Dual-probe Heat-pulse Research Articles

Sensitivity analysis of temperature changes for determining thermal properties of partially frozen soil with a dual probe heat pulse sensor

Determining thermal conductivity (λ) and volumetric heat capacity (C) of partially frozen soils with a dual probe heat pulse (DPHP) sensor is challenging because an applied heat pulse melts ice surrounding the heater probe. Examining DPHP temperature changes with a commonly-used analytical solution that only accounts for heat conduction leads to inaccurate λ and C estimates for partially frozen soils at temperatures between −5 °C and 0 °C. In order to determine λ and C accurately and simultaneously, it is necessary to understand how various properties of partially frozen soil influence the temperature changes produced by DPHP sensors. The objective of this study is to determine the sensitivity of DPHP temperature changes to soil conditions and soil thermal properties. A numerical solution for radial heat conduction with soil freezing and thawing is developed. A series of simulations are performed, in which various errors are imposed onto a selected model parameter while other model parameters are held constant, and sensitivity coefficient values (φ) of the time of maximum probe temperature (tm) and of the maximum probe temperature rise (Tm) for each parameter are calculated. Temperature changes at the measurement probe are quite sensitive to initial soil temperature (φ values for tm and for Tm are −0.99 and 0.99, respectively), λ (φ value for tm is −0.93), and parameters determining the shape of the soil freezing characteristic (FC) curve, i.e., saturated water content θs (φ values for tm and for Tm are 0.59 and −0.73, respectively) and n (φ values for tm and for Tm are −2.7 and 2.4, respectively). Temperature changes are not very sensitive to C (φ values for tm and for Tm are 0.034 and −0.15, respectively). Although previous investigations tried to determine C by inverse analysis, this sensitivity analysis shows that the influence of C on temperature response to a heat pulse is masked by that of the FC. Thus, λ and FC parameters are the best candidate parameters to be determined by inverse analysis of DPHP data. This new result will guide further testing of DPHP sensors in partially frozen soils.

Compensation of temperature effects for in-situ soil moisture measurement by DPHP sensors

Dual probe heat pulse (DPHP) sensors are economical solutions for soil moisture measurements. However, in agriculture fields the temperature significantly changes from time to time during 24h, which affects response of the soil moisture sensor. This paper, analyzes and models the error produced in the response of the DPHP sensors due to variation of the soil temperature. For this purpose, first effect of the soil temperature on the response of the sensor is studied using eight different soil samples. Accordingly, the existing soil moisture model, used for DPHP devices, is modified and used for the temperature compensation. A low power DPHP sensor comprising one heater probe and one temperature sensor probe, placed 0.003m apart, is fabricated. A low power, automated system, dissipating average power of 30mW, is also developed for the field measurements to validate the proposed model. The developed system is deployed in the field and soil moisture is measured for 38h at every 1h interval. Field measurements indicates that volumetric moisture content measured without temperature compensation leads to error of about 3% and with temperature compensation the error is reduced to 0.5%.

Monitoring water content dynamics of biological soil crusts

Biological soil crusts (hereafter, “biocrusts”) dominate soil surfaces in nearly all dryland environments. To better understand the influence of water content on carbon (C) exchange, we assessed the ability of dual-probe heat-pulse (DPHP) sensors, installed vertically and angled, to measure changes in near-surface water content. Four DPHP sensors were installed in each of two research plots (eight sensors total) that differed by temperature treatment (control and heated). Responses were compared to horizontally installed water content measurements made with three frequency-domain reflectometry (FDR) sensors in each plot at 5-cm depth. The study was conducted near Moab, Utah, from April through September 2009. Results showed significant differences between sensor technologies: peak water content differences from the DPHP sensors were approximately three times higher than those from the FDR sensors; some of the differences can be explained by the targeted monitoring of biocrust material in the shorter DPHP sensor and by potential signal loss from horizontally installed FDR sensors, or by an oversampling of deeper soil. C-exchange estimates using the DPHP sensors showed a net C loss of 69 and 76 g C m−2 in control and heated plots, respectively. The study illustrates the potential for using the more sensitive data from shallow installations for estimating C exchange in biocrusts.

