Design methodology and valve sizing for heater drain systemsCASEY LOUGHRIN

IntroductionHeater drain systems in fossil and nuclear power plants have proven to be among the most complex systems to design due to the occurrence of two-phase flow phenomena. The overall performance of heater drain systems directly relates to proper sizing and design of the piping and control valves.Proper sizing is highly dependent on accurate and conservative calculation of two-phase flow pressure losses. Various options for solution methods are available to the engineer. One such method, based on the homogeneous equilibrium model (HEM), is developed which is simple, yet adequate, for the necessary two-phase flow calculations of heater drain systems. This study focuses on plant cycles (both fossil and nuclear) where the feedwater heater drains are cascaded backward (counter to feedwater flow), as shown in Figure 4 for a typical sub-critical fossil plant Rankine cycle. In such systems, flow is driven by the combination of pressure and gravity forces. As such, thephysical location of each feedwater heater, as well as piping arrangement,directly affects the suitability of the heater drain system. The normal drain flow path from each feedwater heater is directed through a heater drain control valve to the subsequent lower-pressure feedwater heater. In the case of the lowest-pressure heater (usually located in the condenser neck), drains are normally directed to the condenser after passing through the heater drain control valve (note that a loop seal might be provided in lieu of a control valve for the lowest-pressure heater). The emergency drain flow path is directed from each heater through a separate heater drain control valve to the condenser, or a flash tank that is vented and drained to the condenser. The use of separate flash tanks generally is dictated by the condenser manufacturer. The control valves, in either the normal or emergency drain lines, maintain the condensate water level in the shell-side of the respective feedwater heater. The normal and emergency drain control valves operate in series, meaning that the emergency drains are used only when the normal drains are not able to maintain the liquid level or when the normal drain destination is unavailable.Figure 4 shows the lowest-pressure heater drains pumped to the next-higher-pressure heater piping. Plants with heater drains pumped forward to higher-pressure heaters can be problematic as well; but proper design of such systems is outside the scope of this work due to differences in the operations and design considerations involved.Improper design of the plant heater drains system results in losses in plant cycle efficiency, as well as plant availability, which is why heater drain performance is critical to overall plant operation.Proper understanding of the two-phase flow phenomena occurring in heater drain systems is essential to proper system design.System definition: Heater drain system arrangement and design criteriaWith proper implementation of the design recommendations presented here, many of the characteristic heater drain system problems can be minimized or avoided completely. The following is an itemized list of design features that have been successfully applied to heater drain systems:Physical location of feedwater heaters The lowest-pressure feedwater heater(s) is usually located in the condenser neck beneath the low-pressure turbine section. Since there is little pressure gradient available to pass the flow, the importance of static head is amplified. The greatest feasible elevation difference should be provided. Successive feedwater heaters (excluding the lowest-pressure feedwater heaters) are usually arranged in the following configurations: Side-by-side on one or two elevations. Vertically stacked in elevated boiler steel or dedicated bay with the deaerator at the top-most elevation due to boiler feed pump NPSH constraints.It is important that the elevation difference between the deaerator and those feedwater heaters whose normal drains are directed to the deaerator is not too great to prevent pressure-driven drainage at part-load plant operation due the decreased heater operating pressure. If this cannot be accommodated, heater drain pumps would be required or the emergency drain system would need to operate.Normal and emergency heater drain piping from the source feedwater heater to the control valve Feedwater heater nozzle sizes should comply with HEI recommendations.(See Equation 1)

Design flows must be carefully evaluated. The operating scenario at full load with the highest mass flow rate might not be the proper design point, as with typical incompressible (liquid-only) flow systems. The pressure gradient also must be considered to ensure that the drain system capacity is adequate at full and reduced pressures occurring at part-load plant conditions. Plant off-design scenarios, such as feedwater heaters out of service, also must be considered for the emergency drains system.Piping from the feedwater heater drain outlet nozzle to the control valve inlet should be designed so that the pressure drop is not sufficient to cause phase change at any point under any operating condition. This typically implies that the control valve must be at a lower elevation than the source feedwater heater (this might not be the case for normal drains to the deaerator, where the valves might be placed at higher elevations to shorten the length of pipe exposed to multiphase flow).Pipe velocities at design conditions typically are in the 3-10 fps range, but verification that the pressure drop is less than that required to reach saturation across all operating scenarios supersedes velocity-based design constraints.Heater drain piping from the control valve to the next-lower pressure feedwater heater for normal drains, and to the condenser or flash tank for emergency drainsPiping generally is at least one nominal size larger than control valve inlet piping, but even larger pipe sizes might be required based on the available pressure gradient and static head.The two-phase flow downstream of the control valve results in high erosion potential, especially at fittings such as elbows, where the high-velocity water droplets have an impact on the walls at changes in direction. Heater drain systems are not particularly high-pressure or temperature; therefore, carbon steel piping materials generally are the most economical from a first-cost perspective. To counteract the erosion potential, the following design features have been incorporated successfully: Increased nominal wall thickness to schedule 80 or greater, as deemed necessary by the engineer. This method is analogous to corrosion allowances applied to piping and does not decrease the erosion potential. Use of higher-grade material, containing chromium, has proven to provide sufficient resistance to erosion. A minimum chrome content of 1.0 percent is recommended (Grades P11, P12, P22 and P5). Hydraulic pockets might be provided in lieu of the elbow immediately downstream of the control valve station.The maximum erosion force at elbows has been established as 75 lbf [Ref. 2]. Supporting data are not provided, but the limits seem appropriate and typically do not result in an uneconomical design. The erosion force can be determined by Equation 2 [Ref. 2].

