Modelling of reactive gas transport in unsaturated soil. A coupled thermo-hydro-chemical-mechanical approach

This thesis presents the development of a reactive gas transport equation under coupled framework of thermal, hydraulic, chemical and mechanical (THCM) behaviour of variably saturated soil. The capabilities of theoretical and numerical modelling of THCM processes have been advanced by the successful implementation of various aspects of the new addition. The previously developed THCM model at the Geoenvironmental Research Centre (GRC) has been extended to include the multicomponent gas transport modelling coupled with chemical/geochemical processes. The mechanisms of advection and diffusion have been considered to define the transport of multicomponent gas and chemicals in respective phases as well as exchange via dissolution and exsolution. The governing mass transfer process is subjected to homogeneous and heterogeneous geochemical reactions under equilibrium condition. Numerical solutions of the governing flow and deformation equations have been achieved by employing finite element method for spatial discretisation and finite difference method for temporal discretisation. Advanced geochemical features of gas-chemical interactions have been incorporated in the transport model, COMPASS by coupling with the geochemical model PHREEQC. A sequential non-iterative approach has been adopted to couple the transport processes and geochemical interactions. Verification of various aspects of the developed gas transfer equation has been commenced via a number of simulation exercises. Good agreement between the results have been achieved which suggests accurate and successful implementation of the theoretical and numerical formulation. The model has been implemented to investigate the gas transport processes in variably saturated compacted clay buffers via a number of conceptual simulation scenarios which are representative of high level nuclear waste disposal. Simulation of gas migration through saturated buffer has been intended to investigate the maximum pressure development as well as the dominant flow mechanisms. Demonstration of the modelling capability in context of reactive gas transport has been carried out considering long term isothermal flow of hydrogen through unsaturated clay buffer. The conclusions drawn from the discussions of simulation results has favoured the understanding of some of the key issues associated with gas generation and migration in compacted porous media, particularly, as a case of high level nuclear waste disposal

3D hybrid coupled dual continuum and discrete fracture model for simulation of CO2 injection into stimulated coal reservoirs with parallel implementation

This work presents the development of a 3D hybrid coupled dual continuum and discrete fracture model for simulating coupled flow, reaction and deformation processes relevant to fractured reservoirs with multiscale fracture system, e.g., coal and shale, efficiently and accurately. In this hybrid model, the natural fracture network and coal matrix are described together by a dual continuum approach and the large fractures are represented explicitly by the discrete fracture approach. A combination of different types of elements is used for spatial discretization. Large fractures are discretised with lower-dimensional interface elements and continuum domains with higher-dimensional elements. The coupling between the two models is achieved via the principle of superposition. To reduce computational time of simulations for complex and large-scale problems, a hybrid MPI/OpenMP parallel scheme is implemented in this work. The developed model is applied to investigate coupled thermal, hydraulic, and mechanical processes associated with CO2 sequestration and enhanced coalbed methane recovery. The results demonstrate capabilities of the model to adequately capture the effects of multiscale fracture system and their coupled behaviour during CO2 injection and methane recovery from coal reservoirs. Performance of the proposed parallelisation scheme was tested by comparing computation times of serial and parallel implementations. A good performance improvement was achieved, the speedup using parallelized scheme reaches up to about 10 times along with satisfactory scalability for considered application example. The findings of this work support developments and improvements of efficient advanced numerical models to study coupled THCM behaviour in fractured porous geomaterials

Technical performance comparison of horizontal and vertical ground-source heat pump systems

The configurations of ground heat exchangers (GHEs) play a significant role in the efficiency and sustainability of ground-source heat pump (GSHP) systems. However, there is a knowledge gap in understanding the performance differences between the horizontal and vertical GSHP systems in the same project under various heating and cooling demands. In this study, a technical performance comparison between GSHP systems coupled with horizontal ground loops and vertical boreholes under three scenarios of heating-to-cooling ratios (6 : 1, 2.4 : 1, and 1 : 1) was conducted. The simulations were based on a coupled thermal–hydraulic model for unsaturated soils that takes into account realistic ground surface boundary, GHE boundary, and the dynamics of heat pump efficiency. The GHEs were designed based on an experimental site located on the campus of a UK university. Results showed significant differences in the development of fluid temperatures and coefficient of performance (COP) of heat pumps between the horizontal and vertical GSHP systems due to the differences in the soil profiles and temperature boundaries. Both the fluid temperatures and heat pump COPs in the horizontal GSHP system reached a steady annual cycle after 2 years regardless of the heating-to-cooling ratios. For the vertical system, a general downward trend in the fluid temperatures and the COP of the heat pump in the heating mode can be found when a heating-to-cooling ratio was 6 : 1 or 2.4 : 1, while an overall upward trend in the fluid temperatures and the COP of the heat pump in the heating mode can be noted in the case of 1 : 1 heating-to-cooling ratio. Additionally, the heat pump operating in the cooling mode was off most of the time when a heating-to-cooling ratio was 6 : 1 or 2.4 : 1, while a declining trend in the COP of the heat pump in the cooling mode was exhibited in the case of a heating-to-cooling ratio of 1 : 1. The technical comparison reveals that the heating-to-cooling ratios would significantly affect the efficiency and sustainability of both GSHP systems

