Heat Tracing Research Articles

Estimating the Thermal Effusivity for Coaxial Thermocouple Using a Quantified Aluminum Nitride Heater

In this paper, a parameter estimation approach, based on a least-square method and a quantified heat flux source, is proposed for estimating the effective thermal effusivity of a co-axial thermocouple. The co-axial thermocouple is inserted in a through hole of a stainless steel 304 sample. From one-dimensional, constant-property, semi-infinite heat conduction theory, a direct integral relationship exists that connects probe temperature, source heat flux, and thermal effusivity. The effective thermal effusivity can be estimated using a highly accurate heat flux source and temperature measurement through a calibration study. This paper describes the calibration of the heat flux source, composed of an aluminum nitride heater with a tungsten heating trace, and the experimental and computational procedures used for estimating the effective thermal effusivity. Once obtained, this value is used in a series of experiments for reconstructing the surface heat flux. The estimated surface heat flux is then compared with the high-quality heat flux source. It is demonstrated that the effective thermal effusivity, when used in conjunction with the co-axial thermocouple temperature, produces an estimated source heat flux that compares favorably with the source heat flux.

Field Experiments of Hyporheic Flow Affected by a Clay Lens

As a typical water exchange of surface water and groundwater, hyporheic flow widely exists in streambeds and is significantly affected by the characteristics of sediment and surface water. In this study, a low-permeability clay lens was chosen to investigate the influence of the streambed heterogeneity on the hyporheic flow at a river section of the Xin’an River in Anhui Province, China. A 2D sand tank was constructed to simulate the natural streambed including a clay lens under different velocity of surface water velocity. Heat tracing was used in this study. In particular, six analytical solutions based on the amplitude ratio and phase shift of temperatures were applied to calculate the vertical hyporheic flux. The results of the six methods ranged from −102.4 to 137.5 m/day and showed significant spatial differences. In view of the robustness of the calculations and the rationality of the results, the amplitude ratio method was much better than the phase shift method. The existence of the clay lens had a significant influence on the hyporheic flow. Results shows that the vertical hyporheic flux in the model containing a clay lens was lower than that for the blank control, and the discrepancy of the hyporheic flow field on both sides of the lens was obvious. Several abnormal flow velocity zones appeared around the clay lens where the local hyporheic flow was suppressed or generally enhanced. The hyporheic flow fields at three test points had mild changes when the lens was placed in a shallow layer of the model, indicating that the surface water velocity only affect the hyporheic flow slightly. With the increasing depth of the clay lens, the patterns of the hyporheic flow fields at all test points were very close to those of the hyporheic flow field without a clay lens, indicating that the influence of surface water velocity on hyporheic flow appeared gradually. A probable maximum depth of the clay lens was 30 to 40 cm, which approached the bottom of the model and a clay lens buried lower than this maximum would not affect the hyporheic flow any more. Influenced by the clay lens, hyporheic flow was hindered or enhanced in different regions of streambed, which was also depended on the depth of lens and surface water velocity. Introducing a two-dimensional sand tank model in a field test is an attempt to simulate a natural streambed and may positively influence research on hyporheic flow.

Prediction of the Weld Qualities Using Surface Appearance Image in Resistance Spot Welding

The quality of the resistance spot weld is predicted qualitatively using information from the weld’s external apparent image. The predicting tool used for weld qualities was a convolution neural network (CNN) algorithm with excellent performance in pattern recognition. A heat trace image of the weld surface was used as information on the external apparent image of welds. The materials used in the experiment were advanced high strength steel (AHSS) with 980 MPa strength, and uncoated cold-rolled (CR) steel sheets and galvannealed (GA) steel sheets were used. The quantitatively predicted weld quality information contained tensile shear strength, nugget diameter, fracture mode of welds, and expulsion occurrence. The predicted performance of the verification step of the model determined through the learning process was as follows; the predicted error rate for tensile shear strength and nugget diameter were 2.2% and 2.6%, respectively. And the predicted accuracy on fracture mode and expulsion occurrence was 100%.

