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This study presents a novel methodology for determining the apparent thermal diffusivity of subsoil in situ, employing two heat transfer models within the subsurface: one method is based on heat conduction caused by air temperature oscillations, while the other considers heat transmission via both conduction and convection due to groundwater flow. Differential equations were solved, and non-linear regression analysis was employed. This method has direct applications in various engineering and environmental domains, such as underground transmission lines, oil and gas pipelines, radioactive waste management, and geothermal systems, especially in the context of implementing horizontal geothermal collectors (HGC). The apparent thermal diffusivity value of 1.514 × 10−6 m2 s−1, within a 95% confidence interval spanning 1.512 × 10−6 m2 s−1 and 1.516 × 10−6 m2 s−1, was obtained from the section between 1.67 and 3.86 m depth in a research borehole located in Asturias, Northern Spain, using twenty-one temperature sensors. The method allowed for the calculation of the subsoil's apparent thermal diffusivity up to a depth of 14.55 m. [ABSTRACT FROM AUTHOR]

This study presents a novel methodology for determining the apparent thermal diffusivity of subsoil in situ, employing two heat transfer models within the subsurface: one method is based on heat conduction caused by air temperature oscillations, while the other considers heat transmission via both conduction and convection due to groundwater flow. Differential equations were solved, and non-linear regression analysis was employed. This method has direct applications in various engineering and environmental domains, such as underground transmission lines, oil and gas pipelines, radioactive waste management, and geothermal systems, especially in the context of implementing horizontal geothermal collectors (HGC). The apparent thermal diffusivity value of 1.514 × 10−6 m2 s−1, within a 95% confidence interval spanning 1.512 × 10−6 m2 s−1 and 1.516 × 10−6 m2 s−1, was obtained from the section between 1.67 and 3.86 m depth in a research borehole located in Asturias, Northern Spain, using twenty-one temperature sensors. The method allowed for the calculation of the subsoil’s apparent thermal diffusivity up to a depth of 14.55 m.

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To determine the effective drainage area, a fluid-solid coupling model of gas-bearing coal rock mass is established, and the geometric model is established using COMSOL Multiphysics software for numerical solution. On the basis of considering the permeability anisotropy, the variation law of gas pressure in different positions around the borehole is studied. The results show that the gas pressure contour map presents an elliptical shape after considering the permeability anisotropy. The permeability anisotropy affects the gas migration in coal. The lower the permeability is, the slower the gas moves in the coal seam. The Darcy velocity is proportional to the permeability, i.e. the Darcy velocity increases with the increase of permeability. The permeability anisotropy makes Darcy velocity contours around boreholes elliptically distributed. The closer to the center of the borehole is, the higher the speed of Darcy velocity is, and the maximum Darcy velocity decreases with the increase of time. When the gas pressure around the drilling hole reaches 0.74 MPa, the effective extraction area of the borehole shows the distribution of large left-right and small upper-lower under the influence of permeability anisotropy. The gas is difficult to be extracted in the place with low permeability.

Abstract The classical methodology to perform and analyze thermal response test (TRT) is unsuccessful when advection contributes to heat transfer in the ground, due to the presence of a groundwater flow. In this study, the applicability, the advantages, and the limitations of the moving line source model to interpret TRT data are discussed. Two real TRT case studies from the Italian Alpine area are reported and analyzed, with both the standard infinite line source approach and the moving line source one. It is shown that the inverse heat transfer problem is ill-posed, leading to multiple solutions. However, besides minimization of the error between measurements and modeling, physical considerations help to discriminate among solutions the most plausible ones. In this regard, the MLS approach proves to be effective in the advection-dominated case. The original time criterion proposed here to disregard initial data from the fitting, based on a resistance–capacitance model of the borehole embedded in a groundwater flow, is validated in terms of convergence of the solution. In turn, in the case when advection and conduction are competitive, the MLS approach results more sensitive to ground thermal conductivity than to Darcy velocity. Although in this case a limited impact of the uncertainty in the groundwater velocity on the boreholes sizing is expected, future studies should focus on the development of a successful TRT methodology for this condition.