Modeling Gas Adsorption–Desorption Hysteresis in Energetically Heterogeneous Coal and Shale

Adsorption of gases in porous adsorbents such as coal and shale generally exhibits the phenomenon of hysteresis. Most of the previous studies on desorption hysteresis were conducted via experimental tests. However, few theoretical models that represent adsorption–desorption hysteresis of gases in porous sorbents are available. To address this issue, this work develops a new adsorption–desorption model for describing adsorption and desorption isotherms of gases with hysteresis. Particularly, the energetically heterogeneous surfaces of an adsorbent are considered via the patchwise model. Based on the change in site energy distribution, a logarithmically pressure-dependent hysteresis index, which is used to measure the degree of hysteresis, is derived for quantitative assessment of the degree of hysteresis. Besides, the correlation between the desorption isotherm and initialized pressure for desorption is established. The accuracy of the proposed model to adequately describe the adsorption–desorption hysteresis of gas in coal and shale is demonstrated by validating the model against laboratory experiments obtained from the literature. The results indicate that the adsorption isotherm depends significantly on site energy distribution. By comparing the site energy distributions for adsorption and desorption isotherms, it is found that the desorption hysteresis can be attributed to the change in pore size distribution caused by adsorption-induced deformation. The analyses support that the proposed model can be used as an effective tool to quantitatively predict the amount of released gas during desorption, which is significant for designing coalbed methane or shale gas production and assessing long-term CO2 storage behavior

Modelling anisotropic adsorption-induced coal swelling and stress dependent anisotropic permeability

To investigate the anisotropy of coal swelling, this study proposes an effective stress model for saturated, adsorptive fractured porous media by considering gas adsorption induced surface stress change on solid-fluid interface. The effective stress model can be used to capture the anisotropic swelling of coal combining anisotropic mechanical properties and to link with the anisotropic permeability. Direction dependent fracture compressibility is used to describe the evolution of anisotropic stress-dependent permeability behaviour. Particularly, the impact of gas adsorption on fracture compressibility is considered in the model. The proposed models were tested against experimental results and compared to relevant existing models available in literatures. The model predicts that the coal swelling in the direction perpendicular to the bedding plane, is greater than that in the parallel plane. Coal permeability in each direction can be affected by the stress changes in any directions. The permeability parallel to the bedding plane is more sensitive to change in stresses than in perpendicular to the bedding due to higher fracture compressibility. The cleat compressibility could increase with gas adsorption, especially for carbon dioxide. Permeability loss in the direction parallel to the bedding plane is more significant than that in the direction perpendicular to the bedding plane. The presented models provide a tool for quantifying gas adsorption-induced anisotropic coal swelling and permeability behaviours

Three-dimensional cleat scale modelling of gas transport processes in deformable fractured coal reservoirs

To understand the flow processes in naturally fractured coal reservoirs, a 3D numerical model for coupled gas flow, adsorption and deformation at the scale of coal cleat and matrix blocks is presented in this study. A discrete fracture matrix (DFM) modelling approach has been adopted where flow patterns in fractures and matrices are described separately and explicitly. Different from previous studies in which constant diffusion coefficient, equilibrium adsorption and lumped deformation of matrix and fracture are assumed, in this study, adsorbed gases are treated as an independent phase and the mass exchange process between free phase and adsorbed phase is described using the Langmuir kinetic model. Different gas transport mechanisms in a porous coal matrix are considered for both phase gas transport. Particularly, an equivalent poroelastic continuum model is applied to represent deformation of fracture-matrix system, in which impacts of fracture deformation on the bulk matrix-fracture deformation is accounted for. The hybrid dimensional elements have been employed to discretize the governing equations where fractures are discretized using lower-dimensional interface elements. The accuracy of developed model is validated against experimental results collected from literatures. The simulation results indicate that the gas diffusion process in coal matrices is pressure dependent, surface diffusion of adsorbed gas can contribute to the bulk gas diffusion in coal matrices. Individual cleat initially exhibits a slight opening, followed by significant closure due to adsorption-induced swelling. Ignoring the effect of fracture on bulk deformation, the aperture change is overestimated

Improving computational efficiency of numerical modelling of horizontal ground source heat pump systems for accommodating complex and realistic atmospheric processes

