Heat Tracing Models

The total cost of the field indirects is 100-130% of direct labor costs (direct hire) plus 15-20% of subcontracts and inversely proportional to project size. In the following breakdown, an asterisk denotes services usually supplied by Construction Manager or General Contractor. 

Roads/fences/parking/drainage/signs/lighting  

Consumables Small Tools Equipment Rentals Equipment Fuels and Lubricants Home Office Supervision Direct Field Supervision Administrative Support Travel Expenses Other 

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The second question asked what would be an excessive temperature for this process. It was recommended that process hot spots (i.e., zones higher than 100°C) should be avoided. This requirement was met by keeping the heating lines, the walls of the melting pot, and the spray head thermally jacketed to maintain the appropriate internal soak temperature. As a result, the model presented a potential for hot spots at the skin surfaces of the lines and equipment walls. This needed to be investigated for its decomposition potential, and in fact, after several batches were processed, the flexible heat-traced lines had to be discarded because of a buildup of a blacked residue on the inner tubing walls. The kinetic model predicted how many batches could be run before this necessary replacement maintenance was required. 

Heat Tracing - The heat tracing units, steam and electrical, were developed in the late 1980 s with the help of construction contractors and have been escalated to late 2000 (C.E. plant cost index of 420). The models used to prepare the unit prices are shown in Appendix J and can be used to adapt them to different circumstanees. 

Having traced through the heat transfer models and given some consideration to the experimental evaluation of heat transfer parameters the time is now opportune to consider the chemical reactor and, in particular, heat transfer therein. 

Figure 12-3 Design Point for TRACE Model (Heat Balance Case HB24).28...

Comparison of Heat Balance Case 24 Design Point and TRACE Model State Points. 27... 

The TRACE model was built in a modular fashion. Individual component models were built for the reactor, recuperator, gas cooler, turbine, compressor and HRS. Each of these sub-models was built and checked against the concept selection heat balance, HB24, and models built using other codes (such as Mathcad). For example, detailed Mathcad models of the recuperator and gas cooler were used to help determine TRACE code model inputs and verify steady state operating performance. 

Future TRACE model updates would have transitioned to an updated gas cooler design. Other future TRACE model updates would have included local assignment of ambient heat losses. TRACE heat structures were in place to distribute ambient losses throughout the plant. In addition, component test results for heat transfer and pressure drop would have been incorporated when available. For the TRACE Brayton components, additional detail was planned for bearing and windage losses (as a function of speed rather than a constant value), and more accurately modeling the alternator heat input (based on variable alternator efficiencies). 

Overall, the TRACE model produces a steady state operating point that is in good agreement with separate heat balance calculations. This comparison is important as the first step in qualifying the Tf CE code and model for a given plant design. 

The default TRACE heat transfer correlation for the working fluid is Dittus-Boelter The helium-xenon binary gas mixture used as the reference coolant in this study has a much tower Prandtl number (0.2 to 0.7) than the air, steam and water fluids normally used in TRACE Reference 12-7 describes a low Prandtl number literature search to determine what heat transfer correlation might be best for the reactor coolant Consistent with this letter, the TRACE model invokes the Petukhov-Popov correlation in the fueled region. This special heat transfer correlation is referred to as the special gas fuel pin heat transfer package. 

TRACE model Coolant Mixture (to match current heat balance) 78.4% He. 21.6% Xe... 

The gas cooler model Is shown in Figure 12-10. The gas cooler design was started using the concept selection heat balance and therefore was sized for about 285 kW. At this power level the cooler was 94% effective. At full power steady state conditions, the TRACE model calculates a gas cooler power level of about 303 kW At these conditions the corresponding gas cooler effectiveness is about 91%. This difference does not have a significant impact on the overall TRACE model performance. The water side of the cooler is designed to operate at about 8 MPa. The gas cooler model is a counterflow design with 400 tubes at 6.35 mm OD and 1.058 mm tube wall thickness. The tube... 

Where (rg - rn) is the fin height and yt, is the fin thickness. For the TRACE gas cooler design, the quantity x" is about 1.5, resulting in a fin efficiency of about 0.6. The actual fin efficiency would be determined with a more detailed equipment design and subsequent testing, The TRACE model uses cylindrical geometry hydraulics and heat structures. The heat structure is nodalized at 40 axial and 5 radial nodes. Axial conduction is enabled. The material properties applied are for Alloy 600. The TRACE heat structure has the same dimensions as an individual tube. A multiplier is used to produce the correct total heat transfer area. The fin surfaces are not explicitly modeled in TRACE. Instead, a gas (outside tube) heat transfer coefficient multiplier is used to account for the additional effective area. 

