% to more
than 20% for the pressure drop. The rigorous modeling shows that the pressure drop increased to a value higher than the limit of 0.6 bar defined in the process. After the revamp and a rede-sign of the heat exchanger, it is possible to calculate the pres-sure drop for the rigorous model below the limit of 0.6 bar.
The rigorous modeling of the heat exchanger is needed to check the performance with new process conditions and to properly design a revamped heat exchanger. The integration of rigorous modeling inside the simulator allows the engineer to check the anticipated heat exchanger performance and take any corrective design actions without leaving the simula-tor environment.
Operation support. In this case study, an existing exchanger on a gas compression system is water-cooled. The process is modeled with a control operation that simulates the adjust-ment of the water flow to achieve a specified outlet tempera-ture for the gas being cooled on the tube side of the heat ex-changer (FIG. 4).
The operator is seeking to reduce the outlet temperature of the heat exchanger to reduce the power consumed by a large compressor. In the process simulator, it is simple to set a lower gas outlet temperature target in the control block, and the coolant flow rate will be increased until the new, higher duty is achieved.
In the rigorous exchanger simulation shown in FIG. 5, it is clear that the pressure drop on the water side is below the maximum allowable for the existing operating conditions.
If a lower gas outlet temperature is prescribed to affect the desired reduced compressor power, the rigorous model in the simulation responds to the increased coolant flow that the adjust mechanism imposes. The exchanger can now achieve the new duty. However, because a rigorous tool is being used, other beneficial calculations can be performed. The results highlighted in FIG. 6 show three issues to consider:
Pressure drop. The increase in water flow has resulted in a pressure drop on the shell side, which exceeds the design al-lowable. This may mean that sufficient pumping capacity will not be available to achieve the required flow.
Dynamic pressure. The Tubular Exchanger Manufacturers Association (TEMA) defines maximum dynamic pressure as:
q = rho v2 (6)
where rho is the fluid density, and v is the fluid velocity.1
TABLE 1. Modeling data for a heat exchanger in a crude preheat chain
Error
Pressure drop, bar Temperature drop, °C Pressure drop, bar Temperature drop, °C
Design conditions UA 0.6 39.4
Rigorous model 0.59 39.7 −1.7% 0.8%
New conditions UA 0.6 33.8
Rigorous model 0.79 35.1 24.1% 3.7%
Revamp 0.59 33.7 −1.7% −0.3%
FIG. 4. Water-cooled exchanger on a gas compression system.
FIG. 5. Rigorous simulation for a water-cooled exchanger.
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