NON-INVASIVE PROCESS FLUID TEMPERATURE DISPLAY WITH REDUCED SUFFICIENCY

Description

BACKGROUND

[0001] Many industrial processes convey process fluids through pipes or other conduits. Such process fluids can include liquids, gasses, and sometimes entrained solids. These process fluid flows may be found in any of a variety of industries including, without limitation, hygienic food and beverage production, water treatment, high-purity pharmaceutical manufacturing, chemical processing, the hydrocarbon fuel industry, including hydrocarbon extraction and processing as well as hydraulic fracturing techniques utilizing abrasive and corrosive slurries.

[0002] It is common to place a temperature sensor within a thermowell, which is then inserted into the process fluid flow through an aperture in the conduit. However, this approach may not always be practical in that the process fluid may have a very high temperature, be very corrosive, or both. Additionally, thermowells generally require a threaded port or other robust mechanical mount / seal in the conduit and thus, must be designed into the process fluid flow system at a defined location. Accordingly, thermowells, while useful for providing accurate process fluid temperatures, have a number or limitations.

[0003] More recently, process fluid temperature has been estimated by measuring an external temperature of a process fluid conduit, such as a pipe, and employing a heat flow calculation. This external approach is considered non-invasive because it does not require any aperture or port to be defined in the conduit. Accordingly, such non-intrusive approaches can be deployed at virtually any location along the conduit. An example of such an approach is disclosed in WO 2017 / 131546 Al, which describes a mounting assembly configured to mount the process fluid temperature estimation system to an external surface of a process fluid conduit, a sensor capsule having an end configured to contact the external surface of the process fluid conduit to form an interface, the sensor capsule having at least one temperature sensitive element disposed therein, measurement circuitry coupled to the sensor capsule and configured to detect an electrical characteristic of the at least one temperature sensitive element that varies with temperature and provide at least process fluid skin temperature information, a controller coupled to the measurement circuitry, the controller being configured to: obtain the process fluid conduit skin temperature information from the measurement circuit; obtain reference temperature information; employ a heat transfer calculation with the process fluid conduit skin temperature information and reference temperature information to generate an estimated process fluid temperature output.

[0004] As recent advances have improved the accuracy of process fluid temperature estimation using non-invasive techniques, new sources of error have been identified. Addressing and correcting these new sources of error will improve the accuracy of non-invasive process fluid temperature estimation.SUMMARY

[0005] The present invention provides a process fluid temperature estimation system and a method of providing non-invasive process fluid temperature estimation relative to a process fluid conduit having a curved surface according to the independent claims. Further embodiments of the invention may be realized according to the corresponding dependent claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0006] FIG. 1 is a diagrammatic view of a heat flow measurement system with which embodiments of the present invention are particularly applicable. FIG. 2 is a block diagram of circuitry within a heat flow measurement system, with which embodiments of the present invention are particularly applicable. FIGS. 3A and 3B are an enlarged depictions of a sensor capsule interface relative to process fluid conduits with different diameters. FIG 3C is a chart illustrating error induced by conduit geometry as a function of conduit diameter. FIG. 4 is a diagrammatic view illustrating thermal resistance of various portions of a sensor capsule / conduit interface. FIG. 5A is a diagrammatic view of a portion of an improved sensor capsule in accordance with an embodiment of the present invention. FIG. 5B is a diagrammatic view of a portion of the sensor capsule shown in FIG. 5A with an encapsulation material applied. FIG. 6 is a diagrammatic view of the portion of a sensor capsule in accordance with an embodiment of the present invention. FIG. 7 is a diagrammatic view of a portion of a sensor capsule in accordance with another embodiment of the present invention. FIG. 8 is a diagrammatic view of a portion of a sensor capsule in accordance with another embodiment of the present invention. FIG. 9 is a diagrammatic view of a portion of a sensor capsule in accordance with another embodiment of the present invention. FIG. 10 is a flow diagram of a method of estimating process fluid temperature non-invasively in accordance with an embodiment of the present invention. DETAILED DESCRIPTION

[0007] Embodiments described herein generally leverage identification and appreciation of additional sources of error in non-invasive process fluid temperature estimation in order to provide solutions with increased accuracy. Two sources of error have been identified and various embodiments described herein can provide solutions to one or both sources.

