Sensor to measure thermal conductivity and heat capacity of reservoir fluids

A thermal sensor module, comprising: a housing, wherein the housing comprises a first end and a second end, wherein the housing is hollow and configured to allow a fluid to flow into the housing through the first end and exit through the second end; a heat source, wherein the heat source is disposed at a central axis of the housing and traverses at least partially through the housing; and a temperature sensor, wherein the temperature sensor is positioned in the housing to measure temperature of the fluid flowing in the housing.

BACKGROUND

During drilling or production operations of a reservoir, the thermophysical properties, such as thermal conductivity, specific heat, and viscosity of the downhole hydrocarbon fluid may affect production efficiency and cost. High viscosity hydrocarbon fluid production may require the application of external heat to reduce the viscosity of the fluid and enable fluid transport from one place in the reservoir to a well location. Efficiency of production may depend upon the external heating power and thermal energy transport within a limited time interval. Higher thermally conductive hydrocarbon fluid may effectively transport the thermal energy further than low thermally conductive fluids. It may be desirable to measure thermal conductivity properties or heat capacity of formation fluids during wireline logging services and during production processes. The formation fluid thermal properties obtained may be used for wellbore completion, production efficiency control, and optimization.

The thermal conductivity properties of the downhole formation fluids may vary with pressure, temperature, and chemical composition or molecular weight. The measurement of thermal conductivity may therefore be used to identify formation fluids. Downhole formation fluids at different geometric locations may also have different thermophysical properties regarding viscosity, density, thermal conductivity, and specific heat capacity. Each of these properties may at least partially govern transportation and mobility of crude oils, including high viscosity crude oils, and may consequently impact the recovery process of the crude oils.

Reservoir hydrocarbon fluids may have similar specific heat capacities or thermal conductivity properties but different viscosity, density, and compressibility. Knowing these thermophysical properties of the hydrocarbon fluid may at least partially enable optimization of downhole tools, well completion design, and crude oil production processes. Presently, most thermophysical properties of the hydrocarbon fluid may typically be measured from samples that are taken downhole and then analyzed in a lab, which can take days, or even months. The potential phase transition may reduce the accuracy of any measurement due to the passage of time since sample collection and environmental changes at the collection point(s), which can occur over time.

DETAILED DESCRIPTION

The present disclosure relates generally to fluid sampling and downhole fluid identification and, more particularly, to an improved sensor module used to measure the thermal conductivity and the specific heat capacity of a reservoir fluid.

When collecting a fluid sample downhole, it may generally be desired that the fluid collected be as representative of the fluid present in the formation prior to disruption by the drilling activity. Unfortunately, filtrate fluid from the drilling mud may enter the formation during drilling such that when fluid is first collected from the formation, a certain proportion of that fluid will be mud filtrate. This may be referred to herein as “contamination” and is expressed as a volumetric ratio in percentage units. To reduce the contamination for the fluid sample collected, fluid may be pumped out of the formation and rejected into the wellbore while monitoring one or more fluid properties which change with the degree of contamination. Desirably, the fluid property being measured may vary monotonically with the degree of contamination and ideally with a linear relationship between the measured quantity and the contamination percentage. Thermal conductivity and heat capacity are two such fluid properties that may be used to provide a measurement contrast between mud filtrate and reservoir fluid during pre-sampling downhole pumpout operations.

Downhole fluid measurements may also be used to characterize the fluid such as its composition, gas-oil-ratio, and other properties. One objective of the downhole measurements may be to obtain sufficient information about the fluid so that its behavior and properties under varying thermodynamic conditions (e.g., pressure and temperature) can be predicted. The measurements may be used to parametrically fit equations-of-state (EOS) to the fluid properties to achieve this purpose. Once an EOS has been “fitted” to a particular set of measured properties, it may be used to predict other properties based on the same parameters. Thermal conductivity and heat capacity are two properties that an EOS may predict and therefore these properties may be used, alone or in combination with other fluid measurements, to fit the EOS parameters.

The improved sensor module in this disclosure may be capable of obtaining real-time measurements of thermal conductivity and specific heat capacity and may be complementary to existing downhole tools.

