Radial reactive solute transport in an aquifer–aquitard system

Radial reactive transport is investigated in an aquifer–aquitard system considering the important processes such as advection, radial and vertical dispersions for the aquifer, vertical advection and dispersion for the aquitards, and first-order biodegradation or radioactive decay. We solved the coupled governing equations of transport in the aquifer and the aquitards by honoring the continuity of concentration and mass flux across the aquifer–aquitard interfaces and recognizing the concentration variation along the aquifer thickness. This effort improved the averaged-approximation (AA) model, which dealt with radial dispersion in an aquifer–aquitard system by excluding the aquitard advection. To compare with our new solution, we expanded the AA model by including the aquitard advection. The expanded AA model considerably overestimated the mass in the upper aquitard when an upward advection existed there. The rates of mass change in the upper aquitard from the new solution and the AA model solution increased with time following sub-linear fashions. The times corresponding to the peak values of the residence time distributions for the AA model, the expanded AA model, and the new model were almost the same. The residence time distributions seemed to follow the Maxwell–Boltzmann distribution closely when plotting the time in logarithmic scale. In addition, we developed a finite-element COMSOL Multiphysics simulation of the problem, and found that the COMSOL solution agreed with the new solution well.     

Estimating Travel Time in Bank Filtration Systems from a Numerical Model Based on DTS Measurements

An approach is presented to determine the seasonal variations in travel time in a bank filtration system using a passive heat tracer test. The temperature in the aquifer varies seasonally because of temperature variations of the infiltrating surface water and at the soil surface. Temperature was measured with distributed temperature sensing along fiber optic cables that were inserted vertically into the aquifer with direct push equipment. The approach was applied to a bank filtration system consisting of a sequence of alternating, elongated recharge basins and rows of recovery wells. A SEAWAT model was developed to simulate coupled flow and heat transport. The model of a two‐dimensional vertical cross section is able to simulate the temperature of the water at the well and the measured vertical temperature profiles reasonably well. MODPATH was used to compute flowpaths and the travel time distribution. At the study site, temporal variation of the pumping discharge was the dominant factor influencing the travel time distribution. For an equivalent system with a constant pumping rate, variations in the travel time distribution are caused by variations in the temperature‐dependent viscosity. As a result, travel times increase in the winter, when a larger fraction of the water travels through the warmer, lower part of the aquifer, and decrease in the summer, when the upper part of the aquifer is warmer.     

Effect of frictional heating and thermal advection on pre-seismic sliding: a numerical simulation using a rate-, state- and temperature-dependent friction law

Laboratory experiments on simulated faults in rocks clearly show the temperature dependence of dynamic rock friction. Since rocks surrounding faults are permeable, we have developed a numerical method to describe the thermo-mechanical evolution of the pre-seismic sliding phase which takes into account both the rate-, state- and temperature-dependent friction law and the heat advection term in the energy equation. We consider a laminar fluid motion perpendicular to a vertical fault plane and assume that fluids move away from the fault plane. A semi-analytical temperature solution which accounts for the variability of slip velocity and stress on the fault has been found. This solution has been generalized to the case of a time varying fluid velocity and then was used to include the thermal pressurization effect. After discretizing the temperature solution, the evolution of the system is obtained by the solution of a system of first order differential equations which allows us to determine the evolution of slip, slip rate, friction coefficient, effective normal stress, temperature and fluid velocity. The numerical solutions are found using a Runge-Kutta method with an adaptative stepsize control in time. When the thermal pressurization effects can be neglected, the heat advection effect gives rise to a delay, with respect to the purely conductive case, of the earthquake occurrence time. This delay increases with increasing permeability H of the system. When the thermal pressurization effects are taken into account the situation is opposite, i.e. the onset of instability tends to precede that of the purely conductive case. The advance in the time of occurrence of instability increases with increasing coefficient of thermal pressurization. In the small permeability range (H ≤ 10^?18 m²), the seismic moment and nucleation length of the pre-seismic phase are significantly smaller than those predicted by the purely conductive model.     