All or a selection of these options might be employed in a single system at the designers discretion. At a minimum, the following items should be considered: Drains from separate heaters, whether for normal or emergency operation, should have separate dedicated nozzles and should not be manifolded under any circumstance. This includes parallel heaters in separate heater trains draining to the same location. Condenser connections often will be supplied with internal baffles or spargers. Baffles are provided only for preventing tube impingement and other common condenser damage mechanisms from high-velocity drain flows. Normal and emergency heater drain design flow rates do not necessarily have to match. At a minimum, normal drain design conditions should cover operating conditions from minimum plant load through full load. Emergency drain design conditions must cover the full range of plant operating conditions from startup through full load, including off-design conditions (heaters out of service, tube breaks). These requirements are summarized in Table 1.

These design features should be considered and accommodated, where feasible. Failure to implement all of the criteria outlined above will not necessarily result in improper system operation, but the system designer should understand the effects and implications before making such a decision.

System model selection: Multiphase flow model overviewThrough the years, many methods/models have been developed for sizing/evaluating multiphase pipe flows. Ultimately, it is at the system designers discretion to select andimplement the most appropriate method. Various options for multiphase flow modelingare outlined by the author inReference 12 with a tabulation of the advantages/disadvantages of each.The various models should be evaluated with the respect to the following criteria: Ease of implementation Accuracy Conservative nature of the calculation methodThe homogenous equilibrium model (HEM) was selected due to its combined advantages in the identified categories. Refer to ASME paper POWER 2009-81116 (Reference 12) for a complete discussion and derivation. The HEM model is shown in Equations 3, 4 and 5.

Component sizing: Heater drain pressure loss calculationsCalculation of the pressure gradient along the heater drain lines is essential for proper system design and component selection. The system designer should be aware of the limitations of the model chosen and the corresponding effects to the calculation results. The simplifying assumptions of HEM are as follows: The fluid is in thermodynamic equilibrium at every point along the flow path. At every cross-section along the flow path, the fluid thermodynamic properties (pressure, temperature, enthalpy, etc.) are homogeneous. Homogeneous distribution of the phases (no separation), and thus no velocity difference or friction effects between the phases. Liquid-to-vapor flashing occurs adiabatically. Heat transfer through the pipe walls is negligible (well insulated).The typical elements of a normal drain system are shown in Figure 3.

The important points along the flow path are indicated in the figure as A through E. Determination of the pressure at these points is necessary to: Verify the adequacy of the selected pipe size and routing Size the feedwater heater level control valve (developed further in the next section)In order to determine the pressures at the indicated positions in the flow path and the corresponding pressure gradient, the pipe segments and components are generally calculated in the following order: Piping from the upstream feedwater heater to the control valve inlet (Segment A-B) Piping from the control valve outlet to the downstream feedwater heater (Segment C-D) Control valve (Segment B-C)For emergency drain systems, the same calculation order is used, but the downstream feedwater heater is replaced with the condenser or drain flash tank. Additional components such as hydraulic spargers can be included in the downstream piping segment.The following is a brief summary of the necessary steps. Please refer to ASME paper POWER 2009-81116 for a more detailed and comprehensive outline of the procedure and calculations.Segment A-B:The piping upstream of the control valve should be designed to maintain single phase flow. As such, any appropriate single phase pressure drop model can be employed. The HEM model also can be used since it simplifies to the common single phase expressions. The derivations are shown in ASME paper POWER2009-81116.Segment C-D:The piping downstream of the control valve might or might not be flashing, depending on the operating conditions and downstream heater pressure. Flashing will occur at the entrance to the downstream heater (or condenser).

The critical exit pressure must first be determined, which is the pressure at point D of Figure 3. The critical exit pressure corresponds to the pressureat which all available flow energy isused for the expansion of the fluid to the lower pressure state in the downstream heater. The critical exit pressure is determined by simultaneously solving the energy and momentum conservation equation shown below.