In the field of assessing reservoir fluids, physical models describing fluid behavior, such as EOS, may be central to geodynamic interpretation. An assessment may be conducted with data from fluid samples as well as downhole fluid analysis. In many cases, it may not be possible to acquire enough open hole fluid samples to adequately describe complex geodynamic processes. Therefore, downhole fluid analysis may be needed to supplement sample data. Further, in order to acquire samples from the optimal locations, preliminary in-situ analysis of reservoir architecture, including fluid compositional grading and reservoir compartmentalization, may be required.

Heat capacity and thermal conductivity may be two of the parameters required in compositional gradient equation of state modeling to account for compositional grading caused by thermal diffusion. Knowing whether or not there is compositional grading within the reservoir compartment may be pertinent in understanding the complex reservoir architecture, including the establishment of an oil-water contact level. Correct estimation of oil-water contact level may play an important role in accurately estimating reservoir proven reserve and hence the decision whether or not a client will develop a reservoir field. In examples, the client may be defined as an individual, group of individuals, or an organization. Although the heat capacity and thermal conductivity of mud filtrate and formation fluid may provide high contrast properties that may be used to trend fit contamination, an equation of state may also be used to quantitatively calculate contamination levels.

FIG.1illustrates a cross-sectional view of a well system100. As illustrated, well system100may include a sensor package105attached to a vehicle110. In examples, it should be noted that sensor package105may not be attached to a vehicle110but may be attached to any other suitable object. Sensor package105may be supported by a rig115at a surface120. Sensor package105may be tethered to vehicle110through a conveyance125. Conveyance125may be disposed around one or more sheave wheels130located on vehicle110. During operations, the one or more sheave wheels130may rotate to lower and/or raise conveyance125downhole. As sensor package105is coupled to conveyance125, sensor package105may be displaced accordingly with conveyance125. Conveyance125may include any suitable means for providing mechanical conveyance for sensor package105including, but not limited to, wireline, slickline, coiled tubing, pipe, drill pipe, drill string, tubular string, downhole tractor, and/or the like. In some embodiments, conveyance125may provide mechanical suspension, as well as electrical connectivity, for sensor package105. In examples, sensor package105may be disposed about a downhole tool (not illustrated). Without limitations, the downhole tool may be any suitable downhole tool configured to perform a well completions operation and/or to obtain measurements while downhole. Information, such as measurements, from the downhole tool may be gathered and/or processed by an information handling system135.

Systems and methods of the present disclosure may be implemented, at least in part, with information handling system135. Information handling system135may include any instrumentality or aggregate of instrumentalities operable to compute, estimate, classify, process, transmit, receive, retrieve, originate, switch, store, display, manifest, detect, record, reproduce, handle, or utilize any form of information, intelligence, or data for business, scientific, control, or other purposes. For example, information handling system135may include a processing unit140, a network storage device, or any other suitable device and may vary in size, shape, performance, functionality, and price. Information handling system135may include random access memory (RAM), one or more processing resources such as a central processing unit (CPU) or hardware or software control logic, ROM, and/or other types of nonvolatile memory. Additional components of the information handling system135may include one or more disk drives, one or more network ports for communication with external devices as well as various input and output (I/O) devices, such as an input device145(e.g., keyboard, mouse, etc.) and a video display150. Information handling system135may also include one or more buses operable to transmit communications between the various hardware components.

Alternatively, systems and methods of the present disclosure may be implemented, at least in part, with non-transitory computer-readable media155. Non-transitory computer-readable media155may include any instrumentality or aggregation of instrumentalities that may retain data and/or instructions for a period of time. Non-transitory computer-readable media155may include, for example, storage media such as a direct access storage device (e.g., a hard disk drive or floppy disk drive), a sequential access storage device (e.g., a tape disk drive), compact disk, CD-ROM, DVD, RAM, ROM, electrically erasable programmable read-only memory (EEPROM), and/or flash memory; as well as communications media such as wires, optical fibers, microwaves, radio waves, and other electromagnetic and/or optical carriers; and/or any combination of the foregoing.

As illustrated, sensor package105may be disposed in a wellbore160by way of conveyance125. Wellbore160may extend from a wellhead165into a subterranean formation170from surface120. Wellbore160may be cased and/or uncased. In examples, wellbore160may include a metallic material, such as a tubular string175. By way of example, tubular string175may be a casing, liner, tubing, or other elongated tubular disposed in wellbore160. As illustrated, wellbore160may extend through subterranean formation170. Wellbore160may generally extend vertically into the subterranean formation170. However, wellbore160may extend at an angle through subterranean formation170, such as horizontal and slanted wellbores. For example, although wellbore160is illustrated as a vertical or low inclination angle well, high inclination angle or horizontal placement of the well and equipment may be possible. It should further be noted that while wellbore160is generally depicted as a land-based operation, those skilled in the art may recognize that the principles described herein are equally applicable to subsea operations that employ floating or sea-based platforms and rigs, without departing from the scope of the disclosure.