Estimation of vertical water fluxes from temperature time series by the inverse numerical computer program FLUX‐BOT

The application of heat as a hydrological tracer has become a standard method for quantifying water fluxes between groundwater and surface water. The typical application is to estimate vertical water fluxes in the shallow subsurface beneath streams or lakes. For this purpose, time series of temperatures in the surface water and in the sediment are measured and evaluated by a vertical 1D representation of heat transport by advection and conduction. Several analytical solutions exist to calculate the vertical water flux from the measured temperatures. Although analytical solutions can be easily implemented, they are restricted to specific boundary conditions such as a sinusoidal upper temperature boundary. Numerical solutions offer higher flexibility in the selection of the boundary conditions. This, in turn, reduces the effort of data preprocessing, such as the extraction of the diurnal temperature variation from the raw data. Here, we present software to estimate water fluxes based on temperatures—FLUX‐BOT. FLUX‐BOT is a numerical code written in MATLAB that calculates vertical water fluxes in saturated sediments based on the inversion of measured temperature time series observed at multiple depths. FLUX‐BOT applies a centred Crank–Nicolson implicit finite difference scheme to solve the one‐dimensional heat advection–conduction equation. FLUX‐BOT includes functions for the inverse numerical routines, functions for visualizing the results, and a function for performing uncertainty analysis. We present applications of FLUX‐BOT to synthetic and to real temperature data to demonstrate its performance.     

Heat transport in the Red Lake Bog,Glacial Lake Agassiz Peatlands

We report the results of an investigation on the processes controlling heat transport in peat under a large bog in the Glacial Lake Agassiz Peatlands. For 2 years, starting in July 1998, we recorded temperature at 12 depth intervals from 0 to 400 cm within a vertical peat profile at the crest of the bog at sub‐daily intervals. We also recorded air temperature 1 m above the peat surface. We calculate a peat thermal conductivity of 0·5 W m^?1 °C^?1 and model vertical heat transport through the peat using the SUTRA model. The model was calibrated to the first year of data, and then evaluated against the second year of collected heat data. The model results suggest that advective pore‐water flow is not necessary to transport heat within the peat profile and most of the heat is transferred by thermal conduction alone in these waterlogged soils. In the spring season, a zero‐curtain effect controls the transport of heat through shallow depths of the peat. Changes in local climate and the resulting changes in thermal transport still may cause non‐linear feedbacks in methane emissions related to the generation of methane deeper within the peat profile as regional temperatures increase. Copyright © 2006 John Wiley & Sons, Ltd.     

Groundwater temperature evolution in the subsurface urban heat island of Cologne,Germany

Long‐term heating of shallow urban aquifers is observed worldwide. Our measurements in the city of Cologne, Germany revealed that the groundwater temperatures found in the city centre are more than 5 K higher than the undisturbed background. To explore the role of groundwater flow for the development of subsurface urban heat islands, a numerical flow and heat transport model is set up, which describes the hydraulic conditions of Cologne and simulates the transient evolution of thermal anomalies in the urban ground. A main focus is on the influence of horizontal groundwater flow, groundwater recharge and trends in local ground warming. To examine heat transport in groundwater, a scenario consisting of a local hot spot with a length of 1 km of long‐term ground heating was set up in the centre of the city. Groundwater temperature‐depth profiles at upstream, central and downstream locations of this hot spot are inspected. The simulation results indicate that the main thermal transport mechanisms are long‐term vertical conductive heat input, horizontal advection and transverse dispersion. Groundwater recharge rates in the city are low (<100 mm a^?1) and thus do not significantly contribute to heat transport into the urban aquifer. With groundwater flow, local vertical temperature profiles become very complex and are hard to interpret, if local flow conditions and heat sources are not thoroughly known. Copyright © 2014 John Wiley & Sons, Ltd.     

