The Interface Between Fresh and Salt Groundwater in Horizontal Aquifers : The Dupuit–Forchheimer Approximation Revisited

We analyze the motion of a sharp interface between fresh and salt groundwater in horizontal, confined aquifers of infinite extend. The analysis is based on earlier results of De Josselin de Jong (Proc Euromech 143:75–82, 1981). Parameterizing the height of the interface along the horizontal base of the aquifer and assuming the validity of the Dupuit–Forchheimer approximation in both the fresh and saltwater, he derived an approximate interface motion equation. This equation is a nonlinear doubly degenerate diffusion equation in terms of the height of the interface. In that paper, he also developed a stream function-based formulation for the dynamics of a two-fluid interface. By replacing the two fluids by one hypothetical fluid, with a distribution of vortices along the interface, the exact discharge field throughout the flow domain can be determined. Starting point for our analysis is the stream function formulation. We derive an exact integro-differential equation for the movement of the interface. We show that the pointwise differential terms are identical to the approximate Dupuit–Forchheimer interface motion equation as derived by De Josselin de Jong. We analyze (mathematical) properties of the additional integral term in the exact interface motion formulation to validate the approximate Dupuit–Forchheimer interface motion equation. We also consider the case of flat interfaces, and we study the behavior of the toe of the interface. In particular, we give a criterion for finite or infinite speed of propagation

Using multiple partially-penetrating wells (MPPWs) to improve the performance of high-temperature ATES systems: Well operation, storage conditions and aquifer heterogeneity

The occurrence of free thermal convection negatively affects thermal recovery efficiencies of High-Temperature Aquifer Thermal Energy Storage (HT-ATES) systems. In this study the potential of applying a Multiple Partially Penetrating Well (MPPW) configuration to counteract the impact for seasonal HT-ATES is tested through numerical modeling with SEAWATv4. For scenarios where the thermal front is close to the HT-ATES well-screen and free thermal convection has considerable effect on the thermal recovery efficiency, the use of a MPPW configuration has great potential. Storage at a moderate temperature contrast (ΔT = 40 °C) between the hot injection volume and cold ambient groundwater in a high-permeability aquifer resulted in significant improvement of the thermal recovery efficiency with a MPPW configuration targeting injection in lower parts of the aquifer and recovery in the upper parts. For conventional, fully screened HT-ATES a thermal recovery efficiency of 0.43 is obtained while this is 0.59 with the MPPW scheme in the first recovery cycle. This recovery efficiency of 0.59 is only 0.11 less than a theoretical case with no buoyancy effects. For seasonal HT-ATES cases that face severe free thermal convection, rapid accumulation of heat in the upper part of the aquifer is observed and the MPPW configuration is less effective due to the long period between injection and recovery. Especially for HT-ATES cases that require a cut-off temperature, thermal recovery can be significantly improved and prolonged. For storage temperatures of 60 and 80 °C in a high-permeability aquifer, approximately 4 times more abstracted usable heat is obtained with the MPPW setup while considering a cut-off temperature of 40 °C. Moreover, the present study shows that the use of MPPW configurations in heterogeneous aquifers should be carefully planned. Improper application of MPPW is particularly vulnerable for simplification of the aquifer characteristics, and therefore proper site heterogeneity investigation and operational monitoring are required to benefit from optimal MPPW operation during HT-ATES

Nonlinear Flow Behavior in Packed Beds of Natural and Variably Graded Granular Materials

Under certain flow conditions, fluid flow through porous media starts to deviate from the linear relationship between flow rate and hydraulic gradient. At such flow conditions, Darcy’s law for laminar flow can no longer be assumed and nonlinear relationships are required to predict flow in the Forchheimer regime. To date, most of the nonlinear flow behavior data is obtained from flow experiments on packed beds of uniformly graded granular materials (Cu = d60/d10 2), the d10 instead of the average grain size (d50) as characteristic pore length should be used. Ergun constants A and B with values of 63.1 and 1.72, respectively, resulted in a reasonable prediction of the Forchheimer coefficients for the investigated granular materials

Contribution to head loss by partial penetration and well completion: implications for dewatering and artificial recharge wells

A wide variety of well drilling techniques and well completion methods is used in the installation of dewatering and artificial recharge wells for the purpose of construction dewatering. The selection of the optimal well type is always a trade-off between the overall costs of well completion and development, the optimal well hydraulics of the well itself, the hydraulic impact of the well on its surroundings, and the required operational life span of the well. The present study provides an analytical framework that can be used by dewatering and drilling companies to quantify the contribution to head loss of typical dewatering and artificial-recharge well configurations. The analysis shows that the placement of partially penetrating wells in high-permeability layers could promote the use of quick and cheap installation of naturally developed wells using jetting or straight-flush rotary drilling. In high-permeability layers, such wells can be favorable over wells completed with filter pack, which require extensive well development to remove the fines from the filter cake layer. The amount of total head loss during discharge/recharge at a volumetric rate of 20 m3/h per meter of filter length, into or from a gravely aquifer layer, is reduced by factors of 3–4 while using naturally developed well types instead of well types completed with a filter pack that contains a filter cake layer due to borehole smearing