In examples, rig115includes a load cell (not shown) which may determine the amount of pull on conveyance125at surface120of wellbore160. While not shown, a safety valve may control the hydraulic pressure that drives a drum180on vehicle110which may reel up and/or release conveyance125which may move sensor package105up and/or down wellbore160. The safety valve may be adjusted to a pressure such that drum180may only impart a small amount of tension to conveyance125over and above the tension necessary to retrieve conveyance125and/or sensor package105from wellbore160. The safety valve may typically be set a few hundred pounds above the amount of desired safe pull on conveyance125such that once that limit is exceeded, further pull on conveyance125may be prevented.

FIG.2illustrates an example in which sensor package105may be included in a drilling system200. As illustrated, wellbore160may extend from wellhead165into subterranean formation170from surface120. A drilling platform205may support a derrick210having a traveling block220for raising and lowering a drill string215. Drill string215may include, but is not limited to, drill pipe and/or coiled tubing, as generally known to those skilled in the art. A kelly225may support drill string215as it may be lowered through a rotary table230. A drill bit235may be attached to the distal end of drill string215and may be driven either by a downhole motor and/or via rotation of drill string215at surface120. Without limitation, drill bit235may include roller cone bits, PDC bits, natural diamond bits, any hole openers, reamers, coring bits, and/or the like. As drill bit235rotates, it may create and extend wellbore160to penetrate various subterranean formations170. A pump240may circulate drilling fluid through a feed pipe245to kelly225, downhole through the interior of drill string215, through orifices in drill bit235, back to surface120via an annulus250surrounding drill string215, and into a retention pit255.

With continued reference toFIG.2, drill string215may begin at wellhead165and may traverse wellbore160. Drill bit235may be attached to a distal end of drill string215and may be driven, for example, either by a downhole motor and/or via rotation of drill string215at surface120. Drill bit235may be a part of a bottom hole assembly260at the distal end of drill string215. Bottom hole assembly260may further include sensor package105. Sensor package105may be disposed on the outside and/or within bottom hole assembly260. As will be appreciated by those of ordinary skill in the art, bottom hole assembly260may be a measurement-while drilling (MWD) and/or logging-while-drilling (LWD) system.

Without limitation, bottom hole assembly260may be connected to and/or controlled by information handling system135, which may be disposed on surface120. Alternatively, information handling system135may be disposed downhole in bottom hole assembly260. Processing of information recorded may occur downhole and/or on surface120. Processing occurring downhole may be transmitted to surface120to be recorded, observed, and/or further analyzed. Additionally, information recorded on information handling system135that may be disposed downhole may be stored until bottom hole assembly260may be brought to surface120. In examples, information handling system135may communicate with bottom hole assembly260through a communication line (not illustrated) disposed in (or on) drill string215. In examples, wireless communication may be used to transmit information back and forth between information handling system135and bottom hole assembly260. Information handling system135may transmit information to bottom hole assembly260and may receive, as well as process, information recorded by bottom hole assembly260. In examples, a downhole information handling system (not illustrated) may include, without limitation, a microprocessor or other suitable circuitry, for estimating, receiving, and processing signals from bottom hole assembly260. Downhole information handling system (not illustrated) may further include additional components, such as memory, input/output devices, interfaces, and the like. In examples, while not illustrated, bottom hole assembly260may include one or more additional components, such as analog-to-digital converter, filter and amplifier, among others, that may be used to process the measurements of bottom hole assembly260before they may be transmitted to surface120. Alternatively, raw measurements from bottom hole assembly260may be transmitted to surface120.

Any suitable technique may be used for transmitting signals from bottom hole assembly260to surface120, including, but not limited to, wired pipe telemetry, mud-pulse telemetry, acoustic telemetry, and electromagnetic telemetry. While not illustrated, bottom hole assembly260may include a telemetry subassembly that may transmit telemetry data to surface120. Without limitation, an electromagnetic source in the telemetry subassembly may be operable to generate pressure pulses in the drilling fluid that propagate along the fluid stream to surface120. At surface120, pressure transducers (not shown) may convert the pressure signal into electrical signals for a digitizer (not illustrated). The digitizer may supply a digital form of the telemetry signals to information handling system135via a communication link265, which may be a wired or wireless link. The data may then be analyzed and processed by information handling system135.