A general in situ probe spacing correction method for dual probe heat pulse sensor

The dual probe heat pulse (DPHP) method is gaining popularity for measuring soil thermal properties. However, because of the fact that the DPHP measured heat capacity (c) of soil is hyper-sensitive to probe spacing variation, probe deflection causes large error in the measured c. To deal with probe deflection, recently, Liu et al. (2013) has proposed an in situ probe spacing correction method, but, their method was based on the inline deflection assumption. Wen et al. (2015) found that for non-inline deflected DPHP sensors, the method of Liu et al. (2013) provided poor reduction of the error in c. To cope with the non-inline deflection, in this study, we introduce a new DPHP sensor design by using three thermistors within the same temperature probe. A related probe spacing correction method for non-inline deflected probes was also presented. Both numerical simulation and experiment were conducted to test the new model. We define θ as the inclination angle of the probe deviation from the vertical direction. For experiment of the outward deflection (5.8°<θ<6.8°), the error in c is in the range from −23% to −76%; after inline in situ correction, the error decreases to the range of 12% to 44%; after using our non-inline in situ correction, the error is between 1% and 8%. Our three-dimensional finite element numerical simulation also demonstrates that, compared with the method of Liu et al. (2013), the new sensor and correcting method can significantly eliminate errors in c caused by probe deflections. The new DPHP sensor design and the non-inline deflection model have the potential to replace the method of Liu et al. (2013), and become the standard method for correcting probe spacing in situ.

The dual probe heat pulse method: interaction between probes of finite radius and finite heat capacity

We analyze the dual-probe heat-pulse (DPHP) method for measuring the thermal properties of soil or other media. The method involves measuring the temperature rise of a receiver probe that is parallel to, and a known distance from, an emitter probe from which a pulse of heat is released. Under the assumption that the probes are perfect conductors, we derive a semi-analytical solution for this method that accounts for the finite radius and finite conductivity of the probes and contact resistance between probe and soil. The solution in the Laplace domain is obtained by writing solutions of the Helmholtz equation around each probe as infinite series of terms involving Bessel and trigonometric functions. Addition theorems are then used to write the solutions centred at each probe in terms of solutions centred at the other probe. Truncating the series and solving a system of linear equations gives numerical values for the series coefficients, which in turn gives values of the Laplace transforms for numerical inversion. We use the solution to investigate the validity of a simpler approximate solution that is being used in conjunction with the DPHP method for thermal property determination. For what we define as typical implementations of the method, our results show that error resulting from use of the approximate solution is sufficiently small that its effect on estimated thermal properties will be negligible. The same general approach can be used to investigate a growing number of DPHP applications for which the approximate solution may be of questionable accuracy.

A Dual‐Probe Heat‐Pulse Sensor with Rigid Probes for Improved Soil Water Content Measurement

The dual-probe heat-pulse (DPHP) method is attractive for measuring soil thermal properties and volumetric water content. The purpose of this study was to develop and test a DPHP sensor having rigid probes made from thick-walled stainless steel tubing (2.38-mm outside diameter). The probes of this sensor are much more resistant to deflection than those of conventional DPHP sensors, decreasing measurement error caused by probe deflection during insertion into the soil. Laboratory experiments were conducted across a wide range of saturation levels with glass beads and three soils of different textures. For inferring soil properties from the proposed sensor, we applied the recently developed identical cylindrical perfect conductors (ICPC) model instead of the infinite line source (ILS) model that is typically used. The ICPC model improves solution for heat transport through the probe–soil system by accounting for the heat capacity and radius of the probes. Our results show a root mean square error of 1.4% volumetric water content and elimination of the measurement bias typically encountered with DPHP measurements. We conclude that the improved sensor, in combination with the ICPC model, provides a general, soil-independent water content estimate that is especially suitable for field soil water content monitoring because of its robust design with rigid probes. Because of its simplicity and measurements independent of soil type, we propose the presented DPHP method as an excellent alternative to other available measurement techniques for soil water content.