On the validity of Darcy’s law for stable high- concentration displacements in granular porous media

Recently, it has been suggested that Darcy's Law might not be applicable for modelling miscible, density-dependent flow in porous media. To investigate this, three sets of careful laboratory column experiments were performed on coarse and medium sands, consisting of upward displacement of water by sodium chloride solutions with concentrations ranging from 5 to 200 g/l. Data on salt concentrations and water pressures were collected in horizontal transects along the flow direction. Salt concentration data were also collected in the influent and exit lines. The experimental data were analysed using a simplified approach based on Darcy's Law alone, applied with the assumption of a sharp interface. Darcy's Law was used to estimate porous medium permeability by fitting predictions to experimental data. Consistent estimates of permeability were obtained for each set of experiments. The results indicate that Darcy's Law adequately describes high concentration displacements through saturated coarse- and medium-grained porous media

Validation of classical density-dependent solute transport theory for stable, high-concentration brine displacements in coarse and medium sands

A series of careful laboratory soil column experiments was carried out for the purpose of providing data for testing recently presented theories of miscible density-dependent flow and transport. In particular, modifications to the standard theory involve extensions to both Darcy's (for flow) and Fick's laws (for diffusive/dispersive solute flux). Both coarse- and medium-grained sands were used in the experiments. All experiments concerned upward (i.e., stable) displacement of fresh water within the soil by a brine solution, under either constant head or constant volume flux conditions. The experimental data were analysed using accurate numerical solutions of the standard governing flow and transport model, as well as models with modified Darcy's and Fick's laws. Model parameters were determined by a step-wise fitting procedure based on the least-squares criterion. The results show clearly that, for large density contrasts, an extended Darcy's law was not necessary. On the other hand, an extension to Fick's Law was needed to model the experimental data accurately

Using multiple partially-penetrating wells (MPPWs) to improve the performance of high-temperature ATES systems: Well operation, storage conditions and aquifer heterogeneity

The occurrence of free thermal convection negatively affects thermal recovery efficiencies of High-Temperature Aquifer Thermal Energy Storage (HT-ATES) systems. In this study the potential of applying a Multiple Partially Penetrating Well (MPPW) configuration to counteract the impact for seasonal HT-ATES is tested through numerical modeling with SEAWATv4. For scenarios where the thermal front is close to the HT-ATES well-screen and free thermal convection has considerable effect on the thermal recovery efficiency, the use of a MPPW configuration has great potential. Storage at a moderate temperature contrast (ΔT = 40 °C) between the hot injection volume and cold ambient groundwater in a high-permeability aquifer resulted in significant improvement of the thermal recovery efficiency with a MPPW configuration targeting injection in lower parts of the aquifer and recovery in the upper parts. For conventional, fully screened HT-ATES a thermal recovery efficiency of 0.43 is obtained while this is 0.59 with the MPPW scheme in the first recovery cycle. This recovery efficiency of 0.59 is only 0.11 less than a theoretical case with no buoyancy effects. For seasonal HT-ATES cases that face severe free thermal convection, rapid accumulation of heat in the upper part of the aquifer is observed and the MPPW configuration is less effective due to the long period between injection and recovery. Especially for HT-ATES cases that require a cut-off temperature, thermal recovery can be significantly improved and prolonged. For storage temperatures of 60 and 80 °C in a high-permeability aquifer, approximately 4 times more abstracted usable heat is obtained with the MPPW setup while considering a cut-off temperature of 40 °C. Moreover, the present study shows that the use of MPPW configurations in heterogeneous aquifers should be carefully planned. Improper application of MPPW is particularly vulnerable for simplification of the aquifer characteristics, and therefore proper site heterogeneity investigation and operational monitoring are required to benefit from optimal MPPW operation during HT-ATES

Nonlinear Flow Behavior in Packed Beds of Natural and Variably Graded Granular Materials

Under certain flow conditions, fluid flow through porous media starts to deviate from the linear relationship between flow rate and hydraulic gradient. At such flow conditions, Darcy’s law for laminar flow can no longer be assumed and nonlinear relationships are required to predict flow in the Forchheimer regime. To date, most of the nonlinear flow behavior data is obtained from flow experiments on packed beds of uniformly graded granular materials (Cu = d60/d10 2), the d10 instead of the average grain size (d50) as characteristic pore length should be used. Ergun constants A and B with values of 63.1 and 1.72, respectively, resulted in a reasonable prediction of the Forchheimer coefficients for the investigated granular materials