1,721,081 research outputs found
Non-Newtonian flow in a variable aperture fracture
No full textThe transmissivity of a variable aperture fracture for flow of a non-Newtonian, purely viscous power-law fluid with behavior index n is studied. The natural logarithm of the fracture aperture is considered to be a two-dimensional, spatially homogeneous and correlated Gaussian random field. We derive an equivalent fracture aperture for three flow geometries: (1) flow perpendicular to aperture variation; (2) flow parallel to aperture variation; (3) flow in an Isotropic aperture field. Under ergodicity, results are obtained for cases 1 and 2 by discretizing the fracture into elements of equal aperture and assuming that the resistances due to each aperture element are, respectively, in parallel and in series; for case 3, the equivalent aperture is derived as the geometric mean of cases 1 and 2. When n = 1, all our expressions for the equivalent aperture reduce to those derived in the past for Newtonian flow and lognormal aperture distribution. As log-aperture variance increases, the equivalent aperture is found to increase for case 1, to decrease for case 2, and to be a function of flow behavior index n for case 3. © 1998 Kluwer Academic Publishers
Type curves for radial flow in heterogeneous aquifers
No full textRadial flow towards wells in variable hydraulic conductivity aquifers is examined: the law of variation of conductivity adopted, typical for fissured rocks, is exponential with depth. Analytical solution for drawdown is achieved through the Boltzmann transformation: results are presented as dimensionless type curves. In particular, for high temporal values, the resulting well function is linear on semilogarithmic paper, as in the Jacob method for a homogeneous aquifer. However, it is showed that the homogeneous hypothesis may lead to erroneous estimation of aquifer characteristics. -from English summar
Estimates of equivalent aperture for non-Newtonian flow in a rough-walled fracture
No full textIn this work, theoretical estimates of equivalent apertures for creeping flow of a purely viscous power-law fluids in a rough-walled fracture have been obtained, generalizing past results for a Newtonian fluid. As expected, the equivalent aperture is lower than the mean in flow perpendicular to the profile, and larger in the parallel flow configuration. In both cases, the equivalent aperture is larger for pseudoplastic fluids than for dilatant ones. It was demonstrated that tortuosity effects decrease equivalent aperture below the mean; the reduction effect is more evident for pseudoplastic fluids
An exact solution for one-dimensional unsteady nonlinear groundwater flow
No full textAfter a brief review of the validity of Darcy's law, a nonlinear flow law is adopted for the analytical solution of a groundwater flow problem. A one-dimensional unsteady flow in plane geometry, with prescribed head at the boundaries, is studies. The solution of the analogous linear case is reviewed through the use of Boltzmann's transformation. A solution for nonlinear flow is obtained through a generalization of this transformation. Detailed expressions for specific discharge and drawdown are derived for two significant values of the exponent of the flow law. All results are presented in dimensionless form for a comparative analysis. Some significant cases are plotted. Finally, some implications of the adoption of a nonlinear flow law are discussed. © 1991 Kluwer Academic Publishers
On non-Newtonian fluid flow in rough fractures
No full textFlow of non-Newtonian fluids between rough walls is of interest in several geophysical and industrial applications. In this work (mainly geared toward fractured media) a governing equation for creeping flow of a purely viscous power law fluid of flow behavior index n in a rough-walled fracture is obtained, generalizing past results for a Newtonian fluid. An equivalent fracture aperture is defined, in analogy to the well-known hydraulic aperture valid for n = 1. Tortuosity is introduced as a vectorial quantity, thereby distinguishing between true and apparent fracture aperture. Examples are provided to illustrate the utility of the proposed approach. It is demonstrated that tortuosity effects significantly decrease the equivalent fracture permeability. Depending on the specific geometry considered, the flow behavior index may or may not have a significant impact on the equivalent fracture permeability. When it does, the reduction effect due to tortuosity is enhanced as the flow behavior index decreases
Permanent Waves in Slow Free-Surface Flow of a Herschel-Bulkley fluid
No full textUnsteady flow of a viscoplastic fluid on an inclined plane is examined. The fluid is described by the three-parameter Herschel-Bulkley constitutive equation. The set of equations governing the flow is presented, recovering earlier results for a Bingham fluid and steady uniform motion. A permanent wave solution is then derived, and the relation between wave speed and flow depth is discussed. It is shown that more types of gravity currents are possible than in a Newtonian fluid; these include some cases of flows propagating up a slope. The speed of permanent waves is derived and the possible surface profiles are illustrated as functions of the flow behavior index
Sull’analisi statistica del fattore di attrito
No full textIl fattore di attrito f per il moto nei condotti è valutato
statisticamente in funzione delle variabili aleatorie:
diametro del condotto, portata defluente, salto
di pressione su una lunghezza assegnata. Il suo valore
effettivo (medio) è paragonato al valore apparente
calcolato a partire dalle quantità medie misurate.