A low-power, low-cost soil-moisture sensor using dual-probe heat-pulse technique

This paper presents the development and testing of an integrated low-power and low-cost dual-probe heat-pulse (DPHP) soil-moisture sensor in view of the electrical power consumed and affordability in developing countries. A DPHP sensor has two probes: a heater and a temperature sensor probe spaced 3mm apart from the heater probe. Supply voltage of 3.3V is given to the heater-coil having resistance of 33Ω power consumption of 330mW, which is among the lowest in this category of sensors. The heater probe is 40mm long with 2mm diameter and hence is stiff enough to be inserted into the soil. The parametric finite element simulation study was performed to ensure that the maximum temperature rise is between 1°C and 5°C for wet and dry soils, respectively. The discrepancy between the simulation and experiment is less than 3.2%. The sensor was validated with white clay and tested with red soil samples to detect volumetric water-content ranging from 0% to 30%. The sensor element is integrated with low-power electronics for amplifying the output from thermocouple sensor and TelosB mote for wireless communication. A 3.7V lithium ion battery with capacity of 1150mAh is used to power the system. The battery is charged by a 6V and 300mA solar cell array. Readings were taken in 30min intervals. The life-time of DPHP sensor node is around 3.6 days. The sensor, encased in 30mm×20mm×10mm sized box, and integrated with electronics was tested independently in two separate laboratories for validating as well as investigating the dependence of the measurement of soil-moisture on the density of the soil. The difference in the readings while repeating the experiments was found out to be less than 0.01%. Furthermore, the effect of ambient temperature on the measurement of soil-moisture is studied experimentally and computationally.

A Simple Rational Approximation for Heat Capacity Determination with the Dual-Probe Heat-Pulse Method

A number of mathematical expressions are available for calculating soil volumetric heat capacity from data obtained with the dual-probe heat-pulse (DPHP) method. One of the more attractive options is a polynomial approximation that is simple to evaluate and yields estimates of heat capacity with error no greater than about 2% for typical DPHP measurement configurations (i.e., configurations with a probe spacing of approximately 6 mm and a heating duration in the range of 8–15 s). Unfortunately, the polynomial approximation is less accurate for measurement configurations with relatively small probe spacing or a relatively long heating duration. In this note we present a rational approximation that is more accurate, has a wider range of applicability, and is even simpler in mathematical form than the polynomial approximation. The rational approximation has error no greater than 0.015% for typical DPHP measurement configurations, but its primary advantage is that it yields heat capacity estimates with error no greater than 0.03% for a wide range of measurement configurations.

Consolidation of Oil Sands Mature Fine Tailings using the Heat Pulse Probe

CSA NewsVolume 60, Issue 2 p. 15-15 Science Consolidation of Oil Sands Mature Fine Tailings using the Heat Pulse Probe First published: 03 February 2015 https://doi.org/10.2134/csa2015-60-2-6 Adapted from Min, L., S.L. Barbour, and B.C. Si. 2015. Measuring solid percentage of oil sands mature fine tailings using the dual probe heat pulse method. J. Environ. Qual. 44:293–298. View the full article online at https://doi.org/10.2134/jeq2014.06.0262 Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume60, Issue2February 2015Pages 15-15 RelatedInformation

Measuring solid percentage of oil sands mature fine tailings using the dual probe heat pulse method.

The reclamation of mature fine tailings (MFT) is a critical challenge for the oil sands industry in western Canada, and a nonradioactive, automated, and inexpensive method to monitor the MFT solidification is needed. The objective of this paper is to evaluate the feasibility of a dual-probe heat pulse (DPHP) method to measure MFT solid percentage. Dual-probe heat pulse measurements were performed on three MFT samples, each at various solid percentages. A linear relationship ( = 0.9495 + 0.0558) was established between the DPHP-measured solid percentage () and that of oven-dry method (). Six additional MFT samples were collected and measured to validate the DPHP method. The specific heats of the six MFT solids were measured independently using a modulated differential scanning calorimetry method, and the sensitivity of DPHP-measured MFT solid percentage to the specific heat of MFT solids was evaluated. The result shows that the DPHP method can be used to accurately measure MFT solid percentages, and the accuracy can be further improved if the specific heat of the MFT solids is measured independently.

