scholarly journals The Theis solution for subdiffusive flow in rocks

Author(s):  
Rajagopal Raghavan ◽  
Chih Chen

The central contribution of this work is the development of a “master” solution similar to the Theis solution to evaluate well responses under subdiffusive flow. Models based on subdiffusion employ fractional constitutive laws, a redefinition of Darcy’s law. Subdiffusive models discussed here are particularly useful to address situations where the internal architecture of the geological medium, such as fluvial and fractured systems, matters and where the existence of topological, geometrical and spatial influences result in distorted flow paths and a loss in connectivity. The developed solution provides the means for addressing these ends.

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.


2013 ◽  
Vol 433-435 ◽  
pp. 1933-1936
Author(s):  
Jing Wen Cui ◽  
Zhi Shang Liu ◽  
Yu Chen Zhang

Extra-heavy oil, polymer solution and some drilling fluids are typical non-Newtonian Herschel-Bulkley fluids, which behave as sheer-thinning with yield stress. In this paper, the Generalized Darcy's law for Herschel-Bulkley fluids flow in porous media was formulated, by the same way formulating the Generalized Darcy's Law for Bingham fluids. Then, the applications of the two type flow models were compared; Bingham type model was still widely applied due to its conciseness and relatively satisfied accuracy. In addition, the Generalized Darcys Law was revised to describe thixotropic non-Newtonian fluids conceptually.


2011 ◽  
Vol 8 (1) ◽  
pp. 2065-2101
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 fieldwork was completed at a research site in the western part of The Netherlands. The assessments were carried 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 the non validity for humified peat soils given by a variable hydraulic conductivity K with the hydraulic gradient. For higher humification degrees, the experiments indeed suggested a variable K, but this seems 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 hydraulic heads showed that there was hardly any evidence of a variation of the hydraulic conductivity with the hydraulic gradient. Therefore, Darcy's law can be used for peat soils. The heterogeneity of the subsoil and the apparent applicability of Darcy's law were taking into account for the detailed heterogeneous model that was prepared for the research site. 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 then extended for a whole hydrological year and for an eight year period with the objective of visualizing the flowpaths 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 flow behavior of the shallow groundwater system, but would be inappropriate for transport modeling through the CCL.


2019 ◽  
Vol 129 ◽  
pp. 70-79 ◽  
Author(s):  
Yuhang Wang ◽  
Saman A. Aryana ◽  
Myron B. Allen

Author(s):  
B Eitzinger ◽  
G Ederer

AbstractThis study investigates by nonlinear constitutive equations the influence of tipping paper, cigarette paper, filter, and tobacco rod on the degree of filter ventilation and draw resistance. Starting from the laws of conservation, the path to the theory of fluid dynamics in porous media and Darcy's law is reviewed and, as an extension to Darcy's law, two different nonlinear pressure drop-flow relations are proposed. It is proven that these relations are valid constitutive equations and the partial differential equations for the stationary flow in an unlit cigarette covering anisotropic, inhomogeneous and nonlinear behaviour are derived. From these equations a system of ordinary differential equations for the one-dimensional flow in the cigarette is derived by averaging pressure and velocity over the cross section of the cigarette. By further integration, the concept of an electrical analog is reached and discussed in the light of nonlinear pressure drop-flow relations. By numerical calculations based on the system of ordinary differential equations, it is shown that the influence of nonlinearities cannot be neglected because variations in the degree of filter ventilation can reach up to 20% of its nominal value.


2005 ◽  
Vol 71 (12) ◽  
pp. 8721-8728 ◽  
Author(s):  
D. L. Stoner ◽  
S. M. Watson ◽  
R. D. Stedtfeld ◽  
P. Meakin ◽  
L. K. Griffel ◽  
...  

ABSTRACT Here we introduce the use of transparent experimental models fabricated by stereolithography for studying the impacts of biomass accumulation, minerals precipitation, and physical configuration of flow paths on liquid flow in fracture apertures. The internal configuration of the models ranged in complexity from simple geometric shapes to those that incorporate replicated surfaces of natural fractures and computationally derived fracture surfaces. High-resolution digital time-lapse imaging was employed to qualitatively observe the migration of colloidal and soluble dyes through the flow models. In this study, a Sphingomonas sp. and Sporosarcina (Bacillus) pasteurii influenced the fluid dynamics by physically altering flow paths. Microbial colonization and calcite deposition enhanced the stagnant regions adjacent to solid boundaries. Microbial growth and calcite precipitation occurred to a greater extent in areas behind the fabricated obstacles and less in high-velocity orifices.


Sign in / Sign up

Export Citation Format

Share Document