The Importance of Using Probabilistic Effective Hydraulic Conductivity in Darcy's Law and Groundwater Flow Calculations

Author(s):  
Hugo A. Loáiciga
2011 ◽  
Vol 15 (9) ◽  
pp. 3017-3031
Author(s):  
P. Trambauer ◽  
J. Nonner ◽  
J. Heijkers ◽  
S. Uhlenbrook

Abstract. The groundwater flow models currently used in the western part of The Netherlands and in other similar peaty areas are thought to be a too simplified representation of the hydrological reality. One of the reasons is that, due to the schematization of the subsoil, its heterogeneity cannot be represented adequately. Moreover, the applicability of Darcy's law in these types of soils has been questioned, but this law forms the basis of most groundwater flow models. With the purpose of assessing the typical heterogeneity of the subsoil and to verify the applicability of Darcy's law, geo-hydrological fieldwork was completed at an experimental field within a research area in the western part of The Netherlands. The assessments were carried out for the so-called Complex Confining Layer (CCL), which is the Holocene peaty to clayey layer overlying Pleistocene sandy deposits. Borehole drilling through the CCL with a hand auger was completed and revealed the typical heterogeneous character of this layer, showing a dominance of muddy, humified peat which is alternated with fresher peat and clay. Slug tests were carried out to study the applicability of Darcy's law, given that previous studies suggested its non-validity for humified peat soils due to a variable horizontal hydraulic conductivity Kh with head differences. For higher humification degrees, the experiments indeed suggested a variable Kh, but this appeared to be the result of the inappropriate use of steady-state formulae for transient experiments in peaty environments. The muddy peat sampled has a rather plastic nature, and the high compressibility of this material leads to transient behavior. However, using transient formulae, the slug tests conducted for different initial groundwater heads showed that there was hardly any evidence of a variation of the hydraulic conductivity with the applied head differences. Therefore, Darcy's law can be used for typical peat soils present in The Netherlands. The heterogeneity of the subsoil and the apparent applicability of Darcy's law were taken into account for the detailed heterogeneous model that was prepared for the research area. A MODFLOW model consisting of 13 layers in which 4 layers represent the heterogeneous CCL was set up for an average year, assuming steady-state conditions; and for the winter of 2009 to 2010, adopting transient conditions. The transient model was extended to simulate for longer periods with the objective of visualizing the flow paths through the CCL. The results from these models were compared with a 10 layer model, whereby the CCL is represented by a single layer assuming homogeneity. From the comparison of the two model types, the conclusion could be drawn that a single layer schematization of the CCL produces flowpath patterns which are not the same but still quite similar to a 4 layer representation of the CCL. However, the single layer schematization results in a considerable underestimation of the flow velocity, and subsequently a longer travel time, through the CCL. Therefore, a single layer model of the CCL seems quite appropriate to represent the general flow behavior of the shallow groundwater system, but would be inappropriate for transport modeling through the CCL.


Author(s):  
William G. Gray ◽  
Michael A. Celia

The mathematical study of flow in porous media is typically based on the 1856 empirical result of Henri Darcy. This result, known as Darcy’s law, states that the velocity of a single-phase flow through a porous medium is proportional to the hydraulic gradient. The publication of Darcy’s work has been referred to as “the birth of groundwater hydrology as a quantitative science” (Freeze and Cherry, 1979). Although Darcy’s original equation was found to be valid for slow, steady, one-dimensional, single-phase flow through a homogeneous and isotropic sand, it has been applied in the succeeding 140 years to complex transient flows that involve multiple phases in heterogeneous media. To attain this generality, a modification has been made to the original formula, such that the constant of proportionality between flow and hydraulic gradient is allowed to be a spatially varying function of the system properties. The extended version of Darcy’s law is expressed in the following form: qα=-Kα . Jα (2.1) where qα is the volumetric flow rate per unit area vector of the α-phase fluid, Kα is the hydraulic conductivity tensor of the α-phase and is a function of the viscosity and saturation of the α-phase and of the solid matrix, and Jα is the vector hydraulic gradient that drives the flow. The quantities Jα and Kα account for pressure and gravitational effects as well as the interactions that occur between adjacent phases. Although this generalization is occasionally criticized for its shortcomings, equation (2.1) is considered today to be a fundamental principle in analysis of porous media flows (e.g., McWhorter and Sunada, 1977). If, indeed, Darcy’s experimental result is the birth of quantitative hydrology, a need still remains to build quantitative analysis of porous media flow on a strong theoretical foundation. The problem of unsaturated flow of water has been attacked using experimental and theoretical tools since the early part of this century. Sposito (1986) attributes the beginnings of the study of soil water flow as a subdiscipline of physics to the fundamental work of Buckingham (1907), which uses a saturation-dependent hydraulic conductivity and a capillary potential for the hydraulic gradient.