The critical exit pressure is unique to each flow, pipe size and enthalpy content, and must be recalculated if any of the parameters change. The critical exit pressure will increase as the pipe size decreases until the pressure gradient in the pipe is too small to pass the required flow.Once the critical exit pressure is determined, the pressure gradient is calculated working backward from the point D to point C at the control valve exit.Control valve:The differential pressure across the control valve (point B to point C) should be evaluated for feasibility and used for the control valve sizing calculations. If the calculated pressure at point C is higher or not sufficiently lower than point B, the downstream pipe size must be increased and step 2 performed again.The preceding calculations can be performed by hand, by spreadsheet or by dedicated calculation or simulation software. Selection of the appropriate method of implementation is based on the desired accuracy as determined by the system designer.Component sizing: Valve sizing and selectionThe heater drain level control valves are sized based on the inlet and outlet pressures calculated by the preceding methods. It is recommended that the following criteria be used for specification/selection of control valves for heater drain service: The control valve trim should be sized to be 75-80 percent open under maximum flow conditions The control valve should not operate at less than 15 percent open under minimum flow conditions Hardened erosion resistance materials should be used for the control valve trim (minimum 400 series stainless) Minimum 1/8 erosion allowance should be included for the control valve body if carbon steel materials are used Erosion-resistant materials should be used for the control valve body (equivalent to the downstream piping) if alloy piping downstream of the control is used Oversized or expanded control valve bodies can be used to reduce the velocity in the valve, and reduce the potential for erosionWhile the overprediction of pressure losses is conservative with respect to pipe sizing, this is not necessarily the case with respect to control valve sizing. HEM-based pressure drop predictions have been shown to vary by as much as +20 percent from experimental data. With respect to control valve selection, smaller-pressure losses through the valve will be predicted than the installed valve will experience. As a result, a larger valve than required might be selected. Use of oversized control valves can lead to several unwanted results: Continuous operation at low opening percentages resulted in degraded valve integrity Limited turndown capacity, resulting in poor or even inadequate performance during startup and low load operationTo address these concerns, it is recommended that the valve operation be evaluated with a 20 percent lower outlet pressure at both maximum and minimum flow conditions. Under these modified conditions, the control valve should still operate within its stable control range.ConclusionMany options, methods and industry experience that have been applied for the design of heater drain systems have been compiled and presented in this work. Ultimately, it is the responsibility of the engineer to determine the necessary design and solution methods to provide an adequate system design.

Design Review ChecklistThe engineer responsible for checking the adequacy of a new or an existing design should include the following items on the review checklist: The pressure drop between the upstream heater and the downstream heater should be adequate to pass the required flow during both full-load and some selected reduced-load operating conditions. Heater locations and elevations should be properly determined, because this can contribute significantly to the total pressure drop between the heaters. The effect is especially true for the lowest HP heater draining to the deaerator, and LP heaters draining to the next lower heater, where the static head becomes significant relative to the difference in heater pressures. The drain line from the heater outlet to the control valve should be designed so that single-phase condensate flow exists up to the control valve. The drain line from the control valve outlet to the receiving heater inlet should be designed for two-phase flow. The two-phase flow should not occur at the control valve outlet but at some distance from the control valve. If the two-phase flow occurs at some distance from the control valve outlet, then the static pressure due to the liquid head must be considered in the pressure drop calculation for the piping downstream of the control valve. The control valve should be properly sized based on correct values of valve inlet pressure P1and valve outlet pressure P2. The inlet pressure P1can be calculated in a straightforward manner by computing the pressure drop between the upstream heater and the control valve using the Darcy equation for single-phase flow. The outlet pressure P2may be based on single-phase or two-phase flow. The computation is more involved for two-phase flow, requiring use of the general flow equation. The control valve should be checked for cavitation against the valve manufacturers recommended index to determine if damage mitigation is required or not. The control valve should be checked for flashing and steps taken to minimize its damaging effect on valve internals and downstream piping.Check Heater Drain Valve Cavitation/Flashing ConditionsThe heater drain control valve may be subject to cavitation or flashing service, which could damage valve internals and piping. It is therefore important to establish clearly whether the valve is subject to cavitation or flashing so the appropriate mitigating methods can be used.The heater drain control valve sizing depends on the allowable pressure drop (Pa) across the valve. The allowable pressure drop is the smaller of the actual pressure drop and the choked pressure drop.The choked pressure drop, for valves installed without inlet/outlet fittings, can be predicted by the following equation: Pchoked= FL2x (P1 FFPv), where FL= liquid pressure recovery factor provided by valve manufacturer; P1= upstream pressure at valve inlet, psia or kPa; FF= liquid critical pressure ratio factor = 0.96 0.28SQRT(PV/PC); PC= critical pressure of liquid, psia or kPa; and PV= vapor pressure of the liquid at flowing temperature, psia or kPa.The choked pressure drop corresponds to choked flow in the valve created by the formation of gas bubbles when the fluid pressure drops below the vapor pressure at the valve vena contracta. The formation of gas bubbles at the valve vena contracta depends on the downstream pressure (P2), meaning the valve could be in cavitating service or flashing service.