[0008] A first source of error is variability in the heat flow path from a first temperature measurement point to a second temperature measurement point. Often the second temperature measurement point is located within an electronics housing of the process fluid estimation system itself and thus the heat flow from the conduit surface sensor (i.e. the sensor measuring a skin temperature of a process fluid conduit) to the reference temperature sensor (e.g., located within the electronics housing) must be tightly controlled. This means that the system must always be mounted the same distance from the process fluid conduit outer surface. This requirement can eliminate some potential applications for non-invasive process fluid temperature estimation, such as remote mount and high-temperature applications. Additionally, the primary heat path from the process fluid conduit to the electronics housing is generally through a sensor sheath. This makes the measurement highly susceptible to changing ambient conditions and can require a user to install insulation around the sensor. This can limit the accuracy of the system and require additional costs and labor for the end user.

[0009] A second source of error is generally believed to be caused by a relatively flat end of a sensor capsule contacting a curved process fluid conduit such as a pipe. This air gap between the flat surface and the curved process fluid conduit varies depending on the curvature of the process fluid conduit. As can be appreciated, in order to provide a solution that is usable with a wide range of diameters, addressing this source of error is important as well.

[0010] FIG. 1 is a diagrammatic view of a heat flow measurement system with which embodiments of the present invention are particularly applicable. System 200 generally includes a pipe clamp portion 202 that is configured to clamp around conduit or pipe 100. Pipe clamp 202 may have one or more clamp ears 204 in order to allow the clamp portion 202 to be positioned and clamped to pipe 100. Pipe clamp 202 may replace one of clamp ears 204 with a hinge portion such that pipe clamp 202 can be opened to be positioned on a pipe and then closed and secured by clamp ear 204. While the clamp illustrated with respect to FIG. 1 is particularly useful, any suitable mechanical arrangement for securely positioning system 200 about an exterior surface of a pipe can be used in accordance with embodiments described herein.

[0011] System 200 includes heat flow sensor capsule 206 that is forced against external diameter 116 of pipe 100 by spring 208. The term "capsule" is not intended to imply any particular structure or shape and can thus be formed in a variety of shapes, sizes and configurations, all having a relatively flat lower surface. While spring 208 is illustrated, those skilled in the art will appreciate that various techniques can be used to force sensor capsule 206 into contact with external diameter 116 of conduit 100. Sensor capsule 206 generally includes one or more temperature sensitive elements, such as resistance temperature devices (RTDs). Sensors within capsule 206 are electrically connected to transmitter circuitry within housing 210, which is configured to obtain one or more temperature measurements from sensor capsule 206 and calculate an estimate of the process fluid temperature based on the measurements from sensor capsule 206, and a reference temperature, such as a temperature measured within housing 210 or one of the sensors of capsule 206, or otherwise provided to circuitry within housing 210.

[0012] In one example, the basic heat flow calculation can be simplified into: T corrected = T skin + T skin − T reference * R pipe / R sensor .

[0013] In this equation, T skin is the measured temperature of the external surface of the conduit. Additionally, T reference is a second temperature obtained relative to a location having a fixed thermal impedance (R sensor ) from the temperature sensor that measures T skin . R pipe is the thermal impedance of the conduit and can be obtained manually by obtaining pipe material information, pipe wall thickness information. Additionally, or alternately, a parameter related to R pipe can be determined during a calibration and stored for subsequent use. Accordingly, using a suitable heat flow calculation, such as that described above, circuitry within housing 210 is able to calculate an estimate for the process fluid temperature (T corrected ) and convey an indication regarding such process fluid temperature to suitable devices and / or a control room. In the example illustrated in FIG. 1, such information may be conveyed wirelessly via antenna 212.

[0014] FIG. 2 is a block diagram of circuitry within housing 210 of heat flow measurement system 200, with which embodiments of the present invention are particularly applicable. System 200 includes communication circuitry 220 coupled to controller 222. Communication circuitry 220 can be any suitable circuitry that is able to convey information regarding the estimated process fluid temperature. Communication circuitry 220 allows heat flow measurement system 200 to communicate the process fluid temperature output over a process communication loop or segment. Suitable examples of process communication loop protocols include the 4-20 milliamp protocol, Highway Addressable Remote Transducer (HART ®< ) protocol, FOUNDATION ™< Fieldbus Protocol, and the WirelessHART protocol (IEC 62591).

