Numerical simulation of underground multiphase and multicomponent fluid migration is a mathematical model of multiphase fluid movement and geochemical migration and diffusion based on the conservation of mass and energy. A large number of linear or nonlinear equations are established by discretization, and then solved by computer calculation, and then the simulation results are displayed by images, so as to achieve the purpose of studying engineering problems, physical problems and even other related problems. The numerical simulation of CO2 geological storage is to solve a series of problems such as migration and transformation of CO2 after it enters the geological storage system, water-rock-gas interaction, the influence of CO2 leakage on shallow aquifers and the physical changes of reservoirs and caprocks through computer simulation, so as to guide the implementation of CO2 geological storage project.
At present, the research work of numerical simulation of CO2 geological storage at home and abroad includes the following aspects:
1. Simulation of supercritical CO2- water multiphase fluid movement
Pruess et al. (2003) simulated the non-isothermal radial flow around a water injection well under the condition of constant flow of CO2 in homogeneous and isotropic saline water layers. When the influence of gravity and inertia force is ignored, there are similar variables ζ = R2/t (where R is the radial flow distance and T is the time) in the simulation results, and CO2 saturation, dissolved CO2 mass fraction, volume fraction of precipitated salt and fluid pressure are all functions of similar variables. This is consistent with the results of O 'Sullivan (198 1) and Dougherty and Proust (1992). The simulation of two-phase flow takes into account the relative permeability and capillary force of CO2 and water (Van Genuchten, 1980), the changes of fluid density, viscosity and CO2 solubility with pressure, temperature and salinity, and the decrease of aquifer permeability caused by salt precipitation.
Doughty and Pruess(2004) used the monitoring data of CO2 sealed in saline water to infer the physical and chemical process after CO2 perfusion. They used TOUGH2 numerical simulation software to simulate a two-phase (liquid, gas) three-component (CO2, water and dissolved NaCl) system. Considering that supercritical CO2 is an immiscible fluid in brine, it can be partially dissolved in brine at 15MPa and 65℃, the influence of boundary setting of multiphase flow system and the selection of relative permeability are analyzed, that is, the transverse boundary is set to be fully open (or fully closed) in the simulation, which leads to the pressure simulation result being too low (or too high) compared with the actual situation. The results show that the lateral boundary has little effect on CO2 diffusion plume due to the blocking effect of overlying faults on CO2. The simulation results also show that the relative permeability function has great influence on the evolution of CO2 diffusion plume. How to determine an appropriate relative permeability to characterize the change of saline water layer injected with CO2 is still an urgent problem to be solved. Doughty and Pruess simulated the change of CO2 plume diffusion with time under the condition of CO2 residual saturation, and found that there was a big difference. When the residual saturation is large, the CO2 plume is tight and moves slowly under the buoyancy. On the contrary, when the residual saturation is small, the CO2 plume is rapidly dispersed and the solubility is significantly improved.
2. Multi-component reaction geochemical migration simulation
Water-sandstone -CO2 interaction often forms a series of secondary minerals, or secondary mineral combinations. Worden et al.(2006) through the petrographic and geochemical simulation of CO2 injection into feldspathic sandstone, it is indicated that ankerite, kaolinite and chronology in upper Jurassic turbidite feldspathic sandstone in Magnus Oilfield in Beihai may be related. Among them, the carbon in ankerite comes from organic CO2. Watson et al.(2004) confirmed that the secondary mineral assemblage related to CO2 gas injection in the sandstone of CO2 gas reservoir in Ladbrokegrove, Oatway Basin, Australia is ankerite-kaolinite-secondary reaction time.
Xu et al. (2005) used the one-dimensional sandstone-shale system model to simulate the chemical reaction process between CO2 injected into the reservoir and minerals and its impact on the reservoir environment. The simulation shows that CO2 is mainly fixed by calcite in sandstone environment, and the precipitation of calcite leads to the decrease of porosity, which in turn leads to the corresponding decrease of permeability. In 654.38 million years, the storage capacity of sandstone reached 90 kg/m3, and these CO2 fixed by minerals can be permanently stored. The simulation of water-mineral -CO2 interaction by Zwingmann et al. using the geochemical simulation software EQ3/6 also shows that if CO2 is injected into the sandstone of the Pleistocene Grey Claw Formation in Niigata Basin in the north-central part of Honshu Island, Japan, CO2 will be sealed in two forms: dissolving in water and forming carbonate minerals, of which the maximum storage capacity of the latter is 2 1.3mol/kgH2O, which can reach 90% of the total storage capacity.