A Deep-Sea Pipeline Skin Effect Electric Heat Tracing System

In order to ensure deep-water flowline safety, this paper combined the axial temperature distribution model of the submarine pipeline and the distributed parameter circuit model of the skin effect electric heat tracing system; such work is conducive to proving that the heating effect of the skin effect electric heat tracing system depends on the distributed circuit parameters and power frequency of the system. Due to the complexity of the power supply device, the frequency cannot be increased indefinitely. Therefore, for the case that the input of the skin electric heat tracing system is constrained, a generalized predictive control algorithm introducing the input softening factor is proposed, and the constrained generalized predictive control strategy is applied to the electric heating temperature control system of the submarine oil pipeline. Simulation results demonstrated that the control quantity of the skin effect electric heat tracing system is effectively controlled within a constraint range, and also the values of heating power and power frequency are obtained by theoretical calculations rather than empirical estimations. Moreover, compared with the conventional control algorithm, the proposed constrained generalized predictive algorithm unfolds more significant dynamic response and better adaptive adjustment ability, which verifies the feasibility of the proposed control strategy.

Feasibility Study of Freeze Recovery Options in Parabolic Trough Collector Plants Working with Molten Salt as Heat Transfer Fluid

Parabolic trough collector (PTC) technology is currently the most mature solar technology, which has led to the accumulation of relevant operational experience. The overall performance and efficiency of these plants depends on several components, and the heat transfer fluid (HTF) is one of the most important ones. Using molten salts as HTFs has the advantage of being able to work at higher temperatures, but it also has the disadvantage of the potential freezing of the HTF in pipes and components. This paper models and evaluates two methods of freeze recovery, which is needed for this HTF system design: Heat tracing in pipes and components, and impedance melting in the solar field. The model is used to compare the parasitic consumption in three molten salts mixtures, namely Solar Salt, HiTec, and HiTec XL, and the feasibility of this system in a freezing event. After the investigation of each of these subsystems, it was concluded that freeze recovery for a molten salt plant is possible.

Heterogeneity and Prior Uncertainty Investigation Using a Joint Heat and Solute Tracer Experiment in Alluvial Sediments

In heterogeneous aquifers, imaging preferential flow paths, and non-Gaussian effects is critical to reduce uncertainties in transport predictions. Common deterministic approaches relying on a singlemodel for transport prediction show limitations in capturing these processes and tend to smooth parameter distributions. Monte-Carlo simulations give one possible way to explore the uncertainty range of parameter value distributions needed for realistic predictions. Joint heat and solute tracer tests provide an innovative option for transport characterization using complementary tracer behaviors. Heat tracing adds the effect of heat advection-conduction to solute advection-dispersion. In this contribution, a joint interpretation of heat and solute tracer data sets is proposed for the alluvial aquifer of the Meuse River at the Hermalle-sous-Argenteau test site (Belgium). First, a density-viscosity dependent flow-transport model is developed and induce, due to the water viscosity changes, up to 25% change in simulated heat tracer peak times. Second, stochastic simulations with hydraulic conductivity (K) random fields are used for a global sensitivity analysis. The latter highlights the influence of spatial parameter uncertainty on the resulting breakthrough curves, stressing the need for a more realistic uncertainty quantification. This global sensitivity analysis in conjunction with principal component analysis assists to investigate the link between the prior distribution of parameters and the complexity of themeasured data set. It allows to detect approximations done by using classical inversion approaches and the need to consider realistic K-distributions. Furthermore, heat tracer transport is shown as significantly less sensitive to porosity compared to solute transport. Most proposed models are, nevertheless, not able to simultaneously simulate the complementary heat-solute tracers. Therefore, constraining the model using different observed tracer behaviors necessarily comes with the requirement to use more-advanced parameterization and more realistic spatial distribution of hydrogeological parameters. The added value of data from both tracer signals is highlighted, and their complementary behavior in conjunction with advanced model/prediction approaches shows a strong uncertainty reduction potential.