[0015] Heat flow measurement system 200 also includes power supply module 224 that provides power to all components of system 200 as indicated by arrow 226. In embodiments where heat flow measurement system 200 is coupled to a wired process communication loop, such as a HART ®< loop, or a FOUNDATION ™< Fieldbus segment, power module 224 may include suitable circuitry to condition power received from the loop or segment to operate the various components of system 200. In such a wired process communication loop embodiments, power supply module 224 may provide suitable power conditioning to allow the entire device 200 to be powered by the loop to which it is coupled. In other embodiments, when wireless process communication is used, power supply module 224 may include a source of power, such as a battery and suitable conditioning circuitry.

[0016] Controller 222 includes any suitable arrangement that is able to generate a heat-flow based process fluid temperature estimate using measurements from sensor(s) within capsule 206 and an additional reference temperature, such as a terminal temperature within housing 210 or a temperature measurement from a second temperature sensor disposed within capsule 206. The reference temperature, in some applications, may be known or estimated for a well-controller process or ambient environment (e.g. the system is located within a climate controlled facility). In one example, controller 222 is a microprocessor. Controller 222 is communicatively coupled to communication circuitry 220.

[0017] Measurement circuitry 228 is coupled to controller 222 and provides digital indications with respect to measurements obtained from one or more temperature sensors 230. Measurement circuitry 228 can include one or more analog-to-digital converters and / or suitable multiplexing circuitry to interface the one or more analog-to-digital converters to sensors 230. Additionally, measurement circuitry 228 can include suitable amplification and / or linearization circuitry as may be appropriate for the various types of temperature sensors employed.

[0018] FIGS. 3A and 3B are diagrammatic views of sensor capsule 206 as it contacts different process fluid conduits 100, 300, respectively. In order to illustrate the variation in air gap caused by different curvatures, two process fluid conduits 100 and 300 are shown. Sensor capsule 206 is shown containing an RTD element 302 therein. Sensor capsule 206 has a relatively flat lower surface 304 that contacts the process fluid conduit. As shown, when flat surface 304 contacts large-diameter process fluid conduit 100, a relatively small air gap 306 is formed between process fluid conduit 100 and flat surface 304. However, as shown in FIG. 3B, when a smaller-diameter process fluid conduit 300 is used, the higher curvature of the process fluid conduit creates a larger air gap 308 between flat surface 304 and the smaller-diameter process fluid conduit 300. The thermal conductivity between the two interfaces contains a small interface air gap that makes up a significant part of the required correction. The corrected temperature estimation is provided by the equation set forth below; T corrected = T sensor + T sensor − T reference * R pipe + R other / R sensor .

[0019] In the above equation, the air gap thermal resistance is included in the R other parameter.

[0020] FIG 3C is a chart illustrating error induced by conduit geometry as a function of conduit diameter. As can be seen, for smaller diameters, the error induced by the geometry can climb significantly. In accordance with one embodiment of the present invention, controller 222 (shown in FIG. 2) is provided with an indication of pipe diameter upon which the process fluid temperature estimation system will be used. The pipe diameter is then used to access an error mapping or compensation curve in order to identify an appropriate parameter that models the air gap thermal resistance for the particular conduit being used. A default value can be set that is appropriate for a wide range of diameters, such as setting a default pipe diameter as 2 or 3 inches. However, an end user can specify a smaller pipe diameter during ordering and acquire a system already having the specified pipe diameter for the compensation curve. Alternately, the pipe diameter can be communicated to controller 222 via process communication using communication circuitry 220 or entered manually via a user interface (not shown). Using such a compensation curve or lookup table, the non-invasive process fluid temperature estimation system can automatically correct for the geometry differences between the sensor capsule and the surface of the process fluid conduit.

[0021] As the pipe diameter decreases, the air gap increases exponentially requiring more correction for small diameter conduits. The compensation curve provides a thermal resistance parameter (R other ) based on pipe diameter that is typically configured by the user. The compensation calculation, set forth above, then adjusts the correction ratio appropriately to provide a more accurate output. Additional configuration options that can be communicated to controller 222 or entered via user interface can indicate if the sensor is mounted perpendicular to a selected geometry, such as a pipe, flat surface, etc.