3. Coupled rock mechanics simulation
It can be seen from the published papers and comprehensive reports of research plans in various countries that the coupling effect of stress field is rarely considered in the analysis and simulation of CO2 migration mechanism in the study of CO2 saline water storage. In fact, the pressure of CO2 perfusion and the buoyancy of supercritical CO2 will change the stress state of the formation, that is, the pore pressure may affect the primary fractures and fissures during the upward migration and lateral diffusion of CO2. Long-term sequestration of CO2 in saline water layer (over a thousand years scale) will change the geochemical state of aquifer, and the chemical action of CO2- saline water-aquifer minerals may lead to changes in the mechanical and hydraulic properties of rock mass.
Japan attaches great importance to the study of mechanical stability of CO2 geological storage, because Japan is located at the junction of four major plates, in the Pacific Rim structural belt, with dense active faults, frequent earthquakes and complex in-situ stress distribution (Li Qi et al., 2002; Li Xiaochun et al., 2003). Li Qi et al (2002; 2004; (2006) proposed a thermal-water-mechanical (THM) coupling simulation framework considering the initial geostress field, grouting pressure, CO2 buoyancy and heat conduction, and considered the two-dimensional plane strain geological storage of faults with different dip angles near the bottom of caprock. The finite element method is used to simulate and analyze the influence of CO2 fluid injection on fault stability. The calculation results show that in order to avoid fault displacement, it is necessary to pay special attention to the control of perfusion pressure, because the influence of CO2 perfusion pressure on fault sliding is far greater than that of CO2 plume buoyancy. After CO2 injection stopped, the rise of CO2 plume became the main factor of stress field disturbance.
(2) Introduction of main software
In recent years, computer simulation technology has been widely used in many research fields, and many excellent simulation software and programs have been developed. Similarly, there are many numerical simulation softwares that can be used to study CO2 geological storage, mainly including PHREEQC, GEM, ECLIPSE, TOUGHREACT, PetroMod, MUFTE-UG and NUFT, all of which have their own characteristics and applicability. Before numerical simulation, it is necessary to evaluate and analyze these numerical simulation software and choose the simulation software suitable for the studied problem. The following is a brief introduction to several commonly used softwares in the world.
1.PHREEQC
PHREEQC is a computer software for calculating various low-temperature hydrogeochemical reactions. Based on the ion association water model, PHREEQC can complete the following tasks: (1) calculate the species of substances and the dissolution saturation index of minerals; (2) simulating geochemical inversion process; (3) Calculate batch reaction and one-dimensional migration reaction. In addition, PHREEQC coupled with multi-component solute transport model can generate a three-dimensional reaction transport simulator PHAST to simulate groundwater flow system. However, PHREEQC is based on the model of single-phase water flow, so it cannot simulate the two-phase flow of supercritical CO2- water.
The simplest application of PHREEQC is to calculate the distribution of various chemicals in solution and the saturation state of minerals and gases in solution. The reverse simulation function can deduce and quantify the chemical reaction equation that can reflect the changes of chemical substances in the flow process. The reaction equations that PHREEQC can deal with include the establishment of mass transport reactions of minerals, surface complexes, cation exchangers, soil solutions, unit partial pressures of gas components, given pressures or given volumes. While simulating these equilibrium reactions, PHREEQC can also simulate kinetic chemical and biological reactions, and simulate the reaction rate from simple linear decay (metabolite degradation or radioactive decay) to complex reaction rate determined by the chemical composition of the solution and the number of microorganisms. These reaction processing functions can be used for batch reaction simulation or one-dimensional convection, diffusion and reaction migration simulation.
2. Gems
GEM v.2009. 13(Nghiem et al., 2004) is a simulator used to simulate the use of CO2 and acid gas to enhance oil recovery. The simulator is completely coupled with the state equation of geochemical composition. GEM uses one-step solution method to solve the state equation. GEM can be used to simulate the balance between convection and dispersion fluid, oil (or supercritical CO2), gas and brine, chemical balance between species in water phase, and dynamic dissolution and precipitation of minerals. The simulator uses adaptive implicit discretization technology to simulate solute transport in porous media by using one-dimensional, two-dimensional or three-dimensional models. The oil phase and gas phase are simulated by state equation, and the solubility of gas in water phase is calculated by Henry's law model. GEM can also be used to simulate the infiltration of water into gas phase, caprock, thermal effect and fracture sealing through evaporation.
Step 3 be eclipsed
ECLIPSE is a parallel mature software, which can simulate black oil, composition and thermal recovery. 1994, Shengli Petroleum Administration Bureau launched the ECLIPSE series software for reservoir numerical simulation, which has been widely used in many aspects, from oil reservoirs to gas reservoirs, from ordinary oil fields to special oil and gas fields, from conventional simulation research to special simulation research. The main modules are main model, black oil, composition, thermal recovery, streamline method, operating platform and ECLIPSE Office.