Modelling horizontal ground loops for a horizontal ground source heat pump (HGSHP) system is complex and computationally expensive. The computation precision is highly reliant on the prescription of an undisturbed ground temperature in the unsaturated ground as well as realistic and accurate atmospheric processes at the ground surface boundary. Conventionally, modelling of such a system would include direct application of the atmospheric processes at the soil-atmosphere boundary and solve it in a single-stage approach. However, low efficiency is found for large spatial domain and long-term transient problems as the boundary processes need to be solved and expressed in terms of primary model variables at each simulation time-step. This paper proposes an equivalent two-stage modelling approach, for the first time, based on an advanced coupled thermal-hydraulic (TH) model to improve computation efficiency while maintaining adequate accuracy. In this approach, firstly, the model is solved for an intact ground that is imposed by complex atmospheric processes, e.g., rainfall, solar radiation, humidity, evaporation, etc. at the soil-atmosphere boundary, and the spatial and temporal variations of the primary model variables are recorded. Afterwards, the recorded data are incorporated in the simulator, as model inputs, for the same ground including a HGSHP system. Predicted results from both 2D and 3D simulations show that the ground temperatures calculated by the proposed two-stage approach are in good agreement with that of the traditional single-stage approach. However, the two-stage approach is computationally robust. For the presented 2D and 3D simulations, it required only 32% and 37% of the time of the single-stage approach, respectively, while maintaining great accuracy. This demonstrates the utility of the proposed two-stage approach for modelling complex scenarios of realistic HGSHP systems installed in a large spatial domain and for long-term operation

A numerical study on performance efficiency of a low-temperature horizontal ground-source heat pump system

Exploitation of shallow ground and its low-grade heat potential is fundamental to designing 5th generation district heating and cooling (DHC) networks. Horizontal ground-source heat pump (HGSHP) systems are a common way to utilize shallow geothermal energy. Realistic estimation and prediction of performance of a HGSHP system and shallow ground thermal behaviour should consider the whole system including building heating and cooling load, heat pump and ground heat exchanger, and the ground. This should be accompanied by realistic atmospheric and ground conditions. In this paper, a three-dimensional coupled thermal-hydraulic model with realistic boundary conditions adopting a whole system approach is presented. Dynamic heat pump coefficient of performance (COP) that depends on seasonal variation of heating/cooling demand and ground conditions are also considered. Model validations are conducted against experimental and analytical results in literatures. The model is applied for evaluating a HGSHP system to support development of a 5th generation DHC network on a potential site in the UK. Several influencing factors, such as ground moisture transfer, building thermal load mode, buried depth of ground loops, and initial ground temperature profile are studied to assess performance efficiency of the HGSHP system and evolution of ground thermal behaviour in response to heat extraction or rejection into the ground. The results show that 5% of the monthly total heat demand of the site could be met by the designed HGSHP system, consisting of 200 U-shaped ground loops buried at the depth of 3 m and pure water as the heat carrier. Overlooking the ground moisture transfer or hyperbolizing the ground saturation would overestimate the load-carrying capacity of the HGSHP system. The HGSHP system is more efficient with a higher heat pump COP under the heating and cooling mode than under the heating-only mode. Predicted performance of the HGSHP system improves with buried depth of the ground loops. The results also show that a 1 ℃ increase in the undisturbed ground temperature could suffice up to 8% of the monthly total heat demand of the site

Estimation and prediction of shallow ground source heat resources subjected to complex soil and atmospheric boundary conditions

5th generation district heating and cooling networks operating at near ground temperature offer a low-cost, zero-carbon energy solution. Detailed understanding and accurate estimation of ground behaviour for its heat storage and recharge potential are of paramount importance for the success of such networks. In this paper, an advanced modelling tool, based on a coupled Thermal-Hydraulic (TH) modelling framework, is presented to calculate and predict temperature and soil-moisture behaviour of a shallow ground under complex atmospheric, temperature and hydraulic boundary conditions. Atmospheric data e.g., solar radiation, rainfall, humidity, air temperature, wind velocity is considered together with subsurface soil data to investigate thermal and hydraulic responses of the ground, and its individual soil layers. Furthermore, a transient method for estimating shallow ground source heat (SGSH) resources is proposed based on the simulated temperature and saturation distributions of the ground. The model is applied to predict the long-term ground temperature and saturation level of a test site located in Warwickshire County, UK. The total heat content per unit area and the annual/seasonal/monthly net heat content per unit area of the site are predicted for a five-year period. The total heat content of the sandy clay layer varied between 2.32 and 11.6 MJ/m2, silty clay from 34.0 to 50.5 MJ/m2, and mudstone from 50.7 to 55.0 MJ/m2. A parametric sensitivity study is also conducted to investigate the effects of soil types and hydraulic drainage conditions on the ground heat supply potential, and it revealed that the spatial and temporal distributions of ground heat is significantly affected by the underlying soils. This study highlights the influences of atmospheric conditions and coupled ground processes, and the parameters that should be considered for designing a 5th generation low-temperature heat network