FIG.3illustrates an example of sensor package105. Concerning the present disclosure, sensor package105may measure and/or collect fluid samples from wellbore160(e.g., referring toFIGS.1-2). In examples, sensor package105may be a reservoir description tool (RDT) with an in-situ formation fluid thermal identification (FTID) module300. The internal components of FTID module300may be illustrated within an expanded circle302from an indicated dashed circle305, showing an example location on sensor package105. Without limitations, sensor package105may include a plurality of modules, such as a position tracking system (PTS) module310, a dynamic positioning system (DPS) module315, a temperature and pressure quartz gauge sensor (QGS) module320, a Flow-Control Pump-Out Section (FPS) module325, a FLDS and magnetic resonance imaging (MRI) lab module330, and a mobile communications system (MCS) module335which are known to persons of ordinary skill in the art and therefore not described in detail. In examples, the plurality of modules may be arranged in any suitable order or fashion. During operations, sensor package105may be coupled to conveyance125(e.g., referring toFIG.1) and disposed downhole. Conveyance125may attach to a first end340of sensor package105through the use of any suitable mechanisms, including, but not limited to, the use of suitable fasteners, threading, adhesives, welding, and/or combinations thereof. Without limitation, suitable fasteners may include nuts and bolts, washers, screws, pins, sockets, rods and studs, hinges and/or any combination thereof. Sensor package105may collect fluid samples using one or more probes that are part of the dynamic positioning system module315and obtain measurements pertaining to this fluid. In one embodiment, fluid may enter a designated probe and exit first end340. Alternately, fluid may come from a probe in another tool (for example, sensor package105) in which case fluid would enter sensor package105from a second end345and travel from the second end345to first end340. In alternate examples, the fluid may enter sensor package105at first end340and travel from the first end340to second end345.

FIG.4illustrates an example of a thermal sensor module400disposed within FTID module300(referring toFIG.3). Thermal sensor module400may include a housing405, a heat source410, and a temperature sensor415. Thermal sensor module400may be configured to determine the thermal conductivity of a fluid by measuring the difference in temperature between the central axis of housing405and an internal wall420of housing405for a given applied current (e.g., energy input to the fluid). In examples wherein the fluid is static, this temperature difference may be uniform along the length of housing405. In examples wherein the fluid is flowing, an axial gradient of temperature may be introduced along the central axis of housing405, with a first end425of housing405being cooler than a second end430of housing405. If housing405is sufficiently long, the radial temperature profile in the fluid at second end430may be the same as for the case in which the fluid is static. The temperature difference between the central axis of housing405and internal wall420, as measured close to second end430, may be used to determine the thermal conductivity of the fluid in the same way as for the static case. The temperature profile of heat source410near first end425, however, may be representative of the heat carrying capacity of the fluid. Measuring temperature at a plurality of locations along this profile may provide, if the flow rate and the density of the fluid is known, the specific heat capacity of the fluid.

In examples, housing405of thermal sensor module400may be disposed within FTID module300(e.g., referring toFIG.3). Housing405may be secured within FTID module300through the use of any suitable mechanisms, including, but not limited to, the use of suitable fasteners, threading, adhesives, welding, and/or combinations thereof. Without limitation, suitable fasteners may include nuts and bolts, washers, screws, pins, sockets, rods and studs, hinges and/or any combination thereof. Housing405may be any suitable size, height, and/or shape. Without limitation, a suitable shape may include, but is not limited to, cross-sectional shapes that are circular, elliptical, triangular, rectangular, square, hexagonal, and/or combinations thereof. In examples, housing405may be a hollow cylinder. It is to be understood that such geometries may provide a response that in many case can be mapped to an effective equivalent cylindrically symmetric geometry making the analysis discussed below usable to those geometries. Said mapping may be achieved from numerical simulation or experiments. In some cases, the mapping to the equivalent axisymmetric case may not be possible and other methods of correlation between measured temperatures (as discussed below) and the thermal conductivity and/or heat capacity may be needed. These may be implemented in fitted equations or look-up tables as required. Without limitation, housing405may include any suitable material such as metals, nonmetals, polymers, ceramics, and/or any combination thereof. In examples, housing405may include stainless steel316, Inconel718, and/or combinations thereof. Housing405may include any suitable coating for improved erosion resistance. Housing405may have a high thermal capacitance and good thermal conductivity so that the temperature of housing405can be assumed to be uniform and approximately constant. For example, a housing405made of copper may have a thermal conductivity of khousing=315 W/(m·K), whereas housing405made of Inconel may have a thermal conductivity of 11.4 W/(m·K) and the temperature may not be as uniform. In certain examples, housing405may maintain a uniform temperature through the use of an external thermo-electric device (not shown). In those examples, the temperature may be forced lower by the thermo-electric device so a greater temperature difference may be produced so as to avoid reaching material property limits of the fluid itself, of heat source410, of other components of thermal sensor module400, and/or combinations thereof. As illustrated, first end425and/or second end430of housing405may be open so as to allow fluids432(as shown as “arrows” flowing through housing405) to flow through housing405. Further, heat source410may be disposed at the central axis of housing405and may traverse through housing405.