We developed and tested the feasibility of computational fluid modeling (CFM) based on dynamic contrastenhanced magnetic resonance imaging (DCE-MRI) for quantitative estimation of interstitial fluid pressure (IFP) and velocity (IFV) in patients with head and neck (HN) cancer with locoregional lymph node metastases. Twenty-two patients with HN cancer, with 38 lymph nodes, underwent pretreatment standard MRI, including DCE-MRI, on a 3-Tesla scanner. CFM simulation was performed with the finite element method in COMSOL Multiphysics software. The model consisted of a partial differential equation (PDE) module to generate 3D parametric IFP and IFV maps, using the Darcy equation and Ktrans values (min-1, estimated from the extended Tofts model) to reflect fluid influx into tissue from the capillary microvasculature. The Spearman correlation (r) was calculated between total tumor volumes and CFM estimates of mean tumor IFP and IFV. CFM-estimated tumor IFP and IFV mean 6 standard deviation for the neck nodal metastases were 1.73 ± 0.39 (kPa) and 1.82 ± 0.9 × (10-7 m/s), respectively. High IFP estimates corresponds to very low IFV throughout the tumor core, but IFV rises rapidly near the tumor boundary where the drop in IFP is precipitous. A significant correlation was found between pretreatment total tumor volume and CFM estimates of mean tumor IFP (r = 0.50, P = 0.004). Future studies can validate these initial findings in larger patients with HN cancer cohorts using CFM of the tumor in concert with DCE characterization, which holds promise in radiation oncology and drug-therapy clinical trials. [ABSTRACT FROM AUTHOR]

Single-borehole tracer dilution tests are used to estimate the Darcy velocity (vd) which is important for investigating contaminant transport and distribution within the aquifers. Although it is generally acknowledged that artefacts other than the horizontal groundwater flow can affect a tracer dilution rate in single-borehole tracer dilution tests, there are no studies which have been carried out to illustrate the effects of these artefacts. As a result, groundwater practitioners have continued to use single-borehole tracer dilution tests without considering the potential influence of these artefacts when estimating the Darcy velocity. This study is primarily designed to investigate the influence of the effect of artefacts other than the horizontal groundwater flow on the single-borehole tracer dilution tests under natural hydraulic gradient. Three single-borehole tracer dilution tests were performed during the experiment in an alluvial aquifer in the main Karoo Basin of South Africa. The data showed that early stage of tracer dilution can be affected by artefacts other than the horizontal groundwater flow. Data affected by the artefacts appear to show fast early stage tracer dilution rates which can result in overestimation of the Darcy velocity. Higher tracer concentrations with respect to the background levels can be considered as the dominant artefacts. The study proposes a simple qualitative approach to identify and remove the data affected by artefacts prior to the estimation of the Darcy velocity. Further studies that will effectively quantify the extent of the effects of these artefacts on tracer dilution rates are urgently needed. [ABSTRACT FROM AUTHOR]

The objective of this study is to assess the suitability of the analytical infinite moving line source (MLS) model in determining the temperature of vertical grouted borehole heat exchangers (BHEs) for steady-state conditions when horizontal groundwater advection is present. Therefore, a numerical model of a grouted borehole is used as a virtual reality for further analysis. As a result of the first analysis, it has been discovered that established analytical methods to determine the borehole thermal resistance as a mean value over the borehole radius can also be applied to BHEs with groundwater advection. Furthermore, the deviation between a finite MLS and the infinite MLS is found to be only less than 5% for BHEs of a depth of 30 m or more, and Péclet numbers greater than 0.05. Finally, the accuracy of the temperature change calculated with the infinite MLS model at the radius of the borehole wall compared to the temperature change at a numerically simulated grouted borehole is addressed. A discrepancy of the g-functions resulting in a poor dimensioning of BHEs by the infinite MLS model is revealed, which is ascribed to the impermeable grouting material of the numerical model. A correction function has been developed and applied to the infinite MLS model for steady-state conditions to overcome this discrepancy and to avoid poor dimensioning of BHEs.

