Sloping Aquifer Research Articles

Analysis of bi-level drainage problem with sloping aquifer

Analysis of bi-level drainage problem with sloping aquifer

Estimating the Maximum Safe Pumping Rate in Sloping Unconfined Coastal Aquifers

AbstractUnconfined coastal aquifers with a sloping aquifer bed are ubiquitous. However, most analytical solutions previously developed to estimate pumping‐induced seawater intrusion considered a horizontal aquifer bed. In this study, we first developed a steady‐state analytical solution to quantify the maximum safe pumping rate in sloping unconfined coastal aquifers with a fixed‐flux inland boundary condition, using the single potential approach. The analytical solution corrected by an empirical factor is validated against the numerical simulation, which reproduces the corresponding numerical results well. It is found that coastal aquifers with a higher aquifer bed toward inland (i.e., a positive sloping angle) yield a higher maximum safe pumping rate than that of coastal aquifers with a horizontal aquifer base, since the elevated freshwater head prevents seawater intrusion and enhances groundwater pumping. Specifically, for the aquifer bases with the sloping angle of 0.01 and −0.01, the maximum safe pumping rate is increased by 42.6% and decreased by 48.4%, respectively, in comparison to the case of a horizontal aquifer base, suggesting that neglecting the aquifer base slop can result in a significant error in estimating the maximum safe pumping rate. Moreover, the sensitivity analysis reveals that the maximum safe pumping rate increases with a lower hydraulic conductivity and a larger dispersivity. Our results provide valuable insights into the effect of the aquifer base slope on the maximum safe pumping in coastal aquifers, and analytical solutions developed can serve as a powerful tool for quick assessment of pumping‐induced seawater intrusion in sloping unconfined coastal aquifers.

Monte Carlo simulation of the maximum migration distance of CO[formula omitted] in a sloping aquifer

Carbon capture and storage in saline aquifers is broadly considered a viable technology for reducing anthropogenic impact on the environment. However, a secure CO2 storage can be compromised by the depositional environments of target reservoirs, which can influence the CO2 migration in subsurface. The disposal of CO2 in a sloping aquifer can result in a substantial gas migration in the updip direction from the injection well until all gas becomes trapped. It thus can reach far more than desired regions from the well where the potential leakage paths to the surface can exist. This study aims at understanding the principal parameters that the maximum migration distance in the updip direction depends on, which can be important for estimating the risks of CO2 leakage through old abandoned wells in the regions of intensive subsurface exploration. Using the Monte Carlo method, an extended parametric study is performed by running 3-D reservoir simulations of CO2 storage in random aquifers characterized by various petrophysical and thermobaric parameters, saturation functions and brine salinity, and for the wells operated under different target rates. Herewith, the modeling accounts for such relevant physical phenomena as the phase transitions, the gravity and capillary forces, the hysteresis behavior of the relative permeability, etc. It is shown that the maximum migration distance at the post-injection stage is characterized by just two similarity criteria and the critical gas saturation for the drainage and imbibition processes. It is found that the CO2 plume shape at the moment of the well shut-in influences the subsequent gas transport. A new simple relation parameterizing the revealed dependence is proposed and validated against the sampled maximum migration distances. The relation is useful for an instant estimating the size of the contaminated zone around a projected CO2 well and for ranking the potential storage sites.

Modifying the water table fluctuation method for calculating recharge in sloping aquifers

Study regionRobit Bata and Dengeshita watersheds, Upper Blue Nile basin, Ethiopia Study focusSustainable development of groundwater in the Ethiopian Highlands requires recharge measurements. The Water Table Fluctuation (WTF) method has been used to measure recharge. Lateral flow in sloping hillside aquifers violates the assumptions on which the original WTF method is based. We modified the original WTF method to include lateral flow controlled by gravity. New hydrological insightsPreviously it was shown that the sum of recharge over the travel time in a sloping aquifer is equal to the base flow. Since recharge cannot be measured directly, the recharge calculated with the modified WTF method was tested using baseflow measurement in two contrasting highland watersheds, Robit Bata and Dengeshita, where groundwater depth and streamflow data were monitored from 2015 to 2018. Baseflow was determined with the one-parameter digital filter technique. Predicted and observed monthly baseflow agreed well with R2 > 0.9 and RMSE < 20 mm during calibration and validation. Recharge in Robit Bata, in which the aquifer underlays 55% of the watershed, was 293 mm a−1 of 1378 mm a−1 precipitation. In Dengeshita, where the entire watershed has an aquifer, the average annual recharge was 525 mm a−1 of 1550 mm a−1. Our findings indicate that the modified WTF method is simple and practical for determining aquifer recharge for highlands and other sloping aquifers.