Heat source410may serve to produce energy in the form of heat so as to create a temperature difference in the surrounding fluid432. Heat source410may utilize any known heating method that works within an in-situ wellbore environment. Without limitations, heat source410may be, for example, heat pumps, heating tape, heating wiring, resistance based, microwave-based, laser flashing or radiant heat based, coiled induction heat based, a heat exchange mechanism, and/or combinations thereof. Without limitation, heat source410may include any suitable material such as metals, nonmetals, polymers, ceramics, and/or any combination thereof. As illustrated, heat source410may be a rod including an optical fiber435, a conductive cable440, and an insulating layer445. Optical fiber435may be used to measure the temperature at a plurality of locations along heat source410. Optical fiber435may be disposed within conductive cable440. Conductive cable440may be any suitable cable capable of providing an electrical current. In examples, conductive cable440may include a graphite-epoxy composite material. Conductive cable440may be an electro-optical hybrid cable including both one or several electrical wires and one or several optical fibers435. In certain examples, conductive cable440may include copper wires and optical fiber435. In other examples, conductive cable440may include heating wires and thermocouples. Conductive cable440may be disposed within insulating layer445. Insulating layer445may serve to insulate conductive cable440from the surrounding fluid432. Without limitations, insulating layer445may include material such as Teflon (PTFE), polyimide, ceramics, glass, and/or combinations thereof. In examples, insulating layer445may be a uniform layer of PEEK.

As illustrated, a temperature sensor415may be disposed within and/or on heat source410. Temperature sensor415may serve to measure the temperature of a substance. Without limitations, temperature sensor415may be any one of thermocouples, thermistors, fiber optic sensors, or resistance temperature detectors (RTDs). In examples, there may be a plurality of Fiber Bragg Gratings disposed in optical fiber435that serve as temperature sensors415. The plurality of Fiber Bragg Gratings may be centered at varying wavelengths, which may enable the independent measurement of designated distances between a pair of Fiber Bragg Gratings. The plurality of Fiber Bragg Gratings may be actuated by information handling system135(e.g., referring toFIGS.1-2) at surface120(referring toFIGS.1-2). In other examples, temperature sensor415may be an optical frequency-domain reflectometer (such as the OBR4600optical backscatter reflectometer produced by Luna Innovations Inc., of Roanoke, Virginia). In those examples, the optical frequency-domain reflectometer may be used in a laboratory environment rather than downhole in a wellbore and may produce measurements in increments of about 0.1 degree Celsius with about a one millimeter spatial resolution. In certain examples, there may be an additional temperature sensor415disposed at any suitable location on housing405. In those examples, temperature sensor415may be disposed on internal wall420to measure the temperature of the fluid432in contact with housing405. In other examples, temperature sensor415may be disposed within and/or on an external wall450of housing405. Because optical fiber sensors such as Fiber Bragg Gratings and OFDR may be sensitive to both strain and temperature, care must be taken in the mechanical design to have a one-to-one relation between strain and temperature in the device (for example, by providing for free thermal expansion of the sensor body), or to have a separate measurement that depends on strain and temperature with a relation that is linearly independent from that of the first measurement so as to permit an unambiguous extraction of the temperature.