[0022] FIG. 4 is a diagrammatic view illustrating various thermal resistance parameters in the sensor capsule / process fluid conduit interface. The diagram shown in FIG. 4 is significantly zoomed relative to that shown in FIG. 3A. The small interface air gap (R air ) is also included. Even though this appears small, R air is the largest contributor to thermal impedance. In one example, values for the various parameters are set forth in the table below. ParameterDescriptionLength (m)Thermal ConductivityThermal ResistanceR comp Thermal Grease0.00233.50.000657143R arg Silver End Cap0.001700164293.96308E-06R air Interface Air Gap0.000050.0260.001923077R other R comp +R arg +R air

[0023] As set forth above, providing an R other parameter that is changeable based on the diameter of the process fluid conduit significantly improves the accuracy of the process fluid temperature estimation calculation set forth above. Further, improved accuracy can still be provided if changes in the end cap material (e.g. something other than silver) is provided as long as the map of compensation curve provided to controller 222 includes an indication of thermal conductivity and length for the selected end cap. The same can be done for variations in thermal grease length and composition. Additionally, it is expressly contemplated that if a diameter is used that is not expressly matched to a given R air parameter, embodiments described herein can interpolate between the two nearest data points.

[0024] Another source of error in process fluid temperature estimation using non-invasive techniques is the potential variability in heat flow from the process fluid conduit skin temperature measurement to a reference temperature measurement. In accordance with another embodiment described herein, this heat flow variability is substantially minimized or at least controlled by providing two temperature sensors disposed within the same sensor capsule and spaced from one another along a heat flow path.

[0025] FIG. 5A is a diagrammatic view of an improved sensor capsule employing a staggered bore process fluid temperature estimation system in accordance with one embodiment of the present invention. As used herein, "staggered bore" means that two bores have a different distance from the external surface of the process fluid conduit and that they also have an offset in at least one other dimension (e.g. along an axis of the conduit, and / or in a direction perpendicular to the axis of the conduit). Sensor capsule 406 employs a machined tip 408 into which multiple sensing elements 410 and 412 are mounted. Sensing elements 410 and 412 are preferably RTD's and are connected to wires running through the length of sensor capsule 406 to be coupled to measurement circuitry 228 (shown in FIG. 2). Sensing elements 410, 412 are held in place within sensor capsule 406 using either mechanical or chemical (i.e. bonding) techniques. The cap can then be welded onto the tube to seal the tip. The machined tip provides precise and consistent sensor spacing between elements 410 and 412. These machined parts are relatively easy to inspect and improve consistency of assembly by allowing the sensors inserted in them to bottom out. This eliminates potential problems of inconsistent element mounting within the sensor capsule since error can arise when the spacing between the elements and the surface directly affects the measurements. Additionally, or alternatively, portions of the sensor capsule may be 3D printed in order to facilitate production of more complicated features, such as square holes.

[0026] The materials used for tip 408 can vary significantly. Materials with high thermal conductivity, such as copper and silver can be used to improve heat transfer but choosing a material with intentionally low thermal conductivity could allow the spacing between elements 410 and 412 to be much smaller and thus to reduce the overall cost. Tip 408 could also be varied to match the pipe and clamp material in order to eliminate galvanic corrosion concerns. As the material of a component of the sensor capsule is varied, the size and thermal conductivity of the component can be stored in the lookup table or compensation curve in order to accurately estimate process fluid temperature. Each material, accordingly, would have different thermal properties and would affect the process fluid temperature estimation, and such variations can be accommodated in the R other parameter of the calculation.

[0027] However, in one example, a single block of homogenous material is used to mount elements 410, and 412 and thus corrections for heat flow between the sensing elements 410 and 412, are easily made. For example, sensing element 410 may be considered a skin temperature sensor and sensing element 412 may be considered a reference temperature sensor. The difference in the measured temperatures will be related to the magnitude of the heat flow through the block of homogenous material and its thermal conductivity. Increasing the precision of placement of elements 410 and 412 allows the spacing between elements 410 and 412 to be reduced thus reducing the overall size of sensor capsule 406. It is believed that this will improve the linearity of the heat gradient across elements 410 and 412 and make the response less affected by external influences. It is preferred, in one example, that temperature sensitive elements 410 and 412 be RTDs, since such devices are generally believed to have higher accuracy and repeatability than other types of temperature sensitive elements, such as thermocouples.

[0028] FIG. 5B shows a portion of sensor capsule 406 where epoxy or some other suitable encapsulation 414 has been applied. Epoxy 414 ensures that temperature sensitive elements 410 and 412 remain secured within their respective bores and also helps to provide strain relief where the lead wires of each individual temperature sensitive element attach to the temperature sensitive element. Accordingly, the machined tip and sensing elements could be prebuilt into a metal capsule with wires. This could allow late customization during manufacture to build a sensor to a final length while maintaining consistency of the measurement.