ECLIPSE is a commercial software, and its kernel part is closed in use, so users can only operate it as a "black box". Its disadvantages are: it can not be obtained for free and can be used and modified at will; Unable to couple the most advanced geological fluid thermodynamic model; It is impossible to add more influencing factors to study specific problems. So ECLIPSE is not suitable for cutting-edge scientific research.
4.TOUGH2/TOUGHREACT
TOUGH2 is the abbreviation of unsaturated groundwater and heat transfer. It is a numerical simulation program used to simulate multiphase flow, multicomponent and non-isothermal water flow and heat transfer in one-,two-and three-dimensional porous or fractured media. TOUGH2 adopts the integral finite difference method (IFD) (Figure 3-8) to solve the problem of spatial discretization in multiphase flow and multicomponent chemical migration simulation (Pruess et al.,1999s; ; Xu et al., 2004). In order to meet the needs of large-scale computing, Zhang et al. (2008) developed a parallel computing version of TOUGH2, namely TOUGH2-MP.
This method is flexible in discretization of geological media and allows the use of irregular grids, which is very suitable for the simulation of fluid flow, migration and water-rock interaction in multi-regional heterogeneous systems and fractured rock systems. For regular mesh generation, the integral finite difference method is equivalent to the traditional finite difference method. Among them, for any region Vn, the conservation equations of mass (for chemical components such as water and gas) and energy (for heat) can be expressed by integration (Equation 3-5):
Figure 3-8 Spatial Discretization and Geometric Parameter Data Composition Diagram in Integral Finite Difference Method
Study on Site Selection Guide for Geological Storage of Carbon Dioxide in China
In the formula, the lower corner mark n represents a cell; The lower angle m represents the grid m connected with the cell n; Δ t is the time step; Mn is the average mass or energy density of the battery n; Anm is the interface of n and m of cell grid; Fnm is the mass or energy flux through the Anm area; Qn is the average source exchange rate per unit volume in cell n.
Xu Tianfu et al. (1998) added the simulation functions of multi-component solute transport and geochemical reaction on the basis of TOUGH2 framework, and formed a relatively complete set of non-isothermal heterogeneous fluid reaction geochemical migration simulation software-Tough React. The software not only includes all the functions of TOUGH2, but also applies to thermal-physical-chemical processes under different hydrogeological and geochemical conditions, such as temperature, pressure, water saturation, ionic strength, pH value and oxidation-reduction potential (Eh). It can also be applied to related numerical simulation research in one-,two-or three-dimensional heterogeneous (physical and chemical) porous or fractured media. Theoretically, it can accommodate any number of chemical components in solid phase, liquid phase or gas phase (but it will be limited by hardware conditions such as computing power and computing time in practical simulation), and a series of chemical equilibrium reactions, such as coordination reaction in solution, gas dissolution or desolventization, ion adsorption, cation exchange and mineral dissolution or precipitation reaction controlled by equilibrium or reaction kinetics, are considered. It can be said that TOUGHREACT is an upgraded version of TOUGH2, which has been widely used in CO2 geological storage research and engineering practice worldwide in recent years.
In addition to all the functions of TOUGH2, TOUGHREACT can also be applied to a series of reaction fluids and geochemical migration problems. For example: (1)Kd linear adsorption and radioactive decay pollutant migration; (2) Chemical evolution of natural groundwater under the surrounding environment; (3) Evaluation of nuclear waste disposal site; (4) Deep sedimentary diagenesis; (5) Geological disposal of 5)CO2. Multiphase fluid movement, multicomponent reaction geochemistry, storage capacity of various storage forms and their changes with time and space; (6) Mineral deposition (such as enrichment of supergene copper deposits); (7) Mineral changes in hot water system under natural and recharge environment.
Through the unremitting efforts of relevant researchers in recent years, TOUGHREACT has been further improved and perfected in practical application, adding some new functions, such as internal reaction kinetics and aqueous biodegradation, improving the calculation method of reaction surface area between minerals and water, and correcting the activity coefficient of gas in gas-water reaction.
5.PetroMod
PetroMod multi-component, multi-phase and multi-dimensional petroleum system simulation software integration platform developed by Germany IES (Integrated Exploration System) company has been recognized by the world petroleum industry. The software integrates fault activity, salt dome upwelling and piercing, volcanic intrusion, gas diffusion effect, oil-gas-water three-phase migration, oil-gas adsorption model and other related technologies.