Viene fornito un esempio numerico che mostra
come la differenza tra le due quantità sia trascurabile
nella maggior parte dei casi
A Channel Model for Bi-viscous Fluid Flow in Fractures
No full textIn the last decade, the interest towards fluids characterized by a complex rheology has increased in the scientific community. Physicochemical, rheological and fluid mechanical approaches are adopted to characterize the peculiarities of non-Newtonian fluids. These fluids show remarkable properties that can be exploited to improve remediation techniques or optimize industrial operations. While the existence of actual yield stress is still debated, the presence of a plug or pseudo-plug zone is frequent in emulsions, soft glassy materials, jammed non-colloidal suspensions or colloidal gels. Even if simple yield stress models are often faulted because of their acknowledged deficiencies, they allow to study important phenomena without introducing excessive complexity. In this study, the randomness describing the aperture field of a natural rock fracture is coupled with a bi-viscous fluid rheology of parameter ε, representing the viscosity ratio; the cases ε= 0 and ε→ 1 represent the Bingham and Newtonian behaviour, respectively. The conceptual model proposed describes the flow of such fluids through a fracture with aperture variable along a single direction, the aperture being constant along the other. The aperture variation is modelled via a generic probability distribution function of assigned mean and variance. Two limit flow cases are considered: (1) parallel arrangement (PA), representing the case of maximum conductance, with the fluid flowing in the direction of channels of constant aperture; and (2) series arrangement (SA), the case of minimum conductance, with flow directed orthogonally to the constant aperture side of the fracture. Results are illustrated for log normal and gamma aperture distributions. The influence of aperture variability and applied pressure gradient on flow rate is investigated for both arrangements. The pressure gradient affects in a nonlinear fashion the flow rate, with a marked increase around a threshold value for both PA and SA. The channel flow rate exhibits a direct dependency upon aperture variability for PA, an inverse one for SA. The shape of the distribution has an impact on model responses: for the PA, the influence is significant but limited to an intermediate threshold range of pressure gradients, while results for the SA are affected in the whole range of pressure gradient. An example application in dimensional form is included
Bingham fluid flow in spatially variable fractures
No full textNon-Newtonian fluid flow in fractured media is of interest to hydrologists, geophysicists, and mining engineers. Since laboratory and field investigations evidence a strong degree of variability in fracture aperture, a large body of literature is specifically concerned with evaluation of an equivalent aperture (or permeability), adopting different constitutive equations and aperture variability models. The equivalent aperture for non-Newtonian fluid flow is defined as the parallel plate aperture which would permit a given volumetric flux under an assigned pressure gradient, thereby generalizing the concept of hydraulic aperture used for Newtonian flow. In this paper, the Bingham model with yield stress 0 has been adopted to describe the fluid rheology; the aperture is taken to vary as a spatially homogeneous and correlated random field with a lognormal aperture density distribution of assigned mean and variance 2. The equivalent fracture aperture is derived for a specific geometry where the flow is perpendicular to the aperture variation. Under ergodicity, results are obtained by discretizing the fracture into elements of equal aperture and assuming that the resistances due to each aperture element are in parallel. The equivalent fracture aperture is greater than the mean, and their ratio is found to depend on aperture variability, represented by log-aperture variance 2, and on a dimensionless parameter , equal to the wall shear stress in a fracture with aperture equal to divided by the Bingham yield stress. The ratio is weakly dependent on , and tends to increase as 2 increases. When tends to infinity, all our expressions reduce to those derived in the past for Newtonian flow and lognormal aperture distribution
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