Influence of nonuniform recharge on groundwater flow in heterogeneous aquifers

&lt;abstract&gt;&lt;p&gt;The composition of soils in aquifers is typically not homogeneous, and soil layers may be cracked or displaced due to geological activities. This heterogeneity in soil distribution within aquifers affects groundwater flow and water level variations. In the present study, we established a two-dimensional (2D) mathematical model that considers the influence of surface recharge on groundwater flow in heterogeneous sloping aquifers. By considering temporal variations in surface recharge, slope angle and aquifer heterogeneity, the simulated results are expected to better reflect real conditions in natural aquifers. The effects of aquifer heterogeneity on groundwater flow and water levels are particularly significant in sloping aquifers. The study's findings indicate that even when the soil composition remains constant, variations in groundwater level and flow may be considerable, depending on factors such as soil alignment, slope angle of the aquifer's base layer and the direction of water flow.&lt;/p&gt;&lt;/abstract&gt;

Modelling of hillslope storage under temporally varied rainfall recharge

Water storage inside hillslopes is a crucial issue of environment and water resources. This study separately built a numerical model and an analytical model employing a hillslope-storage equation to simulate the water storage in a sloping aquifer response to recharge. The variable width of hillslope was hypothetically represented by an exponential function to categorize the hillslope into three types: uniform, convergent, and divergent. An integral transform technique was introduced to derive the analytical solution whereas a finite difference method was employed for the numerical modelling. As a result, under the same scenario a gap existed between the two solutions to distinct forms of the water storage equation, and the gap decreases with a falling recharge rate for convergent hillslopes. Moreover, all outflows gradually approached one value based on different hillslopes under the same accumulative recharge amount for six typical rainfall recharge patterns. Particularly, while the recharge stops, the outflow decreases and then mildly rises for a long time for convergent hillslope because of the slow water release near the upstream boundary where the storage water is relatively abundant due to the widest width.

Delineation of the aquifer structure and estimation of hydraulic properties on the flanks of Mount Meru, Northern Tanzania

Understanding of the aquifer structure and its hydraulic properties provides comprehensive knowledge for proper groundwater utilisation and management. This study delineated the aquifer structure using litho-hydrostratigraphical cross-sections, and estimated the hydraulic parameters using single well pumping tests for various locations on and around Mount Meru. Results show that, the aquifer system on the flanks of Mount Meru is a sloping aquifer with sloping beds. On the far east of the eastern flank, the aquifer is composed of debris avalanche deposits, while on the north-eastern and west flanks the aquifer is composed of weathered fractured lava, whereas on the south-western flank, the aquifer is composed of different layers: pyroclastics on the top, weathered fractured lava, weathered pyroclastics, and weathered fractured lava at the bottom. The aquifer is semi-confined on the north-eastern and western flanks; on the north-eastern flank, the overlying debris avalanche deposits acting as an aquitard, while on the western flank, the overlying layers: pyroclastics and unweathered lava acting as an aquitard and aquiclude, respectively. The aquifer is unconfined on the far east of the eastern flank and south-western flank. The transmissivity of the aquifer on the north-eastern flank is substantially increasing with increasing depth, while variable, both at the shallow depth of hand-dug wells and the larger depth of boreholes, on the south-western flank; indicating aquifer heterogeneity. On the north-eastern flank, the topmost part of the aquifer, exploited by hand-dug wells, has a low transmissivity (T = 1.3 m2/d) and potential for smaller withdrawals for local water supply with limited consumption, while the upper part of the aquifer, captured by boreholes, has an intermediate transmissivity (T = 35 m2/d) and potential for local water supply, whereas the deeper part of the aquifer has a high transmissivity (T = 788 m2/d) with potential of somewhat regional importance. On the western flank, the aquifer has a very low transmissivity (T = 0.4 m2/d) and potential for local water supply with limited consumption. On the south-western flank, on average, the topmost part of the aquifer, exploited by hand-dug wells, has very low to intermediate transmissivity (range of T: 0.3–21 m2/d), leading to variable potential for smaller withdrawals for local water supply (private consumption), whereas the deeper part of the aquifer, captured by boreholes, has low to intermediate transmissivity (range of T: 9–43 m2/d) and potential for local water supply.