FIG.5shows a cross-section of thermal sensor module400and schematically shows the radial temperature profile in fluid housing405at internal wall420and external wall450, fluids432, insulating layer445, conductive cable440, and optical fiber435. An axisymmetric distribution may be assumed. An assumption of uniform temperature along thermal sensor module400may be made, which means temperature gradients present due to heat transfer across the connections and coupling between parts may be neglected. As such, heat transfer that may occur axially across first end425(e.g., referring toFIG.4) and second end430(e.g., referring toFIG.4) may be neglected. This approximation may be valid if the thermal sensor module400is long compared to its diameter. With this assumption, for a static fluid, the radial temperature distribution shown may apply to all z distance values in the range 0≤z≤L.

FIG.6illustrates a graph depicting a temperature profile along heat source410(e.g., referring toFIG.4) for a static fluid. Concerning the present graph, T(r1, z) is the temperature at an outer surface of conductive cable440(e.g., referring toFIG.4) along a designated length of heat source410, T0is the temperature of housing405(e.g., referring toFIG.4) at internal wall420(e.g., referring toFIG.4) at an initial radius, r0, T1is the temperature of heat source410at an outer surface of heat source410, and ΔT is the difference between T1and T0. Temperature difference ΔT may be proportional to the current supplied to heat source410and dependent on the thermal conductivity of the fluid, and L is the length of heat source410. By using this graph, further calculations may be done in order to determine the thermal conductivity of a fluid.

For a static fluid, wherein the mass flow rate, {dot over (m)}, is zero, an initial energy balance may be analyzed to determine the thermal conductivity of the fluid, kfluid, with static flow, shown below as Equation 1.

Where qsourceis the rate of energy output (in watts) of heat source410, which has outer radius r1, in the fluid chamber between first end425(e.g., referring toFIG.4) and second end430(e.g., referring toFIG.4), R is the electrical resistance (in ohms) of the conductive cable440, i is the electrical current (in amperes) passing through conductive cable440, kPEEKis the thermal conductivity of the insulating layer445, with has outer radius rcoat, and kfluidis the thermal conductivity of the fluid432(e.g., referring toFIG.4). By rearranging Equation 1, thermal conductivity of the fluid432may be calculated as shown below in Equation 2.

If heat source410has good thermal conductivity (as previously defined), then T(rf, z)≈T(r1, z). If housing405has a good thermal conductivity, then T(r0, z)≈T (rh, z) where rhis the radius of housing405at external wall450(e.g., referring toFIG.4). If insulating layer445is not present or is thin, rcoat=r1, and Equation 3 may be assumed, as shown below.

In the above analysis, it may be assumed that housing405remains at a fixed temperature of T0. In examples, the temperature of housing405may be measured using one or more separate temperature sensors415(e.g., referring toFIG.4) and this measurement of T0is then used in Equations 1 to 3 above. Several measurements of temperature may be made along housing405, wherein the average of those values is used for T0. Likewise, several measurements of temperature may be made along conductive cable440, and these values may be averaged to provide the value of T1to use in Equations 1 to 3 above.

Additionally, the temperature in heat source410may have a radial distribution, as shown inFIG.5. Therefore, depending on where, radially, the temperature sensor415is positioned, the measurement made may not be T(r1, z) but, rather, T(r<r1, z). For example, an optical fiber435(e.g., referring toFIG.4) may be integrated within a composite rod and centered at r=0. Assuming temperature sensor415may have a negligible impact on the temperature distribution inside the heat source410, the following distribution in Equation 4 may be assumed:

where krodis the thermal conductivity (in the radial direction) of the heat source410. For optical fiber435measuring T_f at r=0, Equation 5 presents:

It may be assumed that both the fluid432(e.g., referring toFIG.4) and heat source410are initially at temperature T0, as well as the surrounding components of thermal sensor module400. If the current runs through heating element440for a known period of time (pulse duration τ), the amount of heat energy placed into the device (Q=R i2τ) may be determined. This energy may be used to increase the temperature of conductive cable440, insulating layer445, fluid432, and, by continued thermal conduction and convection, housing405and the surround medium. Temperature T1may then be a function of time, and the peak temperature achieved may depend on the total heat input Q, the duration τ, as well as the thermal properties of the fluid432and the components of thermal sensor module400. This presents an avenue for the determination of heat capacity of the fluid but a full analysis may be complex. Empirical relations determined experimentally may need to be relied upon. An alternate method to determine heat capacity of the fluid432that does not require pulsing of heat source410may be presented as described below. This approach may require fluid432to be flowing through the thermal sensor module400.