Return flows from beaver ponds enhance floodplain-to-river metals exchange in alluvial mountain catchments

River to floodplain hydrologic connectivity is strongly enhanced by beaver- (Castor canadensis) engineered channel water diversions. The hydroecological impacts are wide ranging and generally positive, however, the hydrogeochemical characteristics of beaver-induced flowpaths have not been thoroughly examined. Using a suite of complementary ground- and drone-based heat tracing and remote sensing methodology we characterized the physical template of beaver-induced floodplain exchange for two alluvial mountain streams near Crested Butte, Colorado, USA. A flowpath-oriented perspective to water quality sampling allowed characterization of the chemical evolution of channel water diverted through floodplain beaver ponds and ultimately back to the channel in ‘beaver pond return flows’. Subsurface return flow seepages were universally suboxic, while ponds and surface return flows showed a range of oxygen concentration due to in-situ photosynthesis and atmospheric mixing. Median concentrations of reduced metals: manganese (Mn), iron (Fe), aluminum (Al), and arsenic (As) were substantially higher along beaver-induced flowpaths than in geologically controlled seepages and upstream main channel locations. The areal footprint of reduced return seepage flowpaths were imaged with surface electromagnetic methods, indicating extensive zones of high-conductivity shallow groundwater flowing back toward the main channels and emerging at relatively warm bank seepage zones observed with infrared. Multiple-depth redox dynamics within one focused seepage zone showed coupled variation over time, likely driven by observed changes in seepage rate that may be controlled by pond stage. High-resolution times series of dissolved Mn and Fe collected downstream of the beaver-impacted reaches demonstrated seasonal dynamics in mixed river metal concentrations. Al time series concentrations showed proportional change to Fe at the smaller stream location, indicating chemically reduced flowpaths were sourcing Al to the channel. Overall our results indicated beaver-induced floodplain exchanges create important, and perhaps dominant, transport pathways for floodplain metals by expanding chemically-reduced zones paired with strong advective exchange.

Transient Heat Transfer Between Two Horizontal Pipelines in a Heat Tracing Enclosure

In this study, a numerical simulation of natural convection between two horizontal differentially heated pipelines inside a circular air-filled enclosure is performed using the finite difference method. The relevant parameters of the problem are the inclinations of the two cylinders (positioned vertically in this study, with the cold cylinder above the hot cylinder), the distance between cylinders and the Rayleigh number. The results show that transient irregular fluctuations in the flow field and heat transfer occur when the Rayleigh number increases or the distance between cylinders decreases. Under the current test conditions, increasing the Rayleigh number significantly increases the average heat transfer coefficient between the cold and hot cylinders.

Engineering aspects and thermal performance of molten salt transfer lines in solar power applications

Concentrating solar thermal power coupled with thermal energy storage is considered as one of the leading technologies to address the decarbonization of the energy sector. The use of molten solar salt (60–40% b.w. NaNO3-KNO3) as heat transfer fluid and thermal storage medium is the current commercial practice, with alternative salt mixtures being under evaluation for the next-generation higher-temperature systems. The main drawback of the molten salts is their high freezing temperature; active means are required for preheating of- and to prevent salt from freezing in- the transfer lines.In this article we present experiences from the PROTEAS facility, where heating tapes as opposed to heating cables are used. The thermal energy losses from the transfer lines are evaluated and compared to those predicted by a one-dimensional heat transfer analysis. Thermal losses between 43 and 100 W/m are found at operating temperatures from 300 to 500 °C. A joint optimization of the capital and operational expenditure for heating tapes and insulation is performed, leading to the optimal insulation thickness and installed heat tracing capacity. Increasing the installed heat tracing capacity with respect to the minimum required to overcome thermal losses, leads to a reduction of the preheating time and, therefore, a reduction in the overall operational expenses of the system. In some situations, this was found to also lead to a reduction in the necessary insulation thickness. Simulations indicate that if the optimal insulation was used, a decrease of 10 and 15% in thermal losses and O&M expenditures, respectively, could be achieved.