Scaling analysis for a 3-D CO[formula omitted] plume in a sloping aquifer at a late stage of injection

We investigate supercritical CO2 injection into a sloping saline aquifer and propose a simple relationship to estimate the maximum gas migration distance in the updip direction. The estimate is derived from the system of governing equations for immiscible flow of gas and formation brine. By writing the equations in non-dimensional form, we guess the scaling law for the migration distance at a late stage of CO2 injection. Then, we verify the scaling law by means of 3-D reservoir simulations of miscible CO2 injection with account for the residual and solubility trapping. We derive an estimate that relates the maximum migration distance with the dip angle, the porosity, the anisotropic permeability, and the end-points of saturation functions. We show that the estimate is rather accurate for different reservoir temperatures and brine salinity and in the case of a flue gas injection. The proposed scaling is useful for a quick assessment of the risk of CO2 reaching a potential leakage site in a large regional aquifer. It can also be applied to estimate the propagation of the uncertainties of reservoir parameters to the uncertainty of the migration distance.

Variable storage behavior controlled by rainfall intensity and profile structure upon saturation excess overland flow generation

The effects of rainfall intensity and terrain structure on hillslope storage behavior upon saturation excess overland flow (SOF) generation are not yet fully understood. Analytical solution techniques that provide direct insights into the hillslope storage behavior were adopted in this study. The Threshold of StOrage (TSO) at critical rainfall intensity N0 (the minimum rainfall intensity to generate SOF) and the storage upon SOF generation (SO) at rainfall intensity N (>N0) were derived using analytical solutions of the kinematic wave equation over unit-width shallow sloping aquifers. The derived analytical solutions match the results of the numerical models of the Boussinesq equation for 25 idealized hillslopes under various rainfall intensities. It was found that as N = N0, TSO is determined by hillslope structures, i.e., TSO on the convex hillslopes is always greater than that on concave hillslopes with the same gradient, and TSO on convex and concave hillslopes gradually approaches as the gradient increases. As N > N0, hillslope storage dynamics is characterised by variable storage behavior as rainfall intensity increasing, i.e., SO increases with N. An inflection point of rainfall intensity N1, below which the curvature of the bedrock profile has a limited effect on SO, was found. Although N1 was greater on steeper hillslope, the corresponding values of SO1 on hillslopes under different gradients are close, which means that the effects of rainfall intensity and profile structure on SO is balanced at N = N1. This study helps to deepen our understanding of the quantitative role of rainfall intensity and profile structure in the process of runoff generation, and has the potential to improve the free storage capacity parameter in conceptual models.

Mathematical Modeling of Transient Water Interactions Between a Sloping Aquifer and an Adjusting Stream

Due to the constantly changing hydrological conditions of the surrounding water reservoirs, estimating water table changes in response to stream-stage variations and downward recharge is an emerging area in hydrology. Mathematical modeling is the emerging tool for predicting water table behavior in many complex geological situations. In this paper, a stream-aquifer model is considered and variations in the water table height have been calculated. At one end, the aquifer is in contact with a constant water level, and at the other end, the water level is rising exponentially from an adjoining stream. An analytical equation is solved by the Laplace Transform method for estimation of water table fluctuations in response to combined effects of bed slope and non-uniform recharge and seepage.