SEAWAT‐Based Simulation of Axisymmetric Heat Transport

Simulation of heat transport has its applications in geothermal exploitation of aquifers and the analysis of temperature dependent chemical reactions. Under homogeneous conditions and in the absence of a regional hydraulic gradient, groundwater flow and heat transport from or to a well exhibit radial symmetry, and governing equations are reduced by one dimension (1D) which increases computational efficiency importantly. Solute transport codes can simulate heat transport and input parameters may be modified such that the Cartesian geometry can handle radial flow. In this article, SEAWAT is evaluated as simulator for heat transport under radial flow conditions. The 1971, 1D analytical solution of Gelhar and Collins is used to compare axisymmetric transport with retardation (i.e., as a result of thermal equilibrium between fluid and solid) and a large diffusion (conduction). It is shown that an axisymmetric simulation compares well with a fully three dimensional (3D) simulation of an aquifer thermal energy storage systems. The influence of grid discretization, solver parameters, and advection solution is illustrated. Because of the high diffusion to simulate conduction, convergence criterion for heat transport must be set much smaller (10^?10) than for solute transport (10^?6). Grid discretization should be considered carefully, in particular the subdivision of the screen interval. On the other hand, different methods to calculate the pumping or injection rate distribution over different nodes of a multilayer well lead to small differences only.     

Effects of rate-limited mass transfer on water sampling with partially penetrating wells

Nonequilibrium concentration type curves are numerically developed and sensitivity analyses are performed to examine the relationships between effluent concentrations in partially penetrating monitoring/extraction wells, the vertical plume shape, and the mass transfer characteristics of the aquifer. The governing two-dimensional, axisymmetric nonequilibrium solute transport equation is solved in three stages using an operator-splitting approach. In the first two stages, the advection and dispersion terms are solved with the Eulerian-Lagrangian method, based on the backward method of characteristics for advection and the standard implicit Galerkin finite element method for dispersion. In the third step, the first-order, immobile-mobile domain mass transfer term is computed analytically for both two-site and lognormally distributed, multirate models. Effluent concentration variations with time and contour plots of the pore water concentration distribution in the aquifer are compared for a wide range of field- and laboratory-measured mass transfer rates, various plume shapes, and relevant physical/chemical parameter values, including pumping rate, vertical anisotropy ratio, retardation factor, and porosity. The simulation results show that rate-limited mass transfer can have a significant impact on sample and aquifer pore water concentrations during three-dimensional transport to a partially penetrating well. An alternative dimensionless form of the nonequilibrium solute transport equation is derived to illustrate the key parameter groupings that quantify rate-limited sorption effects and show the relative importance of individual parameters. A hypothetical field application example demonstrates the fitting of dimensional type curves to discrete-interval sampling data in order to evaluate the mass transfer characteristics of an aquifer and shows how type curve superposition can be used to model complex plume shapes.     

Combined Effect of Climatic Variations and Groundwater Movement on Observed Heat Flow

In most practical situations, the upper part of a geological section consists of loose sediments, in which heat transfer cannot be described as a purely conductive process. To investigate such situations a one-dimensional numerical model of terrestrial temperature field formation under the combined influence of vertical groundwater filtration and ground surface temperature changes has been developed. The model allows one to consider the perturbation of heat flow interval values resulting from short- and long-period temperature waves propagating into permeable rocks under conditions of advective heat transfer, caused by vertical groundwater filtration. The results show that temperature profiles and interval heat flow values are sensitive to both the paleoclimatic history and the rate of groundwater filtration. The latter plays the prevailing role in the variations of geothermal field parameters, especially within the uppermost part of the loose sediments in unconfined aquifers. The problem was solved for a permeable layer, underlaid by an impermeable layer. This schematisation of water exchange is the typically accepted for hydrogeological analysis. Even at very low rates of filtration the intensity of this effect is enhanced substantially for long-period variations. In the extreme case (for periods of temperature variations of the order of 100,000 years) at typical rates of filtration within the permeable layer, an almost gradient-free zone can be formed down to depths of a few hundred metres. For the case of upward filtration, on the contrary, the influence of climatic variations on the terrestrial temperature field becomes substantially attenuated.     

