Reservoir characterization by push-pull tests employing Kinetic Interface Sensitive tracers

A 6M digital twin for modeling and simulation in subsurface reservoirs

Modeling multiphase flow in porous structures remains a challenge due to the complexity of handling multiple interfaces. This paper presents a one-domain pore-resolved simulation approach for immiscible two-phase flows in porous media, using a monolithic fluid–solid coupling framework to implicitly consider the existence of solid objects, with the fluid–fluid interfaces captured through solving an algebraic volume of fluid equation. Fluid interfacial tension is considered by integrating a continuum surface force, and the wall wettability condition is imposed by modifying the contact angle of the fluid interface at the embedded solid surface. The resulting equations are simple and stable, as there are no empirical models or parameters involved for the interface representation. This approach has been validated through performing a series of test-case simulations, including capillary-dominated flow, capillary rise with gravity, Taylor film formation, and finally two-phase flow in a heterogeneous porous structure. The numerical approach is demonstrated to be well suited for investigating pore-scale two-phase flows in realistic porous media.

This study aims to bridge length scales in immiscible multiphase flow simulation by connecting two published governing equations at the pore-scale and continuum-scale through a novel validation framework. We employ Niessner and Hassnaizadeh's [“A model for two-phase flow in porous media including fluid-fluid interfacial area,” Water Resour. Res. 44(8), W08439 (2008)] continuum-scale model for multiphase flow in porous media, combined with the geometric equation of state of McClure et al. [“Modeling geometric state for fluids in porous media: Evolution of the Euler characteristic,” Transp. Porous Med. 133(2), 229–250 (2020)]. Pore-scale fluid configurations simulated with the lattice-Boltzmann method are used to validate the continuum-scale results. We propose a mapping from the continuum-scale to pore-scale utilizing a generalized additive model to predict non-wetting phase Euler characteristics during imbibition, effectively bridging the continuum-to-pore length scale gap. Continuum-scale simulated measures of specific interfacial area, saturation, and capillary pressure are directly compared to up-scaled pore-scale simulation results. This research develops a numerical framework capable of capturing multiscale flow equations establishing a connection between pore-scale and continuum-scale simulations.

Purpose – This paper aims to present a computationally efficient finite element model for the simulation of isothermal immiscible two-phase flow in a rigid porous media with a particular application to CO2 sequestration in underground formations. Focus is placed on developing a numerical procedure, which is effectively mesh-independent and suitable to problems at regional scales. Design/methodology/approach – The averaging theory is utilized to describe the governing equations of the involved unsaturated multiphase flow. The level-set (LS) method and the extended finite element method (XFEM) are utilized to simulate flow of the CO2 plume. The LS is employed to trace the plume front. A streamline upwind Petrov-Galerkin method is adopted to stabilize possible occurrence of spurious oscillations due to advection. The XFEM is utilized to model the high gradient in the saturation field front, where the LS function is used for enhancing the weighting and the shape functions. Findings – The capability of the proposed model and its features are evaluated by numerical examples, demonstrating its accuracy, stability and convergence, as well as its advantages over standard and upwind techniques. The study showed that a good combination between a mathematical model and a numerical model enables the simulation of complicated processes occurring in complicated and large geometry using minimal computational efforts. Originality/value – A new computational model for two-phase flow in porous media is introduced with basic requirements for accuracy, stability, and convergence, which are met using relatively coarse meshes.

Immiscible two-phase flow in porous media with mixed wet conditions was examined using a capillary fiber bundle model, which is analytically solvable, and a dynamic pore network model. The mixed wettability was implemented in the models by allowing each tube or link to have a different wetting angle chosen randomly from a given distribution. Both models showed that mixed wettability can have significant influence on the rheology in terms of the dependence of the global volumetric flow rate on the global pressure drop. In the capillary fiber bundle model, for small pressure drops when only a small fraction of the tubes were open, it was found that the volumetric flow rate depended on the excess pressure drop as a power law with an exponent equal to 3/2 or 2 depending on the minimum pressure drop necessary for flow. When all the tubes were open due to a high pressure drop, the volumetric flow rate depended linearly on the pressure drop, independent of the wettability. In the transition region in between where most of the tubes opened, the volumetric flow depended more sensitively on the wetting angle distribution function and was in general not a simple power law. The dynamic pore network model results also showed a linear dependence of the flow rate on the pressure drop when the pressure drop is large. However, out of this limit the dynamic pore network model demonstrated a more complicated behavior that depended on the mixed wettability condition and the saturation. In particular, the exponent relating volumetric flow rate to the excess pressure drop could take on values anywhere between 1.0 and 1.8. The values of the exponent were highest for saturations approaching 0.5, also, the exponent generally increased when the difference in wettability of the two fluids were larger and when this difference was present for a larger fraction of the porous network.