Hybird, introduced and adopted by the simulation software platform, is the most advanced oil and gas migration simulation algorithm at present, which can not only ensure the simulation accuracy, but also greatly improve the simulation operation speed. Among them, PetroFlow3D is used to simulate oil and gas migration, accumulation, trap and loss, and PetroCharge Express provides us with a map-based rapid analysis tool for oil and gas migration and trap simulation.
6.MUFTE-UG
MUFTE-UG is a combination of mufte and UG. MUFTE MUFTE is a model of multiphase flow, transmission and energy. The software package mainly includes the concept of physical model and discrete methods of isothermal and non-isothermal multiphase and multicomponent flow and migration in porous and fractured media (Helmig,1997; Helmig et al., 1998). It can describe the discreteness of fractured porous media (Dietrich et al., 2005). UG is the abbreviation of unstructured grid, and the data structure it provides can quickly solve discrete partial differential equations based on parallel adaptive multigrid method. MUFTE-UG with modular structure can easily solve various problems with special requirements.
MUFTE-UG with modular structure has many different environments and technical applications. For example, in the field of environmental applications, MUFTE-UG can simulate the following two problems.
(1)NAPL permeates saturated and unsaturated soils. The optimized and improved restoration technology has broad research and development space in the future.
(2) Dissipation of underground CO2. CO2 is injected into the stratum hundreds of meters below the surface at high temperature and high pressure. MUFTE-UG can be used to evaluate the evolution (convection and dispersion migration) of plume in heterogeneous aquifer, accompanied by temperature effect (due to expansion and compression) and mutual dissolution of components (brine and CO2).
7. Nuft
Nuft (Non-isothermal Unstable-Saturated Flow and Migration Model) is a set of numerical solvers for solving the underground pollutant migration in the process of multiphase and multicomponent non-isothermal flow and solute migration in porous media. The software uses simple code to make use of common utilities and input file formats. Recently, this code runs successfully in Unix and DOS systems.
The program uses a complete finite difference space discretization method to solve the equilibrium equation. Newton-Raphson method is used to solve nonlinear equations at each time step, and direct solution and pre-yoke gradient method are used to solve linear equations at each iteration. The model can solve the problems of one-dimensional, two-dimensional and three-dimensional water flow and solute transport. In the future, the model will couple the functions of capillary lag, non-orthogonal mesh discretization, finite element partition and solid nonlinear isothermal adsorption.
(3) Research methods
Generally, the numerical simulation of CO2 geological storage includes the following main processes.
(1) Establishing conceptual model: According to the actual data obtained by various methods, the conceptual model of CO2 geological storage is established, including boundary range, elevation of strata or reservoir cover, determination of reservoir cover, parameters and zoning, source and sink terms, main physical and chemical processes and model dimensions (one-dimensional, two-dimensional and three-dimensional).
(2) Establishment of mathematical model: Establishment of partial differential equations describing multiphase flow and multicomponent reactive solute transport in deep saline aquifer, including initial conditions and boundary conditions.
(3) Model discretization: all kinds of information in the conceptual model are discretized by grid division to form a large number of grid elements, which are then transformed into mass and energy conservation equations by finite difference, finite element and integral finite difference, linearized by various methods to form linear algebraic equations, and then solved.
(4) Model identification and correction: compare and fit the calculated results of the model with the actual monitoring data, and adjust the parameters appropriately and reasonably, so that the model can fully reflect the actual situation. There is a big error in the process of historical fitting, so the conceptual model should be re-examined and revised. For the parameter sensitivity analysis of the model, we should carefully select the more sensitive parameters, and even need to do a lot of experiments to determine them.
(5) Model prediction: After a reliable model is established, simulation prediction can be made.
The key of numerical simulation is the generalization, calculation accuracy and calculation speed of geological model. Because the accuracy of calculation depends on the degree of discretization, and the degree of discretization determines the speed of calculation, which is a contradiction. We should choose the degree of discretization and the speed of calculation according to the needs of solving problems.
The migration and dissolution of CO2 in the reservoir and the chemical reaction with surrounding rocks form a multi-phase and multi-component reaction system, and the main mathematical equations involved include the motion control equation of supercritical CO2- water two-phase fluid, solute migration control equation and chemical reaction equation. Finite difference method, finite element method and integral finite difference method are usually used to establish numerical models.
In practical application, the existing numerical simulation software is often used to simulate a CO2 geological storage process, which does not involve software development and program code writing. Just choose the appropriate software to simulate and predict according to the research needs, and once the software is selected, the mathematical model and numerical model will be basically determined.