The diffusivity of water in a porous material

Soil Research ◽  
1964 ◽  
Vol 2 (1) ◽  
pp. 1 ◽  
Author(s):  
AJ Peck
Keyword(s):  
Steady State ◽  
Porous Material ◽  
Satisfactory Agreement ◽  
Liquid Flow ◽  
Flow Equation ◽  
Transient Experiments ◽  
Cast Doubt

The results of some recent experiments have cast doubt upon the validity of the transient equation for liquid flow in a porous material. Perhaps the most searching trial of the flow equation is to compare diffusivities obtained from transient experiments with those obtained by steady-state methods. Such a trial on one material has indicated that the diffusivities are, in fact, in satisfactory agreement.

scholarly journals Discrimination of ablation, shielding, and interface layer effects on the steady-state formation of persistent bubbles under liquid flow conditions during laser synthesis of colloids

2021 ◽  
Author(s):  
Mark-Robert Kalus ◽  
Riskyanti Lanyumba ◽  
Stephan Barcikowski ◽  
Bilal Gökce
Keyword(s):  
Steady State ◽  
Laser Ablation ◽  
Liquid Flow ◽  
Production Efficiency ◽  
Synthesis Method ◽  
Target Surface ◽  
Interface Layer ◽  
Nanosecond Laser ◽  
Viscous Liquids ◽  
Shielding Effects

AbstractOver the past decade, laser ablation in liquids (LAL) was established as an innovative nanoparticle synthesis method obeying the principles of green chemistry. While one of the main advantages of this method is the absence of stabilizers leading to nanoparticles with “clean” ligand-free surfaces, its main disadvantage is the comparably low nanoparticle production efficiency dampening the sustainability of the method and preventing the use of laser-synthesized nanoparticles in applications that require high amounts of material. In this study, the effects of productivity-dampening entities that become particularly relevant for LAL with high repetition rate lasers, i.e., persistent bubbles or colloidal nanoparticles (NPs), on the synthesis of colloidal gold nanoparticles in different solvents are studied. Especially under batch ablation conditions in highly viscous liquids with prolonged ablation times both shielding entities are closely interconnected and need to be disentangled. By performing liquid flow-assisted nanosecond laser ablation of gold in liquids with different viscosity and nanoparticle or bubble diffusivity, it is shown that a steady-state is reached after a few seconds with fixed individual contributions of bubble- and colloid-induced shielding effects. By analyzing dimensionless numbers (i.e., Axial Peclet, Reynolds, and Schmidt) it is demonstrated how these shielding effects strongly depend on the liquid’s transport properties and the flow-induced formation of an interface layer along the target surface. In highly viscous liquids, the transport of NPs and persistent bubbles within this interface layer is strongly diffusion-controlled. This diffusion-limitation not only affects the agglomeration of the NPs but also leads to high local densities of NPs and bubbles near the target surface, shielding up to 80% of the laser power. Hence, the ablation rate does not only depend on the total amount of shielding matter in the flow channel, but also on the location of the persistent bubbles and NPs. By comparing LAL in different liquids, it is demonstrated that 30 times more gas is produced per ablated amount of substance in acetone and ethylene glycol compared to ablation in water. This finding confirms that chemical effects contribute to the liquid’s decomposition and the ablation yield as well. Furthermore, it is shown that the highest ablation efficiencies and monodisperse qualities are achieved in liquids with the lowest viscosities and gas formation rates at the highest volumetric flow rates.

Moments of the Flow Variables, Part II : The Effective Conductivity

2003 ◽  
Author(s):  
Yoram Rubin
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Effective Conductivity ◽  
Effective Property ◽  
Flow Equation ◽  
Laplace’S Equation ◽  
Flow Conditions ◽  
Laplace's Equation ◽  
Head Gradient ◽  
The Difference

