Vapor-Pressure Lowering in Geothermal Systems

1983 ◽  
Vol 23 (01) ◽  
pp. 157-167 ◽  
Author(s):  
Chih-Hang Hsieh ◽  
Henry J. Ramey

Abstract The water vapor-pressure lowering phenomenon in porous media was investigated for a range of temperatures by measuring vapor pressure vs. mass of water adsorbed in consolidated sandstone cores and unconsolidated silica sands. Experimental results showed that the mass of water adsorbed on the rock surface is much more than the amount of pore steam. Results also revealed that the water adsorption is caused mainly by micropores in the porous medium. Measurement of the mass of methane and ethane adsorbed on dry rocks showed that the amount of adsorption is not great in comparison with the pore gas. It was found that adsorption data for water/sandstone core studies could be normalized with respect to temperature. Although this appears not to have been reported previously, it does agree in principle with findings for solid powders with micropores. Another interesting result was that reanalysis of previous studies of capillarity in sandstones indicates that experimental data probably were influenced mostly by adsorption. Introduction If a container is evacuated and partially filled with a liquid, at temperature, T, the equilibrium pressure, po, can be measured. This pressure po is called the saturated vapor pressure. The phase diagram for a particular pure single-component liquid can be constructed by using sets of (T, po), where po is a function of T only. Vapor-pressure lowering refers to the fact that. under some conditions, the equilibrium pressure, p, may be less than po. The liquid/vapor pressure-temperature (p-T) relationship may depend on other factors such as solution of salts or gases in a pure liquid. An investigation of vapor-pressure lowering is important in understanding the behavior of geothermal steam reservoirs. Traditionally, it has been considered that superheated steam and rock are the only two components in a dry steam geothermal reservoir. From the fundamental physical properties of fluid and rocks, however, there should exist a certain amount of liquid in addition to steam. If the quantity of additional liquid compared with the quantity of superheated steam is significant, material balance computations should account for this. Capillarity has been thought to be the main factor causing vapor-pressure lowering in a porous medium. However, in the course of this study, it became apparent that surface adsorption was the most important factor causing vapor pressure lowering in dry-steam geothermal reservoirs. For this study, adsorption isotherms were obtained for several fluids and consolidated sandstones over a range of temperatures. To reduce the number of variables, only pure single-component fluids were used. For the following, liquids" refers to simple liquids, excluding solutions and other mixtures. Theory Many factors can cause vapor-pressure lowering for pure liquids in porous media. The most important are capillarity and surface adsorption. Capillarity originates from surface tension, and describes the relationship between a liquid phase and a gas phase for a single component fluid in a capillary tube. Surface adsorption is the result of interaction between molecules of the solid surface and the gas molecules in the pore space. Capillarity considers only surface tension forces, and surface adsorption considers forces of attraction between the liquid and the solid surface. The following discussion briefly reviews surface tension and capillarity. SPEJ P. 157^

1982 ◽  
Vol 60 (10) ◽  
pp. 1391-1395 ◽  
Author(s):  
R. C. Sharma ◽  
T. J. T. Spanos

The instability of the plane interface between two uniform, superposed, and streaming fluids through porous media is considered. The configuration is taken to be bottom-heavy. In the absence of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if perturbation in the direction of streaming are ignored, whereas for perturbations in all other directions there exists instability for a certain wavenumber range. The surface tension is able to suppress this Kelvin–Helmholtz instability for small wavelength perturbations and the medium porosity reduces the stability range given in terms of a difference in streaming velocities. For the top-heavy configurations, the surface tension stabilizes a certain wavenumber range.


2014 ◽  
Vol 6 (1) ◽  
pp. 1024-1031
Author(s):  
R R Yadav ◽  
Gulrana Gulrana ◽  
Dilip Kumar Jaiswal

The present paper has been focused mainly towards understanding of the various parameters affecting the transport of conservative solutes in horizontally semi-infinite porous media. A model is presented for simulating one-dimensional transport of solute considering the porous medium to be homogeneous, isotropic and adsorbing nature under the influence of periodic seepage velocity. Initially the porous domain is not solute free. The solute is initially introduced from a sinusoidal point source. The transport equation is solved analytically by using Laplace Transformation Technique. Alternate as an illustration; solutions for the present problem are illustrated by numerical examples and graphs.


Author(s):  
Swayamdipta Bhaduri ◽  
Pankaj Sahu ◽  
Siddhartha Das ◽  
Aloke Kumar ◽  
Sushanta K. Mitra

The phenomenon of capillary imbibition through porous media is important both due to its applications in several disciplines as well as the involved fundamental flow physics in micro-nanoscales. In the present study, where a simple paper strip plays the role of a porous medium, we observe an extremely interesting and non-intuitive wicking or imbibition dynamics, through which we can separate water and dye particles by allowing the paper strip to come in contact with a dye solution. This result is extremely significant in the context of understanding paper-based microfluidics, and the manner in which the fundamental understanding of the capillary imbibition phenomenon in a porous medium can be used to devise a paper-based microfluidic separator.


Fluids ◽  
2021 ◽  
Vol 6 (8) ◽  
pp. 266
Author(s):  
Péter German ◽  
Mauricio E. Tano ◽  
Carlo Fiorina ◽  
Jean C. Ragusa

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).


2015 ◽  
Vol 1101 ◽  
pp. 471-479
Author(s):  
Georges Freiha ◽  
Hiba Othman ◽  
Michel Owayjan

The study of signals propagation inside porous media is an important field especially in the biomedical research related to compact bones. The purpose of this paper is to determine a mathematical formulation of the global coefficients of transmission and reflection of nondestructive ultrasonic waves in any bi-phase porous medium. Local coefficients of transmission and reflection on the interface of the porous medium will be determined based on a study of boundary conditions. The behavior of different waves inside the porous medium will be developed so that we can derive a new formulation of global coefficients that takes interior phenomena into consideration. Results are found independently of the geometrical and physical characteristics of the medium. Note that this study is based on normal incident ultrasonic wave propagation.


2005 ◽  
Vol 40 (4) ◽  
pp. 600-612 ◽  
Author(s):  
L. A. Nasyrova ◽  
I. R. Rakhmatullin ◽  
V. Sh. Shagapov

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