Numerical approximation of water–air two-phase flow by the mixed finite element method

A new model for two-phase flow of water and air in soil is presented. This leads to a system of two mass balance equations and two equations representing conservation of momentum of fluid and gas, respectively. This paper is concerned with the verification of this model for the special case of a rigid soil skeleton by computational experiments. Its numerical treatment is based on the Raviart–Thomas mixed finite element method combined with an implicit Euler time discretization. The feasibility of the method is illustrated for some test examples of one- and two-dimensional two-phase flow problems.     

X-ray Computed Tomography study of the influence of consolidants on the hydric properties of sandstones for stone conservation studies

X-ray Computed Tomography (X-ray CT) has been used to study the petrophysical characteristics of a Jurassic sandstone from Asturias (Northern Spain) used as building stone in several monuments in the region. CT monitoring of water capillarity tests has made it possible to visualize the movement of water inside the samples, to relate this movement with texture characteristics, and to measure the height reached in successive images, thereby determining the capillary penetration coefficient; based on this coefficient, the effective capillary pore radius has also been estimated. An advantage of the use of CT is that, as the information comes from the sample interior, border effects that can be generated in the external faces can be avoided.The CT was also used to visualize how a commercial organosilicon consolidant penetrates inside the rock by means of capillarity, a usual way of consolidant application in stone restoration processes. The coefficient of capillary penetration of the product, determined on the basis of the measurements made on the tomographic images, is 53% less than that of water. The influence of rock texture characteristics on the capillarity both of the consolidant and the water was also observed.The samples underwent CT water capillarity studies before and after the consolidant application, proving that the treatment improves the rock's hydric properties. The coefficient of capillary penetration decreased by 24% following the application of the consolidant, whereas the effective pore radius decreased by more than 40%.     

Rapid imbibition of water in fractures within unsaturated sedimentary rock

The spontaneous imbibition of water and other liquids into gas-filled fractures in variably-saturated porous media is important in a variety of engineering and geological contexts. However, surprisingly few studies have investigated this phenomenon. We present a theoretical framework for predicting the 1-dimensional movement of water into air-filled fractures within a porous medium based on early-time capillary dynamics and spreading over the rough surfaces of fracture faces. The theory permits estimation of sorptivity values for the matrix and fracture zone, as well as a dispersion parameter which quantifies the extent of spreading of the wetting front. Quantitative data on spontaneous imbibition of water in unsaturated Berea sandstone cores were acquired to evaluate the proposed model. The cores with different permeability classes ranging from 50 to 500 mD and were fractured using the Brazilian method. Spontaneous imbibition in the fractured cores was measured by dynamic neutron radiography at the Neutron Imaging Prototype Facility (beam line CG-1D, HFIR), Oak Ridge National Laboratory. Water uptake into both the matrix and the fracture zone exhibited square-root-of-time behavior. The matrix sorptivities ranged from 2.9 to 4.6 mm s^−0.5, and increased linearly as the permeability class increased. The sorptivities of the fracture zones ranged from 17.9 to 27.1 mm s^−0.5, and increased linearly with increasing fracture aperture width. The dispersion coefficients ranged from 23.7 to 66.7 mm² s⁻¹ and increased linearly with increasing fracture aperture width and damage zone width. Both theory and observations indicate that fractures can significantly increase spontaneous imbibition in unsaturated sedimentary rock by capillary action and surface spreading on rough fracture faces. Fractures also increase the dispersion of the wetting front. Further research is needed to investigate this phenomenon in other natural and engineered porous media.     

The influence of capillarity on multiphase flow within porous media: a new model for interpreting fluid levels in groundwater monitoring wells in dynamic aquifers

A new approach is presented to calculate the volume of oil in the underground at an oil spill site from fluid levels in monitoring wells. The approach includes the effects of hysteresis due to irregular pore geometry and to phase entrapment. It is possible to explain the drastic changes in the oil thickness in a monitoring well due to the decrease and increase in the groundwater table. A correct evaluation of the oil volume infiltrated underground from an oil spill and the effective control of remediation works can only be done by using the newly developed approach with a consideration of the dynamic changes in the groundwater table.     