1994 ◽  
Vol 74 (4) ◽  
pp. 431-437 ◽  
Author(s):  
S. E. Allaire ◽  
J. Caron ◽  
J. Gallichand

Pore size, distribution and continuity are important characteristics for the exchange and storage of air and water in artificial mixes. Saturated hydraulic conductivity (Ks) measurements can be used to obtain such a characterization. However, two difficulties are encountered when using Ks in potting media. First, the validity of Ks may be limited because it may not apply in media composed of coarse material or peat. Second, the structure of peat substrates is very sensitive and in situ measurements of potted peat substrates (i.e. measurements made directly in the pots) should be carried out to avoid any disruptive effect due to handling. Such a measurement, when made in pots, may require the evaluation of the water flux reduction resulting from the container outflow configuration. The objectives of this study were therefore to check the validity of Darcy’s law for peat substrates and to propose an approach for estimating the saturated hydraulic conductivity from flow measurements made in nursery containers. For three different substrates, water flow in artificial mixes followed Darcy’s law for hydraulic gradients ranging from 1.1 to 1.6 cm cm−1. Experimental results showed that the measured fluxes in 5-L nursery container filled at five different substrate heights (9, 11.5, 14, 16.5 and 19 cm) with laterally located drainage holes were significantly different from those measured in pots with the bottom removed (therefore equivalent to measurement currently made in cylinders) at P = 0.0022. Fluxes in containers with bottoms removed were 7–31% higher than in intact pots. Water flux measurements may therefore need to be corrected for this flux reduction in order to accurately estimate hydraulic conductivity from flow experiments run in pots. A correction factor based on the results obtained from a finite difference model was derived and calibrated. Then, this correction factor was used to convert flux measurements made in pots with lateral holes into equivalent flux that would have been obtained had the pot had an open bottom. After correction, no significant flux reductions were found between pots with open bottoms and pots with lateral holes (P = 0.55). A correction factor estimated from Laplace’s equation, once calibrated, can therefore be applied to flux measurements obtained from pots to obtain estimates of Ks of undisturbed potted media. Key words: Hydraulic conductivity, peat substrates, container


2021 ◽  
Author(s):  
Ritam Guha ◽  
Soulib Ghosh ◽  
Kushal Kanti Ghosh ◽  
Ram Sarkar

Abstract A novel meta-heuristic nature-inspired optimization algorithm known as Groundwater Flow Algorithm (GWFA) is proposed in this paper. GWFA is inspired from the movement of groundwater from recharge areas to discharge areas. It follows a position update procedure guided by Darcy's law which provides a mathematical framework of groundwater flow. The proposed optimization algorithm has been evaluated on 23 benchmark functions. The significance of the results is statistically validated using Wilcoxon rank-sum, Friedman and Kruskal Walis tests. To prove the robustness of the algorithm, it has been further applied on several standard engineering problems. From these exhaustive experiments, it has been observed that the proposed GWFA can outperform many state-of-the-art optimization algorithms.


2021 ◽  
Author(s):  
Ritam Guha ◽  
Soulib Ghosh ◽  
Kushal Kanti Ghosh ◽  
Ram Sarkar

Abstract A novel meta-heuristic nature-inspired optimization algorithm known as Groundwater Flow Algorithm (GWFA) is proposed in this paper. GWFA is inspired from the movement of groundwater from recharge areas to discharge areas. It follows a position update procedure guided by Darcy's law which provides a mathematical framework of groundwater flow. The proposed optimization algorithm has been evaluated on 23 benchmark functions. The significance of the results is statistically validated using Wilcoxon rank-sum, Friedman and Kruskal Walis tests. To prove the robustness of the algorithm, it has been further applied on several standard engineering problems. From these exhaustive experiments, it has been observed that the proposed GWFA can outperform many state-of-the-art optimization algorithms.


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