A Szegő limit theorem for translation‐invariant operators on polygons

AbstractWe prove Szegő‐type trace asymptotics for translation‐invariant operators on polygons. More precisely, consider a Fourier multiplier on with a sufficiently decaying, smooth symbol . Let be the interior of a polygon and, for , define its scaled version . Then we study the spectral asymptotics for the operator , the spatial restriction of A onto : for entire functions h with we provide a complete asymptotic expansion of as . These trace asymptotics consist of three terms that reflect the geometry of the polygon. If P is replaced by a domain with smooth boundary, a complete asymptotic expansion of the trace has been known for more than 30 years. However, for polygons the formula for the constant order term in the asymptotics is new. In particular, we show that each corner of the polygon produces an extra contribution; as a consequence, the constant order term exhibits an anomaly similar to the heat trace asymptotics for the Dirichlet Laplacian.

The Heat Asymptotics on Filtered Manifolds

The short-time heat kernel expansion of elliptic operators provides a link between local and global features of classical geometries. For many geometric structures related to (non-)involutive distributions, the natural differential operators tend to be Rockland, hence hypoelliptic. In this paper, we establish a universal heat kernel expansion for formally self-adjoint non-negative Rockland differential operators on general closed filtered manifolds. The main ingredient is the analysis of parametrices in a recently constructed calculus adapted to these geometric structures. The heat expansion implies that the new calculus, a more general version of the Heisenberg calculus, also has a non-commutative residue. Many of the well-known implications of the heat expansion such as, the structure of the complex powers, the heat trace asymptotics, the continuation of the zeta function, as well as Weyl’s law for the eigenvalue asymptotics, can be adapted to this calculus. Other consequences include a McKean–Singer type formula for the index of Rockland differential operators. We illustrate some of these results by providing a more explicit description of Weyl’s law for Rumin–Seshadri operators associated with curved BGG sequences over 5-manifolds equipped with a rank-two distribution of Cartan type.

The heat trace for the drifting Laplacian and Schrödinger operators on manifolds

We study the heat trace for both the drifting Laplacian as well as Schr\"odinger operators on compact Riemannian manifolds. In the case of a finite regularity potential or weight function, we prove the existence of a partial (six term) asymptotic expansion of the heat trace for small times as well as a suitable remainder estimate. We also demonstrate that the more precise asymptotic behavior of the remainder is determined by and conversely distinguishes higher (Sobolev) regularity on the potential or weight function. In the case of a smooth weight function, we determine the full asymptotic expansion of the heat trace for the drifting Laplacian for small times. We then use the heat trace to study the asymptotics of the eigenvalue counting function. In both cases the Weyl law coincides with the Weyl law for the Riemannian manifold with the standard Laplace-Beltrami operator. We conclude by demonstrating isospectrality results for the drifting Laplacian on compact manifolds.

ENSURING STABLE OPERATION OF GAS COLLECTION SYSTEM IN CONDITION OF REDUCED WELL PRODUCTION

Any gas condensate field has an extensive gas collection system (GCS), through which gas is delivered from the wells to a Gas Processing Plant by means of reservoir energy. At the final stage of field development the GCS operating conditions undergo significant changes, in particular due to lower temperature of transported gas and increased water cut in the production fluid. In winter, simultaneous action of these factors may lead to formation of ice and hydrate plugs disrupting normal operation of the GCS. Gas stream velocity shall exceed so-called critical velocity to ensure that the flowlines operate in the liquid removal mode. Its value is determined by a pipeline diameter, ratio of gas and liquid density, thermobaric conditions, flowline slope and other factors. Ensuring necessary velocity at the final stage of operation is usually impossible, thus, complete moisture removal is problematic and the hazard of ice formation persists. This paper proposes an innovative technology providing stable GCS operation by preventing ice formation in the flowline. For that end, the gas-liquid mixture in the GCS gets additional heat from heat tracing located inside the GCS. The heat tracing is coiled tubing with constant circulation of liquid heat-transfer medium: methanol-water solution, heated by rejected heat when passing through the air cooler unit (ACU). The coiled tubing forms a closed loop with the methanol pipeline. Changes in heat exchange medium consumption are introduced with a VSD-driven pump, basing on the results of temperature measurement in the flowline. Application of the proposed technique allows not only providing emergency-free GCS operation, but recuperation of rejected heat from the ACU as well.