Many applications require primary information such as average fluxes as a prelude to more complex calculations. In water balance calculations one may be interested only in the average fluxes. For both cases the concept of effective conductivity is useful. The effective hydraulic conductivity is defined by where the angled brackets denote the expected value operator. The local flux fluctuation is defined by the difference qi(x) — (qi(x)). Its statistical properties as well as those of the velocity will be investigated in chapter 6. To qualify as an effective property in the strict physical sense, Kef must be a function of the aquifer’s material properties and not be influenced by flow conditions such as the head gradient and boundary conditions (Landauer, 1978). Our goal in this chapter is to explore the concept of the effective conductivity Kef and to relate it to the medium’s properties under as general conditions as possible. Additionally, we shall explore the conditions where this concept is irrelevant and applicable, the important issue being that Kef is defined in an ensemble sense, but for applications we need spatial averages. Several methods for deriving Kef will be described below. The general approach for defining Kef includes the following steps. First, H is defined as an SRF and is expressed with the aid of the flow equation in terms of the hydro-geological SRFs (conductivity, mostly) and the boundary conditions. The H SRF is then substituted in Darcy’s law and an expression in the form equivalent to (5.1) is sought. If and only if the coefficient in front of the mean head gradient is not a function of the flow conditions will it qualify as Kef. The derivation of the effective conductivity employs the flow equation. In steady-state incompressible flow, for example, Laplace’s equation is employed. Solutions derived under Laplace’s equation are applicable, under appropriate conditions, for other physical phenomena governed by the same mathematical model. For example, the electrical field in steady state is also described by Laplace’s equation.

Approximate and Analytic Solutions for Deformation of Finite Porous Filters

1997 ◽  
Vol 64 (4) ◽  
pp. 929-934 ◽  
Author(s):  
S. I. Barry ◽  
G. N. Mercer ◽  
C. Zoppou
Keyword(s):  
Fluid Flow ◽  
Steady State ◽  
Porous Material ◽  
Deformation Behavior ◽  
Fluid Velocity ◽  
Approximate Solutions ◽  
Analytic Solutions ◽  
Two Dimensional ◽  
Solid Stress ◽  
Side Walls

The deformation, using linear poroelasticity, of a two-dimensional box of porous material due to fluid flow from a line source is considered as a model of certain filtration processes. Analytical solutions for the steady-state displacement, pressure, and fluid velocity are derived when the side walls of the filter have zero solid stress. A numerical solution for the case where the porous material adheres to the side walls is also found. It will be shown, however, that simpler approximate solutions can be derived which predict the majority of the deformation behavior of the filter.

Interpretation of Well-Block Pressures in Numerical Reservoir Simulation With Nonsquare Grid Blocks and Anisotropic Permeability

1983 ◽  
Vol 23 (03) ◽  
pp. 531-543 ◽  
Author(s):  
D.W. Peaceman
Keyword(s):  
Steady State ◽  
Single Phase ◽  
Numerical Solutions ◽  
Flow Equation ◽  
Anisotropic Permeability ◽  
Equivalent Radius ◽  
Square Grid ◽  
Bottom Hole ◽  
Single Well ◽  
Mathematical Derivation

Abstract Previous work on the interpretation of well-block Previous work on the interpretation of well-block pressure (WBP) for a single isolated well is extended to pressure (WBP) for a single isolated well is extended to the case of non square grid blocks (delta x does not equal delta y). Numerical solutions for the single-phase five-spot problem, involving various grid sizes, show that the effective well-block radius (where the actual flowing pressure equals the numerically calculated WBP) is given by This relationship is verified by a mathematical derivation for a single well in an infinite grid. The exact value of the constant is shown to be c -gamma/4, where gamma is Euler's constant. Finally, the analysis is extended to include anisotropic permeability, and an expression for the effective permeability, and an expression for the effective well-block radius in terms of delta x, delta y, kx, and ky is derived. Introduction In the modeling of a reservoir by numerical methods, it is necessary to use grid blocks whose horizontal dimensions are much larger than the diameter of a well. As a result, the pressure calculated for a block containing a well, po, is greatly different from the flowing bottom hole pressure (BHP) of the well, pwf. In a previous paper, the equivalent radius of a well block, ro, was paper, the equivalent radius of a well block, ro, was defined as that radius at which the steady-state flowing pressure for the actual well is equal to the numerically pressure for the actual well is equal to the numerically calculated pressure for the well block. This definition for ro gives (1) For a square grid (delta x = delta y), careful numerical experiments on a five-spot pattern showed that the ratio of ro to delta x ranges from 0. 1936 (for a 3 × 3 grid to a limit (2) It was also shown that the pressures in the blocks adjacent to a well block approximately satisfy the steady-state radial flow equation (3) By assuming that Eq. 3 is satisfied exactly, one can derive the relation (4) SPEJ P. 531

