This research aims to investigate the thermoelastic behavior of a multilayer cylindrical wellbore of a gas well for underground hydrogen storage with an analytical solution. In this research project, a stable analytical solution is developed for predicting the thermomechanical stress-strain behavior of a multilayer borehole when subjected to thermal and pressure loading.
General Introduction to the project
Importance of the Study
A parametric study, likely involving Young's modulus and Poisson's ratios, could be pursued to better understand wellbore conditions. Similar to other studies, the analytical solution was validated by calculating the stress distribution of the pressure vessel using the finite element method.
Problem Statement
Aim and Objectives
Scope and Limitation of the Study
Contribution of the Study
Outline of the Report
The study of cylindrical multi-layer wells is limited to the study of steel and cement casing well materials in two-layer and four-layer construction. The main objective of this project in deriving the thermoelastic behavior of the analytical solution for the cylindrical multi-layer borehole is then presented in the third chapter, although the derivation for the cylindrical borehole of one layer was first presented in the first chapter.
Introduction
Renewable Energy in general
The Renewables 2017 GSR reported that renewable electricity is estimated to contribute 24.5% of global electricity generation compared to non-renewable electricity at 75.5. The Renewables 2018 GSR reported that renewable electricity is estimated to contribute 26.5% of global electricity generation, compared to non-renewable electricity at 73.5.
Hydrogen, Hydrogen Economy and Underground Hydrogen Storage Hydrogen can be produced from renewable resources that are available locally, such
Hydrogen Economy
One important factor that would greatly contribute to the hydrogen economy is light, safe, compact and cost-effective hydrogen storage. As an energy carrier, it stores energy until it is needed and can be transported to required locations. v) Hydrogen has the best ratio of valence electrons to nucleons. vi) Hydrogen can be produced in several ways from different (renewable and non-renewable) primary energy sources. vii).
Hydrogen Storage and Large Scale Storage
The long-term storage nature of these underground stored gases has enabled long-term storage of electrical energy. This is because long-term energy storage currently does not exist in national grid networks (Tichler and Bauer, 2016). The long-term storage option for the energy storage system (via the underground gas storage) is referred to as 'power-to-gas' energy storage.
Underground Gas Storage and Underground Hydrogen Storage
- Underground Depleted Oil and Gas Wells and Aquifers
- Underground Artificial Salt Caverns
- Other Underground Storage Methods
The advantages of using such rooms are their proven and long-tested tank tightness. One of the advantages of salt chamber storage, even at high operating pressure, is the excellent tightness provided by the viscoplastic properties of salt rock. One of the options available is the conversion of abandoned mines into gas reservoirs due to certain circumstances.
Heat Transfer in Single Layer Cylindrical Wellbore
- System of Coordinate for Cylindrical Wellbore
- Single Layer Cylindrical Wellbore Model
- Steady-State One Dimension Radial Flow Heat Conduction
- Non-heat-generation Heat Conduction
The above equation shows the heat conduction of the single layer cylindrical borehole in the radial flow consideration. In addition, the heat consumed or utilized by the cylindrical borehole will never be significant. Referring back to Figure 2.1, the boundary conditions of the single layer cylindrical borehole are as follows.
Thermo-Mechanical Stress in Single Layer Cylindrical Wellbore
- Axisymmetric Structure and Thermal Loading
- Homogeneous Isotropic Properties
- Stress-Strain Relationship
- Mechanical Stress Strain and Thermal Strain Relationship
- Thermo-Mechanical Analysis
Therefore, the stress-strain relationship for the cylindrical coordinate system of Eq. 2.23) can be further arranged to determine the stresses in terms of Young's modulus, strains and Poisson's ratio. Using expressions for constants of integration C1 and C2 of Eq. 2.34), the general expressions for radial displacement, radial stress and circumferential stress are as given below. The temperature distribution as given by Eq. 2.11) can be further reduced to simplified form as below.
Analytical and Finite Element Analysis for Wellbore Structure
Summary
Hydrogen has been highlighted as an energy carrier that is environmentally friendly because it does not release any carbon dioxide CO2 in its conversion cycles from to and from electricity (Gupta, et al presented an overview of hydrogen underground storage technology, including discussions of underground hydrogen storage and conventional storage methods, underground gas storage experiences of various countries and the four common storage patterns i.e. On the other hand, Hartmann, et al., (2018) conducted studies on gas and hydrogen storage structures and an analytical solution of multi-layer thick-walled tubes in thermo-elasticity for application to gas wells. Such underground hydrogen storage technology has evolved from the practices, applications of the well-developed and mature technology and knowledge of natural gas and carbon dioxide underground storage (Bai, et al. al., 2014).