Heated Fiber Optic Distributed Temperature Sensing: A Dual‐Probe Heat‐Pulse Approach

Implementation of the dual‐probe heat‐pulse (DPHP) approach for measurement of volumetric heat capacity (C) and water content (θ) with distributed temperature sensing heated fiber optic (FO) systems presents an unprecedented opportunity for environmental monitoring (e.g., simultaneous measurement at thousands of points). We applied uniform heat pulses along a FO cable and monitored the thermal response at adjacent cables. We tested the DPHP method in the laboratory using multiple FO cables at a range of spacings. The amplitude and phase shift in the heat signal with distance was found to be a function of the soil volumetric heat capacity. Estimations of C at a range of moisture contents (θ = 0.09– 0.34 m3 m−3) suggest the feasibility of measurement via responsiveness to the changes in θ, although we observed error with decreasing soil water contents (up to 26% at θ = 0.09 m3 m−3). Optimization will require further models to account for the finite radius and thermal influence of the FO cables. Although the results indicate that the method shows great promise, further study is needed to quantify the effects of soil type, cable spacing, and jacket configurations on accuracy.

Evaluation of a self-correcting dual probe heat pulse sensor

The dual probe heat pulse method (DPHP) can be used to measure soil thermal properties. However, in situ probe spacing is prone to change resulting in large errors of measured soil heat capacity c. A newly designed DPHP sensor has two thermistors in the temperature probe which can be used to calculate in situ changes in probe spacing. This new sensor has been tested under the limited condition of linear coplanar probe deflection. i.e., probes were deflected in-line but were not bent in different directions. However, actual probe deflections may not always be coplanar linear. In this study the applicability of the new DPHP sensor is evaluated in fine sand and in silica sand for a variety of probe deflections. Probes are deflected at the bottom end (bottom) or top end (top) of probes. Results indicate that the new sensor can significantly eliminate errors in c caused by coplanar and non-coplanar probe deflections. Compared with bottom deflections, top deflections have larger errors in c. Thus, theory used to correct for deflections is more applicable to bottom deflections than to top deflections. The errors in c for saturated soil materials are larger than the errors in c for dry soil materials, because of the finite response times of the thermistors used in the probes. Clearly, the newly designed DPHP sensors have the potential for reducing errors caused by various kinds of probe deflections that may be encountered in the field.

A Self-Calibrated Dual Probe Heat Pulse Sensor for In Situ Calibrating the Probe Spacing

Dual probe heat pulse method (DPHP) is a popular method for measuring soil thermal properties. However when this method is applied in the field, the distance between the temperature probe and the heating probe (probe spacing) may change due to probe deflection, and thus cause error in measured heat capacity (c) of soil. We developed a self-calibrated DPHP for in situ calibration of probe spacing, using a temperature probe with two imbedded thermistors (10 mm apart in the longitudinal direction). Experimental results for sand and fine sand samples indicate that this method can significantly reduce error caused by the probe deflection. If we define σ as the inclination angle of probe deviation from the vertical direction, for inward deflection with 0.8° < θ < 0.9°, the error in c is between –8.1 and –14.3%; after in situ calibration, it is between –0.1 and –4.3%. For outward deflection with 3.2° < θ < 3.5°, the error in c is in the range from 22.9 to 38.8%; after in situ calibration, the error reduces to from –3.8 to –7.8%. This new DPHP design may be applied in the field for reducing error caused by probe deflection.