Chemical evolution of disposal brine of the Cerro Prieto geothermal field during its transport toward surrounding soils, Mexico

The exceeding brines of Cerro Prieto Geothermal Field (CPGF) are disposed into a lagoon and part of them infiltrate into the upper aquifer. This work describes the geochemical processes of how geothermal brine reaches the soils to the south and southwest of CPGF according to local flow lines from piezometric measurements. Soil and groundwater samples were collected and analyzed in the CPGF and the surrounding area. The model was divided into three stages: (a) Capillary rising-evaporation; (b) Mixture: geothermal brine-irrigation water and (c) Mixture-capillary rising-evaporation. The modeling was carried out taking into account the saturation stage of each solution. The mixture models and evaporation process were carried out considering a mass balance. The proposed model shows the pollution processes due to power generation through accumulation of evaporation pond soluble salts on agricultural lands in the CPGF surrounding area.     

Dissolved pollutant transport in tailings ponds

Water and dissolved ion transport in mineral tailings was studied at laboratory scale with three different tailings samples. Percolation rate, determined in column experiments, depends mainly on the granulometric distribution of the solid and varies between 3.0×10^–4 cm/s for a tailings sample with coarser particles (d₉₀>700 m) to 4.0×10^–5 cm/s for the tailings sample with higher content of fine particles (d₉₀<200 m). In stationary conditions, the ascending rate of water by capillarity through the solid bed is controlled by the evaporation rate at the top surface of the tailings. Rates between 2.6×10^–5 cm/s (2.2 mm/day) and 8.1×10^–5 cm/s (7.0 mm/day) have been obtained under forced evaporation at 40 °C. Ion transport in the percolation process is mainly controlled by the hydraulic diffusion of the solution through pores in the solid bed. In the capillarity process, ion transport is controlled by chemical diffusion of the dissolved ion in the ascending solution.     

Upscaling of CO2 vertical migration through a periodic layered porous medium: The capillary-free and capillary-dominant cases

We present an upscaled model for the vertical migration of a CO₂ plume through a vertical column filled with a periodic layered porous medium. This model may describe the vertical migration of a CO₂ plume in a perfectly layered horizontal aquifer. Capillarity and buoyancy are taken into account and semi-explicit upscaled flux functions are proposed in the two following cases: (i) capillarity is the main driving force and (ii) buoyancy is the only driving force. In both cases, we show that the upscaled buoyant flux is a bell-shaped function of the saturation, as in the case of a homogeneous porous medium. In the capillary-dominant case, we show that the upscaled buoyant flux is the harmonic mean of the buoyant fluxes in each layer. The upscaled saturation is governed by the continuity of the capillary pressure at the interface between layers. In the capillary-free case, the upscaled buoyant flux and upscaled saturation are determined by the flux continuity condition at the interface. As the flux is not continuous over the entire range of saturation, the upscaled saturation is only defined where continuity is verified, i.e. in two saturation domains. As a consequence, the upscaled buoyant flux is described by a piecewise continuous function. Two analytical approximations of this flux are proposed and this capillary-free upscaled model is validated for two cases of heterogeneity. Upscaled and cell averaged saturations are in good agreement. Furthermore, the proposed analytical upscaled fluxes provide satisfactory approximations as long as the saturation set at the inlet of the column is in a range where analytical and numerical upscaled fluxes are close.     

Prediction of imbibition from grain-scale interface movement

Processes in porous media governed by capillary forces, such as drainage or imbibition of wetting phase, are of great importance in different branches of soil science, petroleum engineering and hydrology. In this work we describe a new way of modeling imbibition by considering the movement and merger of interfaces at the pore level. The model is based upon a physically consistent dynamic criterion for the imbibition of a single pore originally proposed by Melrose.