Leakage dynamics of fault zones: experimental and analytical study with application to CO2 storage

Fault zones have the potential to act as leakage pathways through low permeability structural seals in geological reservoirs. Faults may facilitate migration of groundwater contaminants and stored anthropogenic carbon dioxide (CO $_2$ ), where the waste fluids would otherwise remain securely trapped. We present an analytical model that describes the dynamics of leakage through a fault zone cutting multiple aquifers and seals. Current analytical models for a buoyant plume in a semi-infinite porous media are combined with models for a leaking gravity current and a new model motivated by experimental observation, to account for increased pressure gradients within the fault due to an increase in Darcy velocity directly above the fault. In contrast to previous analytical fault models, we verify our results using a series of analogous porous medium tank experiments, with good matching of observed leakage rates and fluid distribution. We demonstrate the utility of the model for the assessment of CO $_2$ storage security, by application to a naturally occurring CO $_2$ reservoir, showing the dependence of the leakage rates and fluid distribution on the fault/aquifer permeability contrast. The framework developed within this study can be used for quick assessment of fluid leakage through fault zones, given a set of input parameters relating to properties of the fault, aquifer and fluids, and can be incorporated into basin-scale models to improve computational efficiency. The results show the utility of using analytical methods and reduced-order modelling in complex geological systems, as well as the value of laboratory porous medium experiments to verify results.

Method for estimating the depth of circulation of thermal and non-thermal waters in the upper crust

In this work we consider model formulations that allow better understandings of the relations between Darcy velocity and temperatures in coupled two-dimensional systems. The revised theoretical formulations are capable of accounting for the effects of heat transfer by fluid movements in horizontal and vertical directions. The models have been found useful in estimating the maximum and minimum depths of thermal and non-thermal waters in several geological units in Brazil. The best fitting values encountered are 1.8 to 2.7 km for the Paraná basin, 2.0 to 2.8 km for the Parnaiba basin, 1.6 to 2.3 km for the Amazon basins, 2.0 to 2.7 km for the San Francisco Province, 1.9 to 2.4 km for the Sergipe-Alagoas basins and 2.0 to 2.8 km for the Borborema Province. The models have also allowed estimation the average values of Péclet number and Darcy velocity for groundwater flows in these units. Note that higher horizontal velocities are associated with smaller depths of circulation. This is a natural consequence of the fact that in systems where horizontal velocities are high the quantities of vertical flows are less intense.

An Explanation to the Nusselt–Rayleigh Discrepancy in Naturally Convected Porous Media

We model hydrothermal convection using a partial differential equation formed by Darcy velocity and temperature—the velocity formulation. Using the Elder problem as a benchmark, we found that the velocity formulation is a valid model of hydrothermal convection. By performing simulations with Rayleigh numbers in the non-oscillatory regime, we show that multiple quasi-steady-state solutions can be one of the reasons that caused the Nusselt–Rayleigh discrepancy found in previous experiments. The results reveal more understandings about the nature of uncertainty of convection modes in porous media.

A Mixed Volume Element With Characteristic Mixed Volume Element for Contamination Transport Problem

Nonlinear systems of convection-dominated diffusion equations are used as the mathematical model of contamination transport problem which is an important topic in environ mental protection science. An elliptic equation defines the pressure, a convection-diffusion equation expresses the concentration of contamination, and an ordinary differential equation interprets the surface absorption concentration. The transport pressure appears in the equation of the concentration which determines the Darcy velocity and also controls the physical process. The method of conservative mixed volume element is used to solve the flow equation which improves the computational accuracy of Darcy velocity by one order. We use the mixed volume element with the characteristic to approximate the concentration. This method of characteristic not only preserves the strong computational stability at sharp front, but also eliminates numerical dispersion and nonphysical oscillation. In the present scheme, we could adopt a large step without losing accuracy. The diffusion is approximated by the mixed volume element. The concentration and its adjoint vector function are obtained simultaneously, and the locally conservative law is preserved. An optimal second order estimates in l2-norm is derived.

A fully mixed finite element method for the coupling of the Stokes and Darcy–Forchheimer problems

In this paper we introduce and analyze a fully mixed formulation for the nonlinear problem given by the coupling of the Stokes and Darcy–Forchheimer equations with the Beavers–Joseph–Saffman condition on the interface. This new approach yields non-Hilbert normed spaces and a twofold saddle point structure for the corresponding operator equation, whose continuous and discrete solvabilities are analyzed by means of a suitable abstract theory developed for this purpose. In particular, feasible choices of finite element subspaces include PEERS of the lowest order for the stress of the fluid, Raviart–Thomas of the lowest order for the Darcy velocity, piecewise constants for the pressures and continuous piecewise linear elements for the vorticity. An a priori error estimates and associated rates of convergence are derived, and several numerical results illustrating the good performance of the method are reported.

Stochastic modeling of flow and conservative transport in three-dimensional discrete fracture networks

This study presents the stochastic Monte Carlo simulation (MCS) to assess the uncertainty of flow and conservative transport in 3-D discrete fracture networks (DFNs). The MCS modeling workflow involves a number of developed modules, including a DFN generator, a DFN mesh generator, and a finite element model for solving steady-state flow and conservative transport in 3-D DFN realizations. The verification of the transport model relies on the comparison of transport solutions obtained from HYDROGEOCHEM model and an analytical model. Based on 500 DFN realizations in the MCS, the study assesses the effects of fracture intensities on the variation of equivalent hydraulic conductivity and the exhibited behaviors of concentration breakthrough curves (BTCs) in fractured networks. Results of the MCS show high variations in head and Darcy velocity near the specified head boundaries. There is no clear stationary region obtained for the head variance. However, the transition zones of nonstationarity for x-direction Darcy velocity is obvious, and the length of the transition zone is found to be close to the value of the mean fracture diameter for the DFN realizations. The MCS for DFN transport indicates that a small sampling volume in DFNs can lead to relatively high values of mean BTCs and BTC variations.

Dual Virtual Element Methods for Discrete Fracture Matrix models

The accurate description of fluid flow and transport in fractured porous media is of paramount importance to capture the macroscopic behavior of an oil reservoir, a geothermal system, or a CO2 sequestration site, to name few applications. The construction of accurate simulation models for flow in fractures is challenging due to the high ratio between a fracture’s length and width. In this paper, we present a mixed-dimensional Darcy problem which can represent the pressure and Darcy velocity in all the dimensions, i.e. in the rock matrix, in the fractures, and in their intersections. Moreover, we present a mixed-dimensional transport problem which, given the Darcy velocity, describes advection of a passive scalar into the fractured porous media. The approach can handle both conducting and blocking fractures. Our computational grids are created by coarsening of simplex tessellations that conform to the fracture’s surfaces. A suitable choice of the discrete approximation of the previous model, by virtual finite element and finite volume methods, allows us to simulate complex problems with a good balance of accuracy and computational cost. We illustrate the performance of our method by comparing to benchmark studies for two-dimensional fractured porous media, as well as a complex three-dimensional fracture geometry.