An Adiabatic Boundary Condition Solution for Improved Accuracy of Heat-Pulse Measurement Analysis Near the Soil-Atmosphere Interface

The infinite line source model (ILS model) is widely used in the dual-probe heat pulse (DPHP) method for measuring the thermal conductivity (k), specific heat capacity (c), and thermal diffusivity (α) of soil. However, there exists errors when sensors are located very close to the soil–atmosphere interface. The purpose of this study is to develop a new method to accurately determine k and c near the soil–atmosphere interface. The method of images was used to obtain the ILS solution with an adiabatic boundary condition (ILS–ABC), when DPHP sensors are near the soil–atmosphere interface. Both finite element simulations and DPHP experiments verified that the soil–atmosphere could be approximated by the adiabatic boundary condition (ABC). The new solution performed well in predicting the thermal properties of the samples when compared with the ILS model, which ignored the existence of the soil–atmosphere interface. If the ILS model was used to compute k and c rather than the new ILS–ABC model, the magnitude of the error in k and c increased rapidly with decreases in burial depth (h) and could be larger than 30% at h ≤ 3 mm. The solution may be helpful for better extracting soil thermal properties near the soil–atmosphere interface.

Semianalytical Solution for Dual‐Probe Heat‐Pulse Applications that Accounts for Probe Radius and Heat Capacity

The dual‐probe heat‐pulse (DPHP) method is useful for measuring soil thermal properties. Measurements are made with a sensor that has two parallel cylindrical probes: one for introducing a pulse of heat into the soil (heater probe) and one for measuring change in temperature (temperature probe). We present a semianalytical solution that accounts for the finite radius and finite heat capacity of the heater and temperature probes. A closed‐form expression for the Laplace transform of the solution is obtained by considering the probes to be cylindrical perfect conductors. The Laplace‐domain solution is inverted numerically. For the case where both probes have the same radius and heat capacity, we show that their finite properties have equal influence on the heat‐pulse signal received by the temperature probe. The finite radius of the probes causes the heat‐pulse signal to arrive earlier in time. This time shift increases in magnitude as the probe radius increases. The effect of the finite heat capacity of the probes depends on the ratio of the heat capacity of the probes (C0) and the heat capacity of the soil (C). Compared with the case where C0/C = 1, the magnitude of the heat‐pulse signal decreases (i.e., smaller change in temperature) and the maximum temperature rise occurs later when C0/C &gt; 1. When C0/C &lt; 1, the magnitude of the signal increases and the maximum temperature rise occurs earlier. The semianalytical solution is appropriate for use in DPHP applications where the ratio of probe radius (a0) and probe spacing (L) satisfies the condition that a0/L ≤ 0.11.

Sensor and Numerical Simulator Evaluation for Porous Medium Desiccation and Rewetting at the Intermediate Laboratory Scale

Soil desiccation, in conjunction with surface infiltration control, is considered at the Hanford Site as a potential technology to limit the flux of technetium and other contaminants in the vadose zone to the groundwater. An intermediate‐scale experiment was conducted to test the response of a series of instruments to desiccation and subsequent rewetting of porous media. The instruments include thermistors, thermocouple psychrometers, dual‐probe heat pulse sensors, heat dissipation units, and humidity probes. The experiment was simulated with the multifluid flow simulator STOMP, using independently obtained hydraulic and thermal porous medium properties. All instrument types used for this experiment were able to indicate when the desiccation front passed a certain location. In most cases the changes were sharp, indicating rapid changes in moisture content, water potential, or humidity. However, a response to the changing conditions was recorded only when the drying front was very close to a sensor. Of the tested instruments, only the heat dissipation unit and humidity probes were able to detect rewetting. The numerical simulation results reasonably match the experimental data, indicating that the simulator captures the pertinent gas flow and transport processes related to desiccation and rewetting and may be useful in the design and analysis of field tests.