Solutions for Groundwater Flow to a Pumping Well with an Exponentially Decreasing Variable-Rate in a Sloping Aquifer.

During aquifer pumping tests in the field, the attenuation process of the pumping rate is generally monitored, and the aquifer may be slanted, especially in riverbank terraces, piedmont plain and other similar terrains. The combination of these two factors (attenuation process and aquifer slope) has not received enough academic attention, therefore, a two-dimensional groundwater flow model is developed for an exponentially decreasing variable rate pumping well in a sloping aquifer in this study. The new semi-analytical solution (based on a linearized free-surface boundary) is obtained using the Laplace transform and finite Fourier cosine transform. Meanwhile, to depict the linearized boundary precisely with the first-order free surface equation, a numerical model that considers the decline of the water table is also developed. Results show that under the effect of the variable rate, the time-drawdown curve presents a downward trend at intermediate times. Additionally, the error caused by the linearization of the free-surface equation on the analytical model is found to be acceptable except when the sloping angle is larger than π/6. Furthermore, since this study extends the work of Huang et al. (2014), who considered a constant pumping rate, the new solution was found better to interpret real pumping test data reported by Antonio and Pacheco (2002), and the laboratory experiment results. Overall, the new solution proves to be useful for parameter inversion accurately as the average pumping rate tended to underestimate hydraulic parameters when fitting short-term pumping data.

Groundwater recharge and water table response to changing conditions for aquifers at different physiography: The case of a semi-humid river catchment, northwestern highlands of Ethiopia

Groundwater recharge estimation, aquifer response to meteorological variables, and evapotranspiration calculations have been performed on a semi-humid catchment, in northwestern Ethiopian plateau. The Soil Moisture Balance (SMB), WetSpass water balance model, Water Table Fluctuation (WTF), and Chloride Mass Balance (CMB) methods are applied to estimate the groundwater recharge. Accordingly, 431 mm, 462 mm, and 477 mm recharge amounts are estimated as mean annual value, respectively, using SMB, WetSpass, and CMB methods. Based on the WTF method, the annual recharge rates of the volcanic aquifers range from 157 mm to 760 mm. The SMB and WetSpass methods are less effective for the flat physiographic area, where the recharge rate is storage controlled rather than precipitation amount. The calculated high recharge for maintain-front aquifers using WTF is attributed to extra rising due to lateral groundwater flow, which restricts the reliability of the method for such aquifer geometries. High groundwater level rising rate (121 mm/day) has been observed for the steeply sloping, low rates (11 mm/day) for the flat floodplain, and intermediate rate (52 mm/day) for the gently sloping volcanic aquifers. Similarly, receding rates of 3.18 mm/day were found for the steeply sloping, 0.40 mm/day for the floodplain, and 1.14 mm/day for the gentle sloping aquifers. The recession, in all of the topographies, is happening with second-order polynomial decay function. A strong connection between the shallow and deep groundwater aquifers is noted. Storage change in the relatively deeper volcanic aquifers is due to vertical groundwater flow from the overlying alluvial aquifer. This indicates that the recharge mechanism is local, and may be the reason for the low aquifer productivity of the Dangila wellfield. Diurnal water table fluctuation is detrended from the receding trend of the dry period, and evapotranspiration from the groundwater is estimated at 28% of total ET.

Analysis of subsurface drainage of sloping lands using the homotopy perturbation method

ABSTRACT An analytical model is developed using the homotopy perturbation (HP) method for predicting explicitly the location of water table heights resulting from steady drainage of a homogeneous sloping aquifer overlying a uniformly sloping impervious barrier at a finite distance from the top of the soil. The model assumes the aquifer to receive a steady recharge at its surface, the drains to have equal water level heights in them and the head loss in the vertical direction as negligible. The necessary and a sufficient condition within which the proposed solution is expected to converge are been worked out and also its validity been checked by comparing with the works of others for a few tested situations. The proposed series solution is expected to converge for all hillslope drainage settings so long these drainage layouts respect the necessary and sufficiency conditions of the developed solution. As the existing analytical solutions to the hillslope drainage problem, unlike the present one, do not render a direct determination of the water table profile for such a system, it is hoped that the solution proposed here would relatively be simpler to use in designing subsurface drains in a hillslope aquifer.