Transient Convective Heat Transfer of Air Jet Impinging Onto a Confined Ceramic-Based MCM Disk

2001 ◽  
Author(s):  
W. S. Su ◽  
L. K. Liu ◽  
Y. H. Hung
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Jet Impingement ◽  
Disk Surface ◽  
Separation Distance ◽  
Transient Time ◽  
Nusselt Numbers ◽  
Air Jet ◽  
Transient Experiments ◽  
Transfer Behavior

Abstract Transient heat transfer behavior from a horizontally confined ceramic-based MCM disk with jet impingement has been systematically explored. The relevant parameters influencing heat transfer performance are the steady-state Grashof number, jet Reynolds number, and ratio of jet separation distance to nozzle diameter. In addition, an effective time, ton, representing a certain transient time when the mixed convection effect due to jet impingement and buoyancy becomes significant relative to heat conduction, is introduced. Both the transient chip and average Nusselt numbers on the MCM disk surface decrease with time in a very beginning period of 0 ≤ t < ton, whereas it gradually increases or keeps constant with time and finally approaches the steady-state value in the period of ton ≤ t < ts. As compared with the steady-state results, if the transient chip and average heat transfer behaviors may be considered as a superposition of a series of quasi-steady states, the transient chip and average Nusselt numbers in all the present transient experiments can be properly predicted by the existing steady-state correlations when t ≥ 4 min in the power-on transient period.

Using a pseudo-steady-state flow equation and 4D seismic traveltime shifts for estimation of pressure and saturation changes

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. M11-M24 ◽  
Author(s):  
Sandra Ok Soon Witsker ◽  
Martin Landrø ◽  
Per Avseth
Keyword(s):  
Steady State ◽  
Flow Equation ◽  
P Wave ◽  
Reservoir Engineering ◽  
Order Effects ◽  
Inversion Algorithm ◽  
Steady State Flow ◽  
State Flow ◽  
Simple Inversion ◽  
4D Seismic

Pressure and saturation changes cause a change in seismic P-wave velocity resulting in a shift in 4D traveltime. A discrimination between both effects is important to enhance reservoir management decisions. We explored the possibility of linking the fields of reservoir engineering and 4D seismic. A simple inversion scheme based on a reservoir engineering flow equation for pore pressure predictions combined with the Hertz-Mindlin and Gassmann rock-physics models to discriminate pressure and saturation effects from 4D time shifts was presented. To account for no-flow reservoir boundaries, the pseudo-steady-state flow equation giving the pressure distribution was extended with a superpositioning method. During the inversion, three parameters were determined by a nonlinear, least-squares fitting method: the thickness of the hydrocarbon column, the pressure at the well position, and its decay rate away from the well. We successfully tested our approach on a synthetic and a field data case, where the [Formula: see text] injection well at the Snøhvit field, Norway, served as a good example to demonstrate our method. We observed a good correlation between simulation and inversion in our synthetic study. Our theory was limited to homogeneous reservoir conditions and produces spatially low frequent outputs. To apply the model in complex fields, such as at Snøhvit, we introduced a spatially varying Mindlin-exponent over the field and used the theory as an heuristic model assuming that a variation of the Mindlin-exponent takes a change in pressure sensitivity into account. This assumption provided the possibility to indirectly include heterogeneities in grain sorting and porosity variation and improved the model significantly. We see the advantage of our method in its fast and direct implementation to study first-order effects of pressure and saturation behavior on time-lapse seismic data using a simple inversion algorithm instead of computationally intensive simulations.

Sign in / Sign up

Export Citation Format

Share Document