Single- and Dual-Probe Heat Pulse Probe for Determining Thermal Properties of Dry Soils

Heat pulse methods include the dual-probe (DP) and single-probe (SP) methods. The DP method is a widely used method for determining the thermal conductivity (K) and thermal diffusivity (β) of soil. The SP method has been traditionally used for measuring K only. The objective of this study was to examine if the SP method can be used to estimate the thermal properties of air-dried soils. The thermal properties of three sands were measured using differential scanning calorimetry (DSC) and the DP and SP methods. For the SP method, the small-time and large-time solutions of the perfect conductor model and hollow cylindrical probe model were fitted to the respective small-time and large-time temperature vs. time curves. Both K and β of the soil were determined by the SP method. The DP and SP methods yielded similar K values for the three air-dried soils with a relative deviation <6.1%. In comparison with the DSC measurements, the DP method overestimated the specific heat (c) by 19 to 29%, while the SP method with the hollow cylindrical probe model underestimated c by 21 to 8%, and the SP method with the perfect conductor model resulted in −4 to 7% error. Therefore, the SP method with the perfect conductor model gave the most accurate estimate of c.

Effect of Probe Deflection on Dual‐Probe Heat‐Pulse Thermal Conductivity Measurements

The dual‐probe heat‐pulse (DPHP) method is useful for measuring soil thermal properties; however, the probes of a DPHP sensor can deflect when inserted into the soil. Theoretical analysis has shown that measurements of thermal conductivity (λ) should be unaffected by deflection‐induced changes in probe spacing. To verify this result, the conductivities of water, dry sand, and saturated sand were measured using DPHP sensors with probes subject to inward deflection, no deflection, and outward deflection. No error in λ was detected when probes were deflected inward by an amount that caused a 14% reduction in probe spacing. Outward deflection (15% increase in spacing) caused error in λ estimates, but the errors were small (≤0.04 W m−1 K−1) and likely to be of little consequence in most applications. We conclude that estimates of λ obtained with the DPHP method are largely unaffected by changes in probe spacing caused by deflection.

Dual-probe heat pulse method for snow density and thermal properties measurement

[1] Measuring the density (ρ), thermal conductivity (k) and thermal diffusivity (α) of snow is important for modeling the energy and water balance of the earth's surface. The objective of this letter is to determine if the dual-probe heat pulse (DPHP) method can be used to measure snow density as well as thermal properties k and α. DPHP experiments with 60-s heat pulse duration and variable strength of q′ < 15 W m−1 were carried out on ice and various kinds of snow to avoid melting. There was a linear relationship between the DPHP measured snow density and that of gravimetrically measured density. With calibration, the DPHP method may be accurate for determining snow density.

Correcting Dual‐Probe Heat‐Pulse Readings for Changes in Ambient Temperature

We examined three methods of analyzing dual‐probe heat‐pulse (DPHP) data for estimating volumetric water content of near‐surface materials where diurnal temperature variations can approach ± 20°C. The three methods of analyzing thermal responses include: (i) the single‐point method (SPM); (ii) a method that uses a Levenburg–Marquardt optimization of thermal conductivity, volumetric heat capacity, and drift in ambient temperature with subsequent calculation of water content (LM‐Uncorrected); and (iii) an expansion of the LM‐Uncorrected method that incorporates temperature dependencies of soil thermal conductivity and optimizes on volumetric water content, apparent needle spacing, and drift in ambient temperature during the measurement (LM‐Corrected). Ambient temperature measurements were made with either a soil thermistor installed away from the DPHP sensor (SPM) or from the temperature response of the DPHP sensor itself (LM‐Uncorrected and LM‐Corrected). Methods were tested based on measurements made in April and August 2006 from sensors installed at ground surface in the Mojave Desert. The SPM results showed that large (summertime) diurnal temperature variations led to significant oscillations of water content, recorded as high as ± 0.10 m3 m−3 The LM‐Uncorrected method showed a significant reduction in water content oscillations, but variations were still large. The LM‐Corrected method showed that the time series of water content was significantly smoother than uncorrected water contents (i.e., ± 0.005 m3 m−3 in August). The DPHP‐derived water contents compared favorably to data from water content reflectometers installed nearby. The results show that soil water content estimates from the LM‐Corrected method were substantially less affected by large ambient temperature variations.