The effects of floods on the temperature of riparian groundwater

The transition area between rivers and their adjacent riparian aquifers, which may comprise the hyporheic zone, hosts important biochemical reactions, which control water quality. The rates of these reactions and metabolic processes are temperature dependent. Yet the thermal dynamics of riparian aquifers, especially during flooding and dynamic groundwater flow conditions, has seldom been studied. Thus, we investigated heat transport in riparian aquifers during 3 flood events of different magnitudes at 2 sites along the same river. River and riparian aquifer temperature and water‐level data along the Lower Colorado River in Central Texas, USA, were monitored across 2‐dimensional vertical sections perpendicular to the bank. At the downstream site, preflood temperature penetration distance into the bank suggested that advective heat transport from lateral hyporheic exchange of river water into the riparian aquifer was occurring during relatively steady low‐flow river conditions. Although a small (20‐cm stage increase) dam‐controlled flood pulse had no observable influence on groundwater temperature, larger floods (40‐cm and >3‐m stage increases) caused lateral movement of distinct heat plumes away from the river during flood stage, which then retreated back towards the river after flood recession. These plumes result from advective heat transport caused by flood waters being forced into the riparian aquifer. These flood‐induced temperature responses were controlled by the size of the flood, river water temperature during the flood, and local factors at the study sites, such as topography and local ambient water table configuration. For the intermediate and large floods, the thermal disturbance in the riparian aquifer lasted days after flood waters receded. Large floods therefore have impacts on the temperature regime of riparian aquifers lasting long beyond the flood's timescale. These persistent thermal disturbances may have a significant impact on biochemical reaction rates, nutrient cycling, and ecological niches in the river corridor.     

Heat Tracing in a Fractured Aquifer with Injection of Hot and Cold Water

Heat as a tracer in fractured porous aquifers is more sensitive to fracture-matrix processes than a solute tracer. Temperature evolution as a function of time can be used to differentiate fracture and matrix characteristics. Experimental hot (50 °C) and cold (10 °C) water injections were performed in a weathered and fractured granite aquifer where the natural background temperature is 30 °C. The tailing of the hot and cold breakthrough curves, observed under different hydraulic conditions, was characterized in a log–log plot of time vs. normalized temperature difference, also converted to a residence time distribution (normalized). Dimensionless tail slopes close to 1.5 were observed for hot and cold breakthrough curves, compared to solute tracer tests showing slopes between 2 and 3. This stronger thermal diffusive behavior is explained by heat conduction. Using a process-based numerical model, the impact of heat conduction toward and from the porous rock matrix on groundwater heat transport was explored. Fracture aperture was adjusted depending on the actual hydraulic conditions. Water density and viscosity were considered temperature dependent. The model simulated the increase or reduction of the energy level in the fracture-matrix system and satisfactorily reproduced breakthrough curves tail slopes. This study shows the feasibility and utility of cold water tracer tests in hot fractured aquifers to boost and characterize the thermal matrix diffusion from the matrix toward the flowing groundwater in the fractures. This can be used as complementary information to solute tracer tests that are largely influenced by strong advection in the fractures.     

热带对流热量与水汽收支的数值模拟研究

应用二维云分辨模式,数值研究了热带地区的对流活动,并诊断了热量和水汽的收支,发现在垂直温度平流和凝结潜热释放之间、垂直水汽平流和降水之间都维持着大体平衡,推断出质量加权平均温度及可降水分的局地变化分别由热量及水汽方程中的剩余项决定.机制研究表明,深对流与浅对流在热量及水汽循环中存在较大差异,深对流中水汽的凝结及潜热释放起着主导作用,而大尺度垂直平流的加湿和冷却在浅对流中发挥主导作用.最后讨论了对流触发后热量及水汽循环的调整机制.     