The thermal diffusivity is the key parameter that controls near‐surface temperature where periodic temperature variation is progressively attenuated and delayed with depth. This article presents the results of apparent thermal diffusivity using temperatures recorded by a bedrock temperature measurement network in the fault zones of western Sichuan. High sensitivity temperature sensors (10−4 K) were installed at a maximum depth reaching 30 m. The apparent thermal diffusivities were deduced from both amplitude damping and phase shifting of annual temperature variations between two different depths. Under pure conduction, the thermal diffusivity determined through the phase method (αΦ) should be equivalent to that determined through the amplitude method (αA), whereas effects of the upward (downward) water flow are evidently reflected in the amplitude decay to make αΦ larger (lesser) than αA. The discrepancy between αΦ and αA can thus be a tracer of water movement or convective heat transfer. The calculated αΦ of the measurement stations varies from 1.22 × 10−6 to 3.00 × 10−6 m2/s, and the estimated αA ranges from 0.93 × 10−6 to 2.41 × 10−6 m2/s. Two regimes of heat transfer underground were suggested from the results. Conductive heat transport prevails over the nonconductive processes at five stations, which is characterized by αΦ coincident with αA for the same depth pair. On the contrary, the values of αΦ differ from αA at six stations in the intersection area of the Y‐shaped fault system, implying that convective heat transfer also plays a comparably important role. This finding is consistent with the hot springs distribution of the area. The results also indicate that water moves upward with an average Darcy velocity of approximately −1 × 10−7 m/s in this region. Our research provides new evidence for the hydrothermal activity in the fault zones at the eastern margin of the Tibetan Plateau. [ABSTRACT FROM AUTHOR]

Thermal response tests (TRTs) are a common field method in shallow geothermics to estimate thermal properties of the ground. During the test, a constantly heated fluid is circulated in closed tubes within a vertical borehole heat exchanger (BHE). The observed temperature development of the fluid is characteristic for the thermal properties of the ground and the BHE. We show that, when the BHE is installed in an aquifer with significant horizontal groundwater flow, this test can also be used for hydrogeological characterization of the penetrated subsurface. An evaluation method based on the moving line source equation and considering the natural occurring variability of the thermal transport parameters is presented. It is validated by application to a well-controlled, large-scale tank experiment with 9 m length, 6 m width, and 4.5 m depth, and by data interpretation from a field-scale test. The tank experiment imitates an advection-influenced TRT in a well-known layered aquifer. The field experiment was recorded with a 100 m deep BHE, installed in a gravel aquifer in southwest Germany. The evaluations of both experiments result in similar hydraulic conductivity ranges as determined by standard hydraulic investigation methods such as pumping tests and sieve analyses. Thus, advection-influenced TRTs could also potentially be used to determine integral hydraulic conductivity of the subsurface. [ABSTRACT FROM AUTHOR]

Abstract: In geothermal fields, open faults and fractures often act as high permeability pathways bringing hydrothermal fluids to the surface from deep reservoirs. The Mount Princeton area, in south-central Colorado, is an area that has an active geothermal system related to faulting and is therefore a suitable natural laboratory to test geophysical methods. The Sawatch range-front normal fault bordering the half-graben of the Upper Arkansas valley is characterized by a right-lateral offset at Mount Princeton Hot springs. This offset is associated with the Chalk Cliffs of hydrothermally altered quartz monzonite. Because fault identification in this area is complicated by quaternary deposits (including glacial and fluvial deposits), we use DC electrical resistivity tomography and self-potential mapping to identify preferential fluid flow pathways. The geophysical data (over 5600 resistivity and 2700 self-potential measurements) provide evidence of the existence of a dextral strike slip fault zone (Fault B) responsible for the offset of the Sawatch fault. A segment of this dextral strike slip fault (termed U1) is acting as the dominant vertical flow path bringing thermal waters to a shallow unconfined aquifer. Upwelling of the thermal waters is also observed at two zones (U2 and U3) of an open fracture called Fault A. This fault is located at the tip of the Sawatch fault and is likely associated with an extensional strain regime in this area. Self-potential measurements are used to estimate the flux of upwelling thermal water. The upflow estimate (4±1×103 m3/day for the open segment of the Fault B and 2±1×103 m3/day for Fault A) from the geophysical data is remarkably consistent with the downstream Mt. Princeton hot water production (4.3–4.9)×103 m3/day at approximately 60–86°C). A temperature map indicates that a third upwelling zone termed U4 may exist at the southern tip of the Sawatch fault. [Copyright &y& Elsevier]

Abstract: The effect of immobile water content on contaminant advection and dispersion in unsaturated porous media has been studied using a formulation which assumes that even in the immobile liquid zone, there occurs minor liquid flow. An approach is proposed for computing this liquid velocity. One dimensional numerical simulation is carried out to study the effect of immobile water content on the time of appearance of contaminant at the bottom of an unsaturated column. The numerical model developed is verified using analytical solutions for simple advective-dispersive cases. From the simulations, it was observed that increase in the immobile water content leads to quicker appearance of contaminant. [Copyright &y& Elsevier]