Expansion of Sewer, Water and District Heating Networks in Cold Climate Regions: An Integrated Sustainability Assessment

This study presents an integrated sustainability assessment of technical alternatives for water and heating services provision in suburban areas affected by a cold climate. Each alternative combines a drinking water supply, sewerage (gravity or low-pressure), pipe freeze protection (deep burial or shallow burial with heat tracing) and heating solution (district heating or geothermal heat pumps). An innovative freeze protection option was considered, in which low-temperature district heating (LTDH) is used to heat trace shallow sewer and water pipes. First, the performance of each alternative regarding seven sustainability criteria was evaluated on a projected residential area in Sweden using a systems analysis approach. A multi-criteria method was then applied to propose a sustainability ranking of the alternatives based on a set of weights obtained from local stakeholders. The alternative with a deep buried gravity sewer and geothermal heat pumps was found to have the highest sustainability score in the case study. In the sensitivity analysis, the integrated trench solution with a gravity sewer, innovative heat tracing and LTDH was found to potentially top the sustainability ranking if geothermal energy was used as the district heating source, or if the weight of the cost criterion increased from 24% to 64%. The study highlights the need for integrated decision-making between different utility providers as an integrated solution can represent sustainability gains.

Bayesian Monitoring Design for Streambed Heat Tracing: Numerical Simulation and Sandbox Experiments

Heat tracing methods have been widely employed for subsurface characterization. Nevertheless, there were very few studies regarding the optimal monitoring design for heat tracing in heterogeneous streambeds. In this study, we addressed this issue by proposing an efficient optimal design framework to collect the most informative diurnal temperature signal for Bayesian estimation of streambed hydraulic conductivities. The data worth (DW) was measured by the expected relative entropy between the prior and posterior distributions of the conductivity field. An adaptively refined Gaussian process surrogate was employed to alleviate the computational burden, resulting in at least three orders of magnitude of speed-up. The applicability of the optimal experimental design framework was evaluated by both numerical and sandbox experimental cases. Results showed that the most informative locations centered in the transition zones among the main patterns of the hydraulic conductivity field, while the most informative times centered in a short period after the minimum/maximum temperature appeared. With the fixed number of measurements, extending the calibration period was more beneficial than increasing the monitoring frequency in improving the estimation results. To our best knowledge, this work is the first study on Bayesian monitoring design for streambed characterization with the heat tracing method. The method and results can provide guidance on selecting monitoring strategies under budget-limited conditions.

On the relative heat invariants of the Dirichlet-to-Neumann operators associated with Schrödinger operators

In this paper we study the relative heat invariants of the Dirichlet-to-Neumann operators $$\Lambda _V$$ associated with Schrodinger operators. Using Seeley’s method, we will calculate the first several relative heat trace invariants explicitly, and then give the general structure of the first n relative heat invariants. As applications, we will prove that a number of properties of the potential V are determined by the spectrum of $$\Lambda _V$$ .

Poly-generation energy system driven by associated geothermal water for oilfield in high water cut stage: A theoretical study

Onshore oilfields are also geothermal fields. In order to reduce cost of geothermal wells and simultaneously improve the energy efficiency of geo-plants, a poly-generation energy system driven by associated geothermal water was established for oilfield in high water cut stage. The system consists of four parts: the power generation subsystem, the absorption chiller subsystem, the oil gathering and transportation heat tracing (OGTHT) subsystem and the radiant heating subsystem, and it realizes the combined cooling, heat, power generation, and oil recovery (CCHPOR), with the associated geothermal water ranging from 373.15 K to 423.15 K. The impact of the heat source temperature and the evaporation temperature on system performance was analyzed. The results show that the performances including net power output, thermal efficiency, exergy efficiency, of the TSORC (two-stage series organic Rankine cycle) are better than those of the ORC, and the total energy efficiency of the CCHPOR reaches 75%. Moreover, the CCHPOR system can prolong the effective life of oil wells, especially for those in high water cut stage, which can be adopted in engineering applications.