FIG.7illustrates a graph depicting a temperature profile along heat source410(e.g., referring toFIG.4) for a flowing fluid. For the flowing fluid case, a portion of the heat produced by heat source410may be carried away by the fluid as the fluid travels. Equation 6, shown below, may produce the heat removed by the fluid.
qfluid={dot over (m)}cp_fluid(Tfluid(z=L)−T0)  (6)

It may be assumed that the fluid enters thermal sensor module400(e.g., referring toFIG.4) with a given temperature,Tfluid, whereinTfluid=T0at z=0.Tfluidmay exit thermal sensor module400with the same radial temperature distribution as for the static flow example. Within Equation 4, qfluidis the heat removal of the fluid, and cp_fluidis the specific heat capacity of the fluid. The average temperature of the fluid exiting second end430(e.g., referring toFIG.4) of housing405(e.g., referring toFIG.4) may be obtained by integrating temperature over the annular cross-section at a position of z=L, as shown below in Equation 7.

The axial profile of the temperature of heat source410may be quantified by Equation 8 below:
T1(z)=T0+(T1,L−T0)(1−e−z/lc(8)

The temperature heat transfer length lcis a characteristic of the temperature profile and with sufficient temperature measurement along conductive cable440, lcmay be obtained from a fit through the profile of Eq. (7) through the data. For example, if T0, the temperature of the housing if known, T1,Lthe asymptotic temperature along the heat source410, and at least one additional measurement at a 0<zm<L position where the temperature is as an intermediate between T0and T1,L, lcmay be determined by inversion of Eq. 9 as follows:

This may be repeated for as many intermediate points T(zmi) as are available and the selected value of lcimay be the average of the obtained values. Alternatively, lcmay be obtained from a fit least square fit of equation through the points of temperature values along the heat source410. Equation 9 may be used in Equation 10 below to show the radial heat flux per unit length.

Integrating over a designated length of z may provide the complete radial heat loss, wherein this may be the heat loss due to thermal conduction shown below as Equations 11 and 12.

Equation 12 may require use of the temperature profile decay length lc. This parameter is related to the shape of the profile and not the absolute value of the temperature shift. To obtain it, the temperature of heat source410at a minimum of two positions may be required, and any one of those positions cannot be z=0 (inlet) position. At z=0, it may be known that T1(0)=T0, and therefore does not help to determine the shape of the temperature profile past z=0. Equations 11 and 12 may be used in the following energy balances displayed in Equation 13.
qfluid+qcond=qsource(13)

The heat produced by heat source410may be approximated as Equation 14 below the relation L=∫0Ldz may be utilized so that Equations 12 and 14 both contain integrals over the same domain.

Equations 6, 12, and 14 may be substituted into Equation 13 to produce Equations 15 and 16 below in order to solve for cp_fluid.

It may be assumed that when thermal sensor module400is sufficiently long, e−L/lc<<1. As such, Equation 17 below may be a simplified form of Equation 16.

As depicted inFIG.6, the temperature approaches an asymptotical value as the length of thermal sensor module400is sufficiently large. At this point, T(r1, z3)≈T1, and T1,Lmay be substituted forTfluid(L), as shown below in Equation 18.

Equation 18 may be rearranged as Equation 19 in order to solve for the specific heat capacity of the fluid, cp_fluid.

As illustrated above in Equation 19, knowledge of kfluidand {dot over (m)} may be required in order to determine cp_fluid. In the static example ofFIG.6, kfluidmay be obtained from Equation 3 using measured values T1and T0at any point along 0<z<L and {dot over (m)}=0. In the flowing case ofFIG.7, Equation 3 may still be used using T1and T0measured at z=L if it can be assumed that the temperature difference (T1,L−T0) has reached its asymptotic value. In examples, this may be ascertained by reducing the flow rate ({dot over (m)}) to a value small enough that (T1,L−T0) no longer depends on the flow rate. It may be noted, from Equation 16, that for a given Cp_fluid, decreasing the flow rate ({dot over (m)}) decreases the length of the transition region, which is characterized by the decay length lc. When lc<<L, it may be known that (T1,L−T0) has reached its asymptotic value and can be used in Equation 3 as a proxy for (T1−T0) to supply kfluid.