To study statistics of velocity fields in three-dimensional heterogeneous multi-Gaussian saturated hydraulic conductivity fields and the accuracy of their prediction, we performed high-resolution Monte Carlo (MC) analyses. The MC analyses included variances of the log hydraulic conductivity in the range of 0.5 ≤ σ Y2 ≤ 3.0 and anisotropy ratios in the range of 0.017 ≤ e ≤ 1. The statistics of the velocity fields from the MC analyses are compared with analytical solutions of the first- and second-order approximations of the stochastic flow equation. This paper shows that the second-order approximations fit significantly better to the univariate statistics of the Darcy velocity from the MC analyses. For isotropic cases the second-order approximations correspond fairly well to the univariate statistics of the velocity. For anisotropic cases the accordance is given only for the mean velocity and the variance of the transverse vertical component of the velocity. The MC analyses show that the spatial correlation of the velocity decreases more rapidly with increasing σ Y2. This was more pronounced for the anisotropic than for the isotropic case. The negative correlations, in absolute terms, of the transverse velocity components simultaneously decrease with increasing σ Y2. This is in contrast to the first-order approximation of the spatial correlations of the velocity. It is assumed that the discrepancies between approximate solutions of the stochastic flow equation and the results of the MC analyses are strongly dependent on the nonnormality of the probability density distributions of the velocity. [ABSTRACT FROM AUTHOR]

Given a P1 conforming or nonconforming Galerkin finite element method (GFEM) solution ph, which approximates the exact solution p of the diffusion-reaction equation - ∇·Κ ∇+ αp = f with full tensor variable coefficient Κ, we evaluate the approximate flux uh to the exact flux u = -Κ ∇p by a simple but physically intuitive formula over each finite element. The flux is sought in the continuous (in normal component) or the discontinuous Raviart­Thomas space. A systematic way of deriving such a formula is introduced. This direct method retains local conservation property at the element level, typical of mixed methods (finite element or finite volume type), but avoids solving an indefinite linear system. In short, the present method retains the best of the GFEM and the mixed method but without their shortcomings. Thus we view our method as a conservative GFEM and demonstrate its equivalence to a certain mixed finite volume box method. The equivalence theorems explain how the pressure can decouple basically cost free from the mixed formulation. The accuracy in the flux is of first order in the H(div;Ω) norm. Numerical results are provided to support the theory. [ABSTRACT FROM AUTHOR]

The objective of this study is to assess the suitability of the analytical infinite moving line source (MLS) model in determining the temperature of vertical grouted borehole heat exchangers (BHEs) for steady-state conditions when horizontal groundwater advection is present. Therefore, a numerical model of a grouted borehole is used as a virtual reality for further analysis. As a result of the first analysis, it has been discovered that established analytical methods to determine the borehole thermal resistance as a mean value over the borehole radius can also be applied to BHEs with groundwater advection. Furthermore, the deviation between a finite MLS and the infinite MLS is found to be only less than 5% for BHEs of a depth of 30 m or more, and Péclet numbers greater than 0.05. Finally, the accuracy of the temperature change calculated with the infinite MLS model at the radius of the borehole wall compared to the temperature change at a numerically simulated grouted borehole is addressed. A discrepancy of the g-functions resulting in a poor dimensioning of BHEs by the infinite MLS model is revealed, which is ascribed to the impermeable grouting material of the numerical model. A correction function has been developed and applied to the infinite MLS model for steady-state conditions to overcome this discrepancy and to avoid poor dimensioning of BHEs. [ABSTRACT FROM AUTHOR]