Introduction
Methodology
Multi-layer Cylindrical Wellbore Model
- Geometrical model
- Material model
- Boundary conditions
- Non-heat-generation Heat Conduction Equations
On the inner surface (of the cylindrical hole), temperature, pressure and radial stress are marked as follows: temperature on the inner surface of the first layer with radius ̅ = temperature on the inner surface with radius . temperature at the innermost surface of the cylindrical well. radial stress on the inner surface of the first layer with a radius of = pressure on the inner surface at the radius of. pressure on the innermost surface of the cylindrical well. On the outer surface, the relevant boundary conditions are as follows: temperature on the outer surface of the nth layer with radius ̅ = temperature on the inner surface with radius. temperature at the outermost surface of the cylindrical well. radial stress on outer surface of nth layer with a radius of = pressure on outer surface at radius of. pressure on the outermost surface of the cylindrical well. And the temperature of the outer surface of the layer is given by. 3.22) gives the expression for the temperature at the interface as. 3.20) is rearranged into the expressions for the temperatures on the inner surface and the outer surface of layer i and becomes.
Derivation of Analytical Solution of Thermo-elastic Behaviour of Multi- layer Cylindrical Wellbore
For a cylindrical wellbore, its equilibrium equation for axial symmetry is as follows. 3.38), the equilibrium equation is now expressed in terms of radial displacement as. Applying the radial stresses to the two adjacent layers, layer i and layer i+1, gives the respective related interface pressures. Applying the radial stresses to the outer surface of layer i-th gives corresponding related contact surface pressure as. 3.59) gives the corresponding related contact surface pressure.
Computational Algorithm
Next, in terms of recurrence terms with their corresponding boundary conditions, determine yields. 3.25) for each layer and then use them to calculate the variable for 〈 〉 in Eq. 3.43) and the radial displacement in Eq. The proposed analytical solution as well as the calculation algorithm shall apply to the models proposed in the following chapter 4, of which the details of the two proposed multi-layer cylindrical wellbore models of two- and four-layer construction with their respective geometry and material model, as well as the corresponding boundary conditions are all presented here.
Numerical Simulation using Finite Element Method Software ANSYS Numerical study on the models in this research project is carried out in Finite
Then, in the modeling main menu, model areas are created by specifying the x, x1, and x2 coordinates, which represent the inner and outer radius of the element, and the y, y1, and y2 coordinates, which are used to specify the height of the model. in study. Then, under the Solution command of the Main Menu, the analysis is new and the analysis type is specified as steady state. Under the Select command of the main menu, the current load step is selected and a horizontal axis graph of the Cumulative Iterative Number versus the vertical axis of the Absolute Convergence Rate is automatically generated and displayed.
Summary
For this study, the results simulated and generated by the Ansys in the log file are extracted and transferred to another separate excel spreadsheet. They are then plotted in the respective charts in the Excel file whose Matlab analytical results have already been previously plotted in the same chart for comparison.
Introduction
Result Generation and Comparison for Two-Layer Model
Comparison of Results and Discussions for Two-layer Model
The comparison of analytical solution and numerical simulation results for the two-layer model and their interpretations are shown in Figure 4.2 to Figure 4.6. From the graphs in Figure 4.2, it can be observed that the temperature distribution is found to be in very good agreement with those from the Ansys numerical finite element model. From the graphs of Figure 4.3 to Figure 4.6, it can be observed that the radial stresses, axial stresses and circumferential stresses are found to be in very good agreement with those generated by the Ansys numerical finite element model.
Result Generation and Comparison for Four-Layer Model
Comparison of Results and Discussions for Four-layer Model
The comparison of results of analytical solution and numerical simulation for four-layer models and their interpretations are presented in Figure 4.8 to Figure 4.12. The analytical solution for the four-layer cylindrical wellbore in terms of temperature distribution across the four layers is presented in the graph in Figure 4.8 together with the result obtained from numerical simulation using Ansys. In other words, the analytical solution to analyze the four-layer cylindrical wellbore must be in order, as their results are verified by the very close similar patterns generated from Ansys numerical simulation.
Effect of Number of Layer to Stress Distribution
The result of the temperature distribution as well as the radial, axial, peripheral and von Mises stress distribution plotted over the non-dimensionalized radial distance for both two-layer and four-layer cylindrical bore is shown in Figure 4.13 to Figure 4.17. At the outer surface for both two-layer and four-layer cylindrical well bores, the circumferential stress magnitudes are almost the same. Peripheral stress at the inner surface of the first layer of four-layer cylindrical wellbore has a much lower value compared to the value of two-layer cylindrical wellbore, as expected.
Summary
The four-layer model is presented in a similar way to the two-layer model and its results, comparisons and discussion are also presented. Third objective of this project applying the analytical solution to evaluate the effect of number of layer on the stress distribution over wall by simultaneously comparing the result of both two-layer model and four-layer model together through the non-dimensionalized radial distance. The temperature distribution, radial stress, axial stress showed very similar with respect to the number of layers, but the circumferential stress distribution for both models is quite different from each other, with the four-layer model having a smaller size compared to the two-layer model.
Conclusions
Recommendations for Further Research
Large-scale underground hydrogen storage for grid integration of renewable energy and other applications. Science and Engineering of Hydrogen-Based Energy Technologies: Hydrogen Production and Practical Applications in Power Generation. Overview of large-scale underground energy storage technologies for renewable energy integration and criteria for reservoir identification.