Variation of Groundwater Flow Caused by Any Spatiotemporally Varied Recharge

The objective of this study was to develop a complete analytical solution to determining the effect of any varying rainfall recharge rates on groundwater flow in an unconfined sloping aquifer. The domain of the unconfined aquifer was assumed to be semi-infinite with an impervious bottom base, and the initial water level was parallel to the impervious bottom of a mild slope. In the past, similar problems have been discussed mostly by considering a uniform or temporally varying recharge rate, but the current study explored the variation of groundwater flow under temporally and spatially distributed recharge rates. The presented analytical solution was verified by comparing its results with those of previous research, and the practicability of the analytical solution was validated using the 2012 and 2013 data of a groundwater station in Dali District of Taichung City, Taiwan.

Provenance and Sediment Maturity as Controls on CO2 Mineral Sequestration Potential of the Gassum Formation in the Skagerrak

In order to meet the increasing demand to decarbonize the atmosphere, storage of CO2 in subsurface geological reservoirs is an effective measure. To maximize storage capacity, various types of saline aquifers should be considered including dynamic storage options with open or semi-open boundaries. In sloping aquifers, assessment of immobilization potential for CO2 through dissolution and mineralization along the flow path is a crucial part of risk evaluations. The Gassum Formation in Skagerrak is considered a nearshore CO2 storage option with layers shallowing northwards. In this study, petrographic data and provenance analysis provide the basis for estimating reactivity of the sandstones with respect to CO2 immobilization potential. These analyses are integrated with seismic interpretation, well-log analysis and sedimentological observations of sedimentary facies to estimate mineral distribution and corresponding reactivity in the proposed injection area. Here the Gassum Formation comprises south-prograding, shoreface-fluvial para-sequences, sourced from northern hinterlands. Pronounced differences in the mineralogical maturity in the studied area are identified and explained by the sediment transport distances and the type of sediment source. This is possible because the U-Pb ages of zircon grains in the sediments can be used to pinpoint the areas where they originate from in the Fennoscandian Shield, such as Telemarkia (gneissic) or Idefjorden (granitic) terranes. Of special importance are the most reactive mineral phases like albite and Fe-rich chlorite, of which the feldspar occurs in largest abundance and the grain-coating chlorite has largest surface area. Their distribution is partly controlled by provenance, so their abundance decreases basinwards with increasing sediment maturity. The abundance of fluvial sandstones presumably increases northwards in basal parts of para-sequences, while shoreface sandstones comprise the top part of sandy units. CO2 injected in the proposed area will migrate upwards within the reservoir and up-dip along the seal, towards more immature sediments (i.e. higher contents of albite and chlorite) and higher proportions of Telemarkian-derived sediment. Thus, the mineralization potential increases along the migration path, while kinetic reaction rates will decrease in shallower, lower temperature regions. Identifying these parameters is important to estimate the CO2 mineral sequestration potential and ensure safe storage of CO2.

Simulation of Groundwater Flow in an Unconfined Sloping Aquifer Using the Element-Free Galerkin Method

Numerical simulation of groundwater flows in real aquifers has been commonly based on Finite Difference (FDM) and Finite Element Methods (FEM). These mesh-based methods require a computational grid, which can be costly to generate in case of complex geometries and can significantly increase the computational cost when adaptive remeshing is required. This work presents the Element-Free Galerkin Method (EFGM) for solution of the groundwater equation and demonstrates its application to a real unconfined sloping aquifer. EFGM uses the Moving Least Square (MLS) method for approximating the unknown head and computing the EFGM shape function, leading to increased accuracy, stability in function approximation and higher convergence rate than mesh-based methods. In the present study, EFGM is initially applied to one- and two-dimensional hypothetical problems, and validated with analytical solutions. Subsequently, EFGM is applied to the simulation of groundwater flow in the Blue Lake Aquifer (BLA) in North California, and the simulation results are compared with those obtained using MODFLOW. The results demonstrate the potential of EFGM for analyzing real aquifer problems.

