Geofluids

Volume 2017 (2017), Article ID 9010572, 12 pages

https://doi.org/10.1155/2017/9010572

## A Numerical Investigation on the Effect of Gas Pressure on the Water Saturation of Compacted Bentonite-Sand Samples

^{1}State Key Laboratory for Geomechanics and Deep Underground Engineering and School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, China^{2}State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu, Sichuan 610059, China^{3}CNNC Beijing Research Institute of Uranium Geology (BRIUG), Beijing 100029, China^{4}Key Laboratory of Deep Coal Resource Mining, Ministry of Education of China, China University of Mining and Technology, Xuzhou 221116, China^{5}Laboratoire de Mécanique de Lille (CNRS, LML) and École Centrale de Lille, CS 20048, 59651 Villeneuve-d’Ascq Cedex, France

Correspondence should be addressed to Jiang-Feng Liu; moc.liamtoh@uilfaej and Bing-Xiang Huang; moc.kooltuo@tmucxbgnauh

Received 8 June 2017; Revised 19 September 2017; Accepted 8 October 2017; Published 27 December 2017

Academic Editor: Qinghui Jiang

Copyright © 2017 Jiang-Feng Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In deep geological disposal for high-level radioactive waste, the generated gas can potentially affect the sealing ability of bentonite buffers. There is a competition between water and gas: the former provides sealing by swelling bentonite, and the latter attempts to desaturate the bentonite buffer. Thus, this study focused on numerically modelling the coupling effects of water and gas on the water saturation and sealing efficiency of compacted bentonite-sand samples. Different gas pressures were applied to the top surface of an upper sample, whereas the water pressure on the bottom side of the lower sample was maintained at 4 MPa. The results indicated that gas pressure did not significantly affect the saturation of the bentonite-sand sample until 2 MPa. At 2 MPa, the degree of water saturation of the upper sample was close to 1.0. As the gas pressure increased, this influence was more apparent. When the gas pressure was 6 MPa or higher, it was difficult for the upper sample to become fully saturated. Additionally, the lower sample was desaturated due to the high gas pressure. This indicated that gas pressure played an important role in the water saturation process and can affect the sealing efficiency of bentonite-based buffer materials.

#### 1. Introduction

The management of high-level radioactive waste is an important issue for countries with nuclear power. Currently, deep geological disposal methods are used by most countries. In deep geological disposal systems, barriers include natural geological barriers and engineered barrier systems (EBSs). EBSs may comprise various subsystems or components, such as waste forms, canisters, buffers and backfills, seals, and plugs. Bentonite or bentonite-based materials (e.g., a bentonite/sand mixture was used in this study) have been used by several countries as buffer and backfill materials [1–7]. In most repository concepts, bentonite is only partially saturated. After the repository is closed, groundwater in the host formation will invade the bentonite barriers. Underground water seepage will cause bentonite swelling and consequently disposal pit sealing.

Nevertheless, in the long term, gases may be produced in the repository by several methods, such as metal corrosion, water radiolysis, and organic waste microbial degradation, which produce hydrogen, oxygen, methane, and carbon dioxide [8–10]. Over time, gas pressure will increase and build up if generation rates are high and transport is within the repository. This pressure may be sufficient to affect the repository structure and properties, particularly those of bentonite/sand mixtures. Water is favourable for the saturation of bentonite, whereas gas has the opposite effect. Therefore, the sealing provided by swollen bentonite competes with the effects of gas, which attempts to be desaturated and migrate through the buffer to the surrounding host rock and potentially the environment and simultaneously remove radionuclides [11].

In recent decades, researchers have tried to evaluate the sealing efficiency of engineered barriers. One approach is to measure the gas permeability of samples under different confining pressures [12–14]. Another approach is to measure the gas breakthrough pressure of samples under constant confining pressures [5, 6, 15–18]. Regarding these two approaches, one of the most important factors is the water saturation degree, which has a close relationship with the sealing ability of the samples. However, it is difficult to measure the degree of saturation of a sample during a traditional triaxial test because the sample cannot be removed from the triaxial cell during the test. Therefore, numerical modelling is a good method to evaluate the degree of saturation. Additionally, we can obtain the distribution of the degree of saturation in different potions of the sample.