生产油井井下温度场数值模拟分析

An improved numerical simulation method is presented to calculate the downhole temperature distribution for multiple pay zones in producing oil wells. Based on hydrodynamics and heat transfer theory, a 2-D temperature field model in cylindrical coordinates is developed. In the model, we considered general heat conduction as well as the heat convection due to fluid flow from porous formation to the borehole. We also take into account the fluid velocity variation in the wellbore due to multiple pay zones. We present coupled boundary conditions at the interfaces between the wellbore and adjacent formation, the wellbore and pay zone, and the pay zone and adjacent formation. Finally, an alternating direction implicit difference method （ADI） is used to solve the temperature model for the downhole temperature distribution. The comparison of modeled temperature curve with actual temperature log indicates that simulation result is in general quite similar to the actual temperature log. We found that the total production rate, production time, porosity, thickness of pay zones, and geothermal gradient, all have effects on the downhole temperature distribution.     

Evaluation of approximations in modelling the cooling of magmatic bodies

The cooling of a magmatic intrusion is simulated by a simple model of a non-homogeneous earth, with thermal properties depending on temperature, in which heat transfer is assumed to take place by conduction only. The mathematical problem consists in solving a non-linear partial differential equation with continuity conditions on temperature and heat flux imposed at the contacts between different rocks. This has been done numerically by a finite difference method. The model is then adopted as “reality” against which a number of commonly used approximations are tested. It is found that the effect of latent heat liberation can be reasonably taken into account by attributing an effective initial temperature to the magma (errors within 20°C for t > 10⁵ years, when the temperature of the magma is still as high as 600°C); the effective specific heat approximation does not work as well. The dependence of thermal conductivity and specific heat on temperature may be eliminated by maintaining the errors within 30°C for t < 5 × 10⁵ years. The assumption that magma and country rocks have the same thermal properties allows an estimate of the temperature field in the host rocks with errors of 50°C at most. The assumption that all rocks have the same constant conductivity yields results that are far from “reality” (errors of 100–200°C even at shallow depth).     

Near‐surface temperatures and heat balance of bare outcrops exposed to solar radiation

Subsurface temperatures in rocks naturally fluctuate under the influence of local meteorological conditions. These fluctuations play a role in mechanical weathering, thus creating the environmental conditions conducive to natural hazards such as rockfalls and providing important sediment source terms for landscape evolution. However, the physics that control heat penetration into rocks are not fully understood, which makes the underground thermal state difficult to interpret when temperature measurements are available and even more difficult to estimate for unmonitored sites. This is an important lacuna given possible impacts of future climate change on mechanical weathering processes. The natural daily variations of subsurface temperatures were investigated on a bare gneiss outcrop exposed to solar radiation, where temperatures at various depths (up to 50 cm), as well as the solar radiation reaching a pyranometer, were monitored hourly for several months. This detailed times series of thermal data was used to gain insight into the heat balance at the inclined free surface of the rock mass. Attention was focused on two major contributors to the heat balance; the heat flux entering the rock mass through conduction and the incoming shortwave (solar) radiation. A Fourier decomposition of the temperature measurements provided an estimate of the in situ thermal conductivity of the rock and was used to calculate the conductive term. The shortwave radiation term was determined on the basis of the pyranometer measurements adjusted to account for the angle of incidence of the sun. It is shown that, throughout clear‐sky periods, heat exchanges at the surface are mainly controlled by direct solar radiation during the day, and by a roughly constant outgoing heat flux during the night. Subsurface temperatures can be reliably estimated with a semi‐infinite medium model whose boundary condition is derived from an analytical insolation model that takes atmospheric attenuation into account. Copyright © 2011 John Wiley & Sons, Ltd.     