We present a review of pore-scale simulations of immiscible fluid transport with focus on two of the most popular approaches: lattice Boltzmann modeling for direct simulations on digital models of the pore space and simulations on network models extracted from the pore space. This review focuses on covering basic theory and implementation strategies and gives the readers input and motivation to start their own pore-scale simulations and relate them to realistic porous media. We present a review of recent and relevant applications and how a digital workflow that combines advanced pore-scale imaging and simulations can give very useful input to different fields of science and industry, including reservoir characterization. Given the large span in methods and applications, this review does not aim to cover all methods or applications. However, it covers popular methods and describes to some extent their applicability to different types of transport problems.

In this paper, the lattice-Boltzmann method is developed to investigate the behavior of isothermal two-phase fluid flow in porous media. The method is based on the Shan-Chen multiphase model of nonideal fluids that allow coexistence of two phases of a single substance. We reproduce some different idealized situations (phase separation, surface tension, contact angle, pipe flow, and fluid droplet motion, et al) in which the results are already known from theory or laboratory measurements and show the validity of the implementation for the physical two-phase flow in porous media. Application of the method to fluid intrusion in porous media is discussed and shows the effect of wettability on the fluid flow. The capability of reproducing critical flooding phenomena under strong wettability conditions is also proved.

Use of preconditioned bi-conjugate gradient method in modeling two-phase fluid flow in porous media

A lattice Boltzmann study of viscous coupling effects in immiscible two-phase flow in porous media

We compute the fluid flow time-correlation functions of incompressible, immiscible two-phase flow in porous media using a 2D network model. Given a properly chosen representative elementary volume, the flow rate distributions are Gaussian and the integrals of time correlation functions of the flows are found to converge to a finite value. The integrated cross-correlations become symmetric, obeying Onsager's reciprocal relations. These findings support the proposal of a non-equilibrium thermodynamic description for two-phase flow in porous media.

1.1 Motivation This chapter focusses on the description and modeling of mass transfer processes occurring between two fluid phases in a porous medium. The principle underlying physical process comprises a transport of particles from one phase to the other phase. This process takes place across fluid–fluid interfaces (see Fig. 1) and may constitute evaporation, dissolution, or condensation, for example. Such mass transfer processes are crucial in many applications involving flow and transport in porous media. Major examples are found in soil science (where the evaporation from soils is of interest), soil and groundwater remediation (like thermally-enhanced soil vapor extraction where dissolution, evaporation, and condensation play a role), storage of carbon dioxide in the subsurface (where the dissolution of carbon dioxide in the surrounding groundwater is a crucial storage mechanism), CO2-enhanced oil recovery (where after primary and secondary recovery, carbon dioxide is injected into the reservoir in order to mobilize an additional 8-20 per cent of oil), and various industrial porous systems (such as certain types of fuel cells). Let us have a closer look at a few of these applications and identify where interphase mass transfer is relevant. Four specific examples are shown in Fig. 2 and briefly described.

The locations of a significant number of industrial facilities, landfills, and almost all mineral ore bodies are characterized by high in situ stresses and fractures, which act as flow paths for fluids underground. Toxic chemical transport is one of the main reasons for loss in groundwater quality and reactive transport modelling is an important tool necessary for predicting and controlling their fate. Modelling reactive transport has largely been achieved using the hydrodynamic transport equation, with an additional reaction and/or decay term. To date, however, most approaches to modelling reactive transport often consider an already existing mixture (multi-phase and/or multi-species) undergoing such transport in homogeneous media. The motivation of this research is to use the transport solutions of two single-phase species in homogeneous media to describe the reactive transport of two species before and after mixing, due to formation heterogeneity. This practical scenario can be observed where regional-scale fracture systems transporting