At the time of writing, a few modelling studies have been performed to simulate gas/water transport in clayey materials. Fall et al. [19] utilized a coupled hydromechanical (HM) model to predict and analyse gas migration in sedimentary rock. This model considered elastic degradation due to microcracks or damage and mechanical damage-controlled gas flow. Xu et al. [20] simulated gas migration in water-saturated argillaceous rock with a two-phase flow and a mechanics-coupled numerical model (H^{2}M). In this model, intrinsic permeability and mechanical and hydraulic conditions were varied during the gas migration process. Gonzalez-Blanco et al. [21] simulated gas migration in a Cenozoic clay with a fully coupled hydromechanical model, which incorporated an embedded fracture permeability model. Additionally, other researchers performed a series of numerical modelling assays to determine gas migration in clayey materials [16, 22–24].

In situ water pressure is approximately 4-5 MPa, whereas gas pressure increases gradually and decreases again when breakthrough occurs. This indicates that a coupling effect exists between a constant water pressure and an increasing gas pressure. However, many researchers overlooked this phenomenon. Thus, our modelling aimed to reproduce the competition between water and gas and their coupling effects on the water saturation of bentonite-based buffers. This study is a supplementary work in conjunction with our other FORGE (Fate of Repository Gases) experiments [6]. The overall project aims to investigate and quantify gas generation and migration in the underground disposal of radioactive wastes.

#### 2. Theoretical Model

##### 2.1. Governing Equation

Flow in unsaturated medium is commonly described by the Richards equation [26–28]:where is the hydraulic conductivity (Darcy law), is the hydraulic pressure, and is the vector of gravity (the value is −1 for the vertical direction, and the value is 0 for the horizontal direction). The effective water saturation can be expressed as follows:where is the volume water content, is the residual water content, and is the saturated water content (i.e., 1.0). With (2), we can rewrite (1) as where is the apparent porosity in water (in this case, the water content is defined by the ratio of the water volume to the sample volume), is the water permeability, is the relative water permeability, is the viscosity of water, is the density of water, is the acceleration of gravity, and is the water pressure. In the nonsaturated case, , where is the gas pressure and is the capillary pressure.

There are three unknown parameters in (3): , , and ( and are constant and directly determined by laboratory experiments, and is equal to 1.0 × 10^{−3} Pa·s). Therefore, (3) requires two additional equations to solve, which are presented as follows.

##### 2.2. Kelvin-Laplace Equation

The Kelvin-Laplace equation describes the relationship between capillary pressure and relative humidity RH. The relative humidity of the air above the meniscus in a capillary pore is given by the Kelvin equation [29], as cited by Galvin [30]:where is the molar volume, is the universal gas constant, is the temperature, is the surface tension, is the radius of the droplet, and is the contact angle. Indeed, for a porous medium, this equation is assumed to describe the relationship between the inside relative humidity and the maximum radius of the pores, which are filled with water. With the Young-Laplace equation [31, 32]the relationship between the capillary pressure and the relative humidity RH is

##### 2.3. Retention and Relative Permeability Models

The relationship between water saturation and the capillary pressure is defined by the Van Genuchten (VG) model [33]:where and are two parameters that are related to the pore size distribution of the porous medium.

The sorption isotherm, which reflects the relationship between the water saturation and the relative humidity, can be determined by the Van Genuchten model and the Young-Laplace equation. Using laboratory experimental results, parameters and can be determined by the least-squares method.

The relative permeability is given by the Mualem model [34]:Based on the Van Genuchten model, (5) and (6) can be rewritten as follows:For all tests, the temperature was maintained at 20°C; therefore, the temperature effect was neglected in our numerical simulations. The effect of water gravity was also assumed to be negligible.

#### 3. Geometric Model and Boundary Conditions

##### 3.1. Modelling Scheme Design

In situ experiments require several years to several decades. Therefore, laboratory experiments are used to provide useful data for the design and construction of in situ geological repositories and essential parameters for numerical modelling. For the in situ model, as shown in Figure 1, a significant water saturation gradient is observed between the core and the periphery of the buffer because of underground water seepage [25]. The partially saturated core is gradually saturated with water because the saturated peripheral samples are in direct contact with underground water from the surrounding host rock. To reproduce this phenomenon, an original laboratory experiment and a numerical model were established.