Vectorized simulation of groundwater flow and contaminant transport using analytic element method and random walk particle tracking

Groundwater contaminant transport processes are usually simulated by the finite difference (FDM) or finite element methods (FEM). However, they are susceptible to numerical dispersion for advection‐dominated transport. In this study, a numerical dispersion‐free coupled flow and transport model is developed by combining the analytic element method (AEM) with random walk particle tracking (RWPT). As AEM produces continuous velocity distribution over the entire aquifer domain, it is more suitable for RWPT than FDM/finite element methods. Using the AEM solutions, RWPT tracks all the particles in a vectorized manner, thereby improving the computational efficiency. The present model performs a convolution integral of the response of an impulse contaminant injection to generate concentration distributions due to a permanent contaminant source. The RWPT model is validated with an available analytical solution and compared to an FDM solution, the RWPT model more accurately replicates the analytical solution. Further, the coupled AEM‐RWPT model has been applied to simulate the flow and transport in hypothetical and field aquifer problems. The results are compared with the FDM solutions and found to be satisfactory. The results demonstrate the efficacy of the proposed method.     

Application of subsurface temperature measurements in geothermal prospecting in Iceland

In geothermal areas in Iceland aquifers are in most cases found to occur in highly permeable near-vertical fractures in the low permeability basaltic crust. Therefore heat transfer in the rocks surrounding the aquifers is mainly conductive.Temperature profiles in shallow non-flowing boreholes are used to construct a two dimensional model of the temperature distribution in the vicinity of near vertical aquifers. This is done by finite element solution of the equation of heat transfer which requires knowledge of the regional temperature gradient outside the area of geothermal activity and some constraints on the temperature within the aquifers. The model is helpful in estimating dip and location of near-vertical water bearing fractures and thus in siting production wells.An example of successful use to the method and of soil temperature measurements from a geothermal field in North-Iceland is demonstrated.     

Heat as a groundwater tracer in shallow and deep heterogeneous media: Analytical solution,spreadsheet tool,and field applications

Groundwater flow advects heat, and thus, the deviation of subsurface temperatures from an expected conduction‐dominated regime can be analysed to estimate vertical water fluxes. A number of analytical approaches have been proposed for using heat as a groundwater tracer, and these have typically assumed a homogeneous medium. However, heterogeneous thermal properties are ubiquitous in subsurface environments, both at the scale of geologic strata and at finer scales in streambeds. Herein, we apply the analytical solution of Shan and Bodvarsson ( 2004 ), developed for estimating vertical water fluxes in layered systems, in 2 new environments distinct from previous vadose zone applications. The utility of the solution for studying groundwater‐surface water exchange is demonstrated using temperature data collected from an upwelling streambed with sediment layers, and a simple sensitivity analysis using these data indicates the solution is relatively robust. Also, a deeper temperature profile recorded in a borehole in South Australia is analysed to estimate deeper water fluxes. The analytical solution is able to match observed thermal gradients, including the change in slope at sediment interfaces. Results indicate that not accounting for layering can yield errors in the magnitude and even direction of the inferred Darcy fluxes. A simple automated spreadsheet tool (Flux‐LM) is presented to allow users to input temperature and layer data and solve the inverse problem to estimate groundwater flux rates from shallow (e.g., <1 m) or deep (e.g., up to 100 m) profiles. The solution is not transient, and thus, it should be cautiously applied where diel signals propagate or in deeper zones where multi‐decadal surface signals have disturbed subsurface thermal regimes.     

Flow in an aquifer charged with hot water from a fault zone

Many geothermal anomalies are intersected by vertical fault zones (narrow zones of fractured material with large effective permeability). These conduits are probably responsible for much of the upwelling of hot water from depth. This paper considers a shallow aquifer intersected by a vertical fault. The fluid flow in the aquifer is numerically modeled as a two-dimensional problem. It is observed that the temperature distribution in the aquifer is governed primarily by lateral flow of hot water supplied from the intersecting vertical fault and only secondarily by conduction. The numerical results also provide a possible explanation for the local temperature maxima and inversions occasionally observed in borehole measurements. The present model is an alternative to that based on mushroom-shaped isotherm distributions found in high Rayleigh number large-scale circulation cell calculations.