Simple Summary: High vessel permeability, poor perfusion, low lymphatic drainage, and dense abundant stroma elevate interstitial fluid pressures (IFP) in pancreatic ductal adenocarcinoma (PDAC). The present study aims to monitor longitudinal changes in simulated tumor IFP and velocity (IFV) values using a dynamic contrast-enhanced (DCE)-MRI-based computational fluid modeling (CFM) approach in PDAC. Nine PDAC patients underwent DCE-MRI acquisition on a 3-Tesla MRI scanner at pre-treatment (TX (0)), immediately after the first fraction of stereotactic body radiotherapy (SBRT, (D1-TX)), and six weeks post-TX (D2-TX). The partial differential equation of IFP formulated from the continuity equation using the Starling Principle of fluid exchange and Darcy velocity–pressure relationship was solved in COMSOL Multiphysics software to generate IFP and IFV parametric maps using relevant tumor tissue physiological parameters. Initial results suggest that after validation, IFP and IFV can be imaging biomarkers of early response to therapy that may guide precision medicine in PDAC. The present study aims to monitor longitudinal changes in simulated tumor interstitial fluid pressure (IFP) and velocity (IFV) values using dynamic contrast-enhanced (DCE)-MRI-based computational fluid modeling (CFM) in pancreatic ductal adenocarcinoma (PDAC) patients. Nine PDAC patients underwent MRI, including DCE-MRI, on a 3-Tesla MRI scanner at pre-treatment (TX (0)), after the first fraction of stereotactic body radiotherapy (SBRT, (D1-TX)), and six weeks post-TX (D2-TX). The partial differential equation of IFP formulated from the continuity equation, incorporating the Starling Principle of fluid exchange, Darcy velocity, and volume transfer constant (Ktrans), was solved in COMSOL Multiphysics software to generate IFP and IFV maps. Tumor volume (Vt), Ktrans, IFP, and IFV values were compared (Wilcoxon and Spearman) between the time- points. D2-TX Ktrans values were significantly different from pre-TX and D1-TX (p < 0.05). The D1-TX and pre-TX mean IFV values exhibited a borderline significant difference (p = 0.08). The IFP values varying <3.0% between the three time-points were not significantly different (p > 0.05). Vt and IFP values were strongly positively correlated at pre-TX (ρ = 0.90, p = 0.005), while IFV exhibited a strong negative correlation at D1-TX (ρ = −0.74, p = 0.045). Vt, Ktrans, IFP, and IFV hold promise as imaging biomarkers of early response to therapy in PDAC. [ABSTRACT FROM AUTHOR]

For assessing the radionuclide transport parameters, the apparent diffusion coefficient and the rock capacity factor η R (being the product of the accessible porosity η and the retardation factor R) in host rocks used for nuclear waste disposal, mainly two classes of experiments are used: pure diffusive experiments e.g. through-diffusion, and experiments where next to a concentration gradient also a pressure gradient is applied e.g. pulse injection experiments. In Boom Clay, through-diffusion and pulse injection experiments lead to similar values for the accessible porosity of tritiated water (HTO), while for another unretarded tracer, iodide, significantly higher values are obtained by pulse injection. Similarly, in recompacted Na-illite, for chloride (another unretarded anion), lower accessible porosity values are observed by through-diffusion than by pulse injection. The difference increases while lowering the ionic strength. The reason for the discrepancy lies in the models used for analysing the migration experiments with a pressure gradient. Experiments with a pressure gradient allow fitting the apparent velocity V app of a tracer. The rock capacity factor is estimated as the ratio V Darcy / V app of the Darcy velocity V Darcy and V app. This is correct for HTO, but not for anions because the water flow through anion inaccessible porosity is neglected. Making a correct water flow mass balance by taking the water flow through inaccessible porosity into account, demonstrates that the rock capacity factor is given by the product F V V Darcy / V app with F V the fraction (0 ≤ F V ≤ 1) of the Darcy velocity flowing through tracer accessible porosity. Previously determined η R values are in reality the ratio η R / F V and overestimate η R. In agreement with the experimental results, a lower ionic strength leads for (unretarded) anions to a lower accessible porosity η and consequently a lower F V and more overestimation of η. Besides charge related inaccessible porosity, porosity can also be inaccessible because of the size of the transported species: the accessible porosity becomes zero in case the particle size approaches the pore throat. Because the intention of experiments with a pressure gradient is to know η R , we propose two models, which are basically two tracer distributions over a pore, for estimating F V. Considering Poiseuille flow, we calculate a typical pore radius, the hydraulic conductivity and for both distributions the accessible porosity, the fraction F V and the fitted ratio η R / F V. Application to experimental data shows anisotropy in the pore radius, corresponding to the observed anisotropy in hydraulic conductivity. For anion exclusion, the model describes qualitatively the experimentally observed evolution as a function of double layer width. Because also for cations there is presently no valid relation between V app and η R , migration experiments with a pressure gradient only provide a reasonable estimate for the rock capacity factor η R in case of small (with respect to the average pore size) neutral particles like HTO. • Pressure gradient experiments may not allow determining the accessible porosity. •Flow changes concentration in the accessible porosity when entering/ leaving a core. •Anisotropy of clay pore radius explains anisotropy of hydraulic conductivity. •It can be unclear what is the length in the Péclet number. •Typical distance of back diffusion is ratio of dispersion coefficient and velocity. [ABSTRACT FROM AUTHOR]