[0029] FIG. 6 is a diagrammatic view of a portion of a sensor capsule providing a staggered bore for a plurality of temperatures sensitive elements, as well as a curved end to match the curvature of a selected process fluid conduit. In this sense, the embodiment illustrated in FIG. 6 can be thought of as addressing both sources of error. By providing a curvature to end 502 that is matched to the curvature of the process fluid conduit, an air gap between end 502 and the process fluid conduit is minimized. Further, providing a staggering between bores 504 and 506 using machining techniques provides a highly reliable location technique for temperature sensors, such as elements 410 and 412, to be mounted therein. Since the curvature of surface 502 must be selected during the ordering process, the embodiment shown in FIG. 6 is not particularly amenable to an end user making changes to process fluid conduit diameters without requiring an entirely new sensor capsule 500.

[0030] FIG. 7 is a diagrammatic view of a portion of a sensor capsule in accordance with another embodiment of the present invention. Sensor capsule 600 includes bores 602 and 604 terminating further from flat surface 606 (i.e. the hot end) than the embodiments shown in FIGS. 5A, 5B, and 6. Terminating bores 602 and 604 further from surface 606 may reduce high temperature exposure to the sensitive elements, which may provide additional advantages for higher temperature applications.

[0031] FIG. 8 illustrates another portion of a sensor capsule in accordance with another embodiment of the present invention. Specifically, sensor capsule 700 includes machined tip 702 that is larger or equal diameter to tube 704 to provide more space for sensing elements within bores 706, 708. Tip 702 is attached to tube 704 in accordance with any suitable techniques, such as welding.

[0032] FIG. 9 is a diagrammatic view of a portion of a sensor capsule 800 in accordance with another embodiment of the present invention. Sensor capsule 800 includes an insert 802 that that is formed to include bores 804, 806. Bores 804, 806, are sized to receive temperature sensitive elements, such as elements 410, 412 (shown in FIG. 5A). Additionally, the walls of insert 802 may be tapered away from side wall 810 of a tube in order to provide better insulation from ambient conditions.

[0033] FIG. 10 is a flow diagram of a method of estimating process fluid temperature non-invasively in accordance with an embodiment of the present invention. Method 900 begins at block 902 where an end user provides an indication of conduit curvature. Such indication can be provided in the form of communication (e.g. process communication and / or interaction with a user interface) to a process fluid temperature estimation system, as indicated at block 904. Alternatively, the indication can be provided to a manufacturer during acquisition of the process fluid temperature system, such that the curvature of the conduit is already entered into the system when it is shipped to the end user, as indicated at block 906. The curvature can also be set by the end user ordering a system with a sensor capsule having a curvature that matches the curvature of the conduit, as indicated at block 908.

[0034] At block 910, the process fluid estimation system is installed on the process fluid conduit. Next, at block 912, the R other term is obtained or calculated. Note, for embodiments that do not have a sensor capsule with a conduit-matched curved end, the R other parameter will have a value that is influenced by R air based on the diameter of the process fluid conduit, as indicated at block 914. As set forth above, the R other parameter may be obtained from a lookup table based on the selected conduit curve. Further, other heat flow variables, such as end cap thickness and / or material can be obtained from a lookup table. Further still, thermal grease heat flow information can also be obtained. These other factors that affect R other are indicated diagrammatically at reference numeral 916.

[0035] Next, at block 918, the system obtains a skin temperature of the process fluid conduit. At block 920, a reference temperature is measured. The reference temperature may be obtained from a temperature sensor coupled to a terminal located within an electronics housing of the system or it may be obtained from an additional temperature sensitive element located within the sensor capsule but positioned in such a way that a known thermal impedance exists between the skin temperature sensor and the reference temperature sensor, such as shown in FIGS. 5-9.

[0036] At block 922, controller 222 (shown in FIG. 2) performs a heat flow calculation using the measured skin temperature, reference temperature, and R other . In embodiments where the sensor capsule has a curved end that matches the curvature of the process fluid conduit, the R other parameter may not include a value for R air . However, in such cases, R other may still model other heat flow characteristics, such as the heat flow through the curved cap as well as through the particular thermal grease employed. At block 924, the estimation of process fluid temperature, based on the heat flow calculation performed at block 922, is provided as an output. Then, method 900 repeats by returning to block 918 to obtain another skin temperature.