Finite-rank approximations of spectral zeta residues

We use the asymptotic expansion of the heat trace to express all residues of spectral zeta functions as regularized sums over the spectrum. The method extends to those spectral zeta functions that are localized by a bounded operator.

Quantitative analysis of riverbank groundwater flow for the Qinhuai River, China, and its influence factors

AbstractInteractions of surface water and groundwater (SW–GW) play an important role in the physical, chemical, and ecological processes of riparian zones. The main objective of this study was to describe the two‐dimensional characteristics of riverbank SW–GW interactions and to quantify their influence factors. The SW–GW exchange fluxes for six sections (S1 to S6) of the Qinhuai River, China, were estimated using a heat tracing method, and field hydrogeological and thermodynamic parameters were obtained via inverse modelling. Global sensitivity analysis was performed to compare the effects of layered heterogeneity of hydraulic conductivity and river stage variation on SW–GW exchange. Under the condition of varied river stage, only the lateral exchange fluxes at S1 apparently decreased during the monitoring period, probably resulting from its relatively higher hydraulic conductivity. Meanwhile, the SW–GW exchanges for the other five sections were quite stable over time. The lateral exchange fluxes were higher than the vertical ones. The riverbank groundwater flow showed different spatial variation characteristics for the six sections, but most of the higher exchange fluxes occurred in the lower area of a section. The section with larger hydraulic conductivity has an apparent dynamic response to surface water and groundwater level differences, whereas lower permeabilities severely reduced the response of groundwater flow. The influence of boundary conditions on SW–GW interactions was restricted to a limited extent, and the impact extent will expand with the increase of peak water level and hydraulic conductivity. The SW–GW head difference was the main influence factors in SW–GW interactions, and the influence of both SW–GW head difference and hydraulic conductivity decreased with an increase of the distance from the surface water boundary. For each layer of riverbank sediment, its hydraulic conductivity had greater influence on its groundwater flow than the other layers, whereas it had negligible effects on its overlying/underlying layers. Consequently, the variations in river stage and hydraulic conductivity were the main factors influencing the spatial and temporal characteristics of riverbank groundwater flow, respectively.

Rethinking the Use of Seabed Sediment Temperature Profiles to Trace Submarine Groundwater Flow

AbstractSubmarine groundwater fluxes across the seafloor facilitate important hydrological and biogeochemical exchanges between oceans and seabed sediment, yet few studies have investigated spatially distributed groundwater fluxes in deep‐ocean environments such as continental slopes. Heat has been previously applied as a submarine groundwater tracer using an analytical solution to a heat flow equation assuming steady state conditions and homogeneous thermal conductivity. These assumptions are often violated in shallow seabeds due to ocean bottom temperature changes or sediment property variations. Here heat tracing analysis techniques recently developed for terrestrial settings are applied in concert to examine the influences of groundwater flow, ocean temperature changes, and seabed thermal conductivity variations on deep‐ocean sediment temperature profiles. Temperature observations from the sediment and bottom ocean water on the Scotian Slope off eastern Canada are used to demonstrate how simple thermal methods for tracing groundwater can be employed if more comprehensive techniques indicate that the simplifying assumptions are valid. The spatial distribution of the inferred groundwater fluxes on the slope suggests a downward groundwater flow system with recharge occurring over the upper‐middle slope and discharge on the lower slope. We speculate that the downward groundwater flow inferred on the Scotian Slope is due to density‐driven processes arising from underlying salt domes, in contrast with upward slope systems driven by geothermal convection. Improvements in the design of future submarine hydrogeological studies are proposed for thermal data collection and groundwater flow analysis, including new equations that quantify the minimum detectable flux magnitude for a given sensor accuracy and profile length.