Note that this dependence of the temperature profile on {dot over (m)} cp_fluidmay provide flexibility during calibration and operation of thermal sensor module400as a sensor for heat capacity. For calibration, rather than changing fluid types to change specific heat capacity (by varying cp_fluid), the fluid may remain the same (cp_fluidis constant), but the flow rate, {dot over (m)}, may be changed instead. Likewise, during use of thermal sensor module400, changing the flow rate may change the profile of the temperature along heat source410. This may be used to optimize the contrast in temperature between temperature sensors415(e.g., referring toFIG.4) for T(r1, z1), T(r1, z2), and T(r1, z3).

This method and system may include any of the various features of the compositions, methods, and system disclosed herein, including one or more of the following statements.

Statement 1. A thermal sensor module, comprising: a housing, wherein the housing comprises a first end and a second end, wherein the housing is hollow and configured to allow a fluid to flow into the housing through the first end and exit through the second end; a heat source, wherein the heat source is disposed at a central axis of the housing and traverses at least partially through the housing; and a temperature sensor, wherein the temperature sensor is positioned in the housing to measure temperature of the heat source within the housing.

Statement 2. The thermal sensor module of statement 1, wherein the heat source is selected from a group consisting of a heat pump, heating tape, heating wiring, resistance based, microwave-based, laser flashing or radiant heat based, coiled induction heat based, a heat exchange mechanism, and a combination thereof.

Statement 3. The thermal sensor module of statement 1 or 2, wherein the heat source comprises: an optical fiber; a conductive cable, wherein the optical fiber is disposed within the conductive cable; and an insulating layer, wherein the conductive cable is disposed within the insulating layer.

Statement 4. The thermal sensor module of statement 3, wherein the conductive cable comprises graphite fibers, epoxy, or combinations thereof.

Statement 5. The thermal sensor module of statement 4, wherein the conductive cable further comprises copper wires, heating wires, thermocouples, or combinations thereof.

Statement 6. The thermal sensor module of statement 3, wherein the insulating layer comprises a material selected from a group consisting of polytetrafluoroethylene, polyimide, ceramics, glass, and combinations thereof.

Statement 7. The thermal sensor module of statement 3, wherein the insulating layer is a uniform layer of polyether ether ketone.

Statement 8. The thermal sensor module of statement 1, wherein there are a plurality of temperature sensors within the thermal sensor module, wherein at least one of the plurality of temperature sensors is disposed on the housing, wherein remaining temperature sensors of the plurality of temperature sensors are disposed within the heat source.

Statement 9. The thermal sensor module of statement 8, wherein the temperature sensors disposed within the heat source are Fiber Bragg Gratings, wherein the Fiber Bragg Gratings are disposed within the optical fiber.

Statement 10. The thermal sensor module of any one of the previous statements, wherein the temperature sensor is an optical frequency-domain reflectometer.

Statement 11. A method for determining a thermophysical property of a fluid, comprising: disposing a sensor package downhole into a wellbore with a conveyance; receiving a sample of the fluid with a thermal sensor module disposed within the sensor package; applying heat to the sample of the fluid with a heat source disposed within a housing of the thermal sensor module; and determining a thermal conductivity of the sample of the fluid.

Statement 12. The method of statement 11, wherein receiving the sample of the fluid comprises of pumping the sample of the fluid through the thermal sensor module to model a flowing fluid.

Statement 13. The method of statement 11 or 12, wherein receiving the sample of the fluid comprises of containing the sample of the fluid within the thermal sensor module to model a static fluid.

Statement 14. The method of any one of statements 11 to 13, further comprising of measuring a temperature of the sample of the fluid with at least one temperature sensor.

Statement 15. The method of statement 11, wherein the at least one temperature sensor is disposed within the heat source.

Statement 16. The method of statement 15, wherein the heat source comprises an optical fiber disposed within a conductive cable, wherein the conductive cable is disposed within an insulating layer, wherein the at least one temperature sensor is a Fiber Bragg Grafting disposed within the optical fiber.

Statement 17. The method of claim16, wherein the insulating layer is a uniform layer of polyether ether ketone.

Statement 18. The method of any one of statements 11 to 15, wherein applying heat to the sample of the fluid comprises of applying a current in a pulsed mode.

Statement 19. The method of any one of statements 13 to 15, or 17, further comprising of determining a specific heat capacity of the sample of the fluid with the thermal conductivity.

Statement 20. The method of any one of statements 13 to 15, 17, or 18, wherein the temperature sensor is a fiber optic cable.