[0037] As set forth above, a number of embodiments of the present invention have been set forth that provide various solutions to multiple sources of error in non-invasive process fluid temperature estimation systems. Embodiments may include any combination of the solutions set forth above.

Claims

1. A process fluid temperature estimation system (200) comprising: a mounting assembly (202) configured to mount the process fluid temperature estimation system (200) to an external surface (116) of a curved process fluid conduit (100); a sensor capsule (206) having an end configured to contact the external surface (116) of the process fluid conduit (100), said sensor capsule (206) having a relatively flat lower surface (304), to form an interface having a contact region and an air gap (306) between the relatively flat lower surface (304) and the curved process fluid conduit (100), the sensor capsule (206) having at least one temperature sensitive element (302, 410, 412) disposed therein; measurement circuitry (228) coupled to the sensor capsule (206) and configured to detect an electrical characteristic of the at least one temperature sensitive element (302, 410, 412) that varies with temperature and provide at least process fluid conduit skin temperature information (Tskin); a controller (222) coupled to the measurement circuitry (228), the controller (222) being configured to: obtain the process fluid conduit skin temperature information (Tskin) from the measurement circuitry (228); obtain reference temperature information (Treference), obtain a heat flow parameter related to the air gap (306) of the interface, and employ a heat transfer calculation with the process fluid conduit skin temperature information (Tskin), reference temperature information (Treference), and heat flow parameter to generate an estimated process fluid temperature output.

2. The process fluid temperature estimation system (200) of claim 1, wherein the reference temperature information (Treference) is obtained by the controller (222) using the measurement circuitry (228).

3. The process fluid temperature estimation system (200) of claim 2, wherein the measurement circuitry (228) is coupled to a temperature sensitive element (302, 410, 412) disposed in an electronics housing of the process fluid temperature estimation system (200).

4. The process fluid temperature estimation system (200) of claim 2, wherein the measurement circuitry (228) is coupled to a reference temperature sensitive element (412) in the sensor capsule (206).

5. The process fluid temperature estimation system (200) of claim 4, wherein the reference temperature sensitive element (412) and a skin temperature sensitive element (410) are each disposed in respective machined bores (504, 506, 602, 604, 706, 708, 804, 806) in the sensor capsule (206).

6. The process fluid temperature estimation system (200) of claim 5, wherein each of the reference temperature sensitive element (412) and the skin temperature sensitive element (410) are resistive temperature sensitive devices.

7. The process fluid temperature estimation system (200) of claim 6, wherein the machined bores (504, 506, 602, 604, 706, 708, 804, 806) are staggered bores (504, 506, 602, 604, 706, 708, 804, 806).

8. The process fluid temperature estimation system (200) of claim 7, wherein each of the reference temperature sensitive element (412) and the skin temperature sensitive element (410) is disposed within one of thermal grease and epoxy (414) in its respective staggered bore (504, 506, 602, 604, 706, 708, 804, 806).

9. The process fluid temperature estimation system (200) of claim 8, wherein the controller (222) is further configured to obtain a second heat flow parameter related to the thermal grease and perform the heat flow calculation using the skin temperature information (Tskin), reference temperature information (Treference), and heat flow parameters to generate the estimated process fluid temperature output.

10. A method of providing non-invasive process fluid temperature estimation relative to a process fluid conduit (100) having a curved surface, the method comprising: receiving an indication of process fluid conduit curvature; coupling a sensor capsule (206) to the curved external surface (116) of the process fluid conduit (100), said sensor capsule (206) having an end configured to contact the curved external surface (116) of the process fluid conduit (100), and said sensor capsule (206) having a relatively flat lower surface (304), said coupling forming an interface having a contact region and an air gap (308); obtaining a process fluid conduit skin temperature; obtaining a reference temperature from a location having a fixed thermal impedance from a location where the process fluid conduit skin temperature was obtained; and employing a heat flow calculation using the process fluid conduit skin temperature, reference temperature, and a heat flow parameter related to the air gap of the interface, to provide a process fluid temperature estimation that is at least partially compensated for error caused by the process fluid conduit curvature.

11. The method of claim 10, wherein receiving an indication of process fluid conduit curvature includes storing information related to the process fluid conduit curvature within a process fluid estimation system (200).