At steady state conditions the typical water temperatures entering and exiting the gas cooler are 375 K and 501 K respectively. This temperature drop is significantly less than the HB24 value of 151 K (530 395 K). The TRACE model AT is less because a higher water mass flow rate is used and the total cooler power is somewhat lower (303 vs. 309 kW). Later versions of the heat balance spreadsheet were updated with more consistent water based HRS design parameters and became more consistent with the TRACE results. 

Currently the standard TRACE code heat transfer (Dittus-Boelter) and fluid pressure drop (Churchill and Moody) correlations are applied to the gas cooler. Use of the Churchill correlation and Moody curves, and mathematical representations of the curves, for calculation of the single-phase friction factor in a variety of flow-channel geometries is a common engineering practice. Information on the TRACE default correlations is available in the TRACE theory manual (Reference 12-9). A surface roughness of 2E-6 m is used with the TRACE single phase friction correlations. In order to match the HB24 pressure drop prediction, additional frictional flow factors are included in the hydraulic model. The TRACE model also includes plenums to provide a location to specify form loss factors for the gas cooler. The heat transfer and pressure drop correlations would have been updated as the cooler design was determined and as test data was collected. 

The HRS in TRACE is modeled after the PB1 design described in Reference 12-11 and further discussed in Section 9.6. There are two water HRS loops in the TRACE model, one connected to each Brayton loop as shown in Figure 12-12. The gas cooler is the connection between the primary gas loop and the HRS water loop. The water flows out of the gas cooler after being heated and enters the heat transport loop assembly further discussed in Section 9.6.2.1. Each heat transport loop assembly consists of four sections of parailel circular water ducts that are connected to slab heat structures. These heat structures represent the radiator panel assemblies as described in Section 9.6.2.2. The four sections of pipes feed into a larger return duct that leads to a centrifugal pump and accumulator before returning to the inlet of the gas cooler. 

The TRACE Tgve was defined as the average between reactor inlet and outlet plenum temperatures. Once the TRACE model has been defined, the only constraints applied to the steady state run were the Tave (1024 1.5K), Brayton speed (4712.4 rad/s), and radiation heat transfer heat sink temperature (200 K). TRACE reactor power is allowed to float to a new state point. The TRACE fuel temperature rise is about 273K (1162 K - 889 K) at a reactor power level of almost 900 kWt. 

Qualitative examples abound. Perfect crystals of sodium carbonate, sulfate, or phosphate may be kept for years without efflorescing, although if scratched, they begin to do so immediately. Too strongly heated or burned lime or plaster of Paris takes up the first traces of water only with difficulty. Reactions of this type tend to be autocat-alytic. The initial rate is slow, due to the absence of the necessary linear interface, but the rate accelerates as more and more product is formed. See Refs. 147-153 for other examples. Ruckenstein [154] has discussed a kinetic model based on nucleation theory. There is certainly evidence that patches of product may be present, as in the oxidation of Mo(lOO) surfaces [155], and that surface defects are important [156]. There may be catalysis thus reaction VII-27 is catalyzed by water vapor [157]. A topotactic reaction is one where the product or products retain the external crystalline shape of the reactant crystal [158]. More often, however, there is a complicated morphology with pitting, cracking, and pore formation, as with calcium carbonate [159]. 

Here not only does the resistive portion of the capacitor model cause problems, but if the PCB is laid out asymmetrically between paralleled capacitors, the trace inductance causes unbalanced heating within the capacitors, thus shortening the life of the hottest capacitor. 

The lower trace in Figure 1 shows the results of heating the tunnel junctions (complete with a lead top electrode) in a high pressure cell with hydrogen. It is seen that the CO reacts with the hydrogen to produce hydrocarbons on the rhodium particles. Studies with isotopes and comparison of mode positions with model compounds identify the dominant hydrocarbon as an ethylidene species (12). The importance of this observation is obviously not that CO and hydrogen react on rhodium to produce hydrocarbons, but that they will do so in a tunneling junction in a way so that the reaction can be observed. The hydrocarbon is seen as it forms from the chemisorbed monolayer of CO (verified by isotopes). As... 

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