Improved Solutions to the Linearized Boussinesq Equation with Temporally Varied Rainfall Recharge for a Sloping Aquifer

Sloping unconfined aquifers are commonly seen and well investigated in the literature. In this study, we propose a generalized integral transformation method to solve the linearized Boussinesq equation that governs the groundwater level in a sloping unconfined aquifer with an impermeable bottom. The groundwater level responses of this unconfined aquifer under temporally uniform recharge or nonuniform recharge events are discussed. After comparing with a numerical solution to the nonlinear Boussinesq equation, the proposed solution appears better than that proposed in a previous study. Besides, we found that the proposed solutions reached the convergence criterion much faster than the Laplace transform solution did. Moreover, the application of the proposed solution to temporally changing rainfall recharge is also proposed to improve on the previous quasi-steady state treatment of an unsteady recharge rate.

Comment on “Appropriate Boundary Condition for Dupuit‐Boussinesq Theory on the Steady Groundwater Flow in an Unconfined Sloping Aquifer With Uniform Recharge” by Wu et al.

AbstractBy neglecting unsaturated flow, Wu et al. (2018, https://doi.org/10.1029/2018WR023070) claimed that the zero volumetric discharge at the upstream boundary results in two possible boundary conditions of either zero groundwater table or zero seepage velocity based on the original Dupuit‐Boussinesq theory. They further concluded that a steeper and/or shallower aquifer has a zero‐groundwater table if the downstream groundwater table is shallower. Here we point out that the conceptual model adopted by Wu et al. (2018) not reasonable and the results are quite different from those with unsaturated flow considered in the real hillslope aquifer. Specifically, the water table at the upstream boundary could be positive or negative due to the lateral unsaturated flow effect, and hence, the seepage velocity must be set to zero to satisfy the zero discharge boundary condition at the upstream boundary. In addition, the zero groundwater table cannot ensure a zero discharge at the upstream boundary. Furthermore, we argue that the discharge with respect to the groundwater table is linearly distributed along the slope distance only when both saturated and unsaturated flows are considered. The saturated flow discharge itself is not distributed linearly. Our comment highlights the importance of unsaturated flow in studying steady groundwater flow in an unconfined sloping aquifer with uniform recharge using the Dupuit‐Boussinesq theory.

Reply to comment by Kong et al. on “Appropriate Boundary Condition for Dupuit‐Boussinesq Theory on the Steady Groundwater Flow in an Unconfined Sloping Aquifer With Uniform Recharge”

AbstractThe article aims to respond a comment made on our paper about appropriate boundary condition for the original Dupuit‐Boussinesq theory for two‐dimensional steady groundwater flow in an unconfined sloping aquifer with uniform rainfall recharge. To respond to the comments arguing the existence of lateral groundwater flows and negative groundwater table, clarifications are made for our analysis focusing on two‐dimensional groundwater flow without considering lateral effects by using the original and classical approximate theory.

Appropriate Boundary Condition for Dupuit‐Boussinesq Theory on the Steady Groundwater Flow in an Unconfined Sloping Aquifer With Uniform Recharge

AbstractThe application of Dupuit‐Boussinesq theory on the two‐dimensional steady groundwater flow in an unconfined sloping aquifer with uniform recharge is theoretically investigated. The examination of conditions at the downstream and upstream is performed. The method of phase plane is used to geometrically interpret the characteristics of the nonlinear theory by various initial conditions. For phase portrait analysis, three configurations for aquifers are considered. In each type of aquifer three conditions of recharges as well as downstream groundwater tables are also considered for comprehensive analysis. Based on the phase portrait analysis, one explicit formula in terms of known parameters and downstream boundary condition is derived to easily and straightforwardly determine an appropriate upstream boundary condition. The derived explicit formula can facilitate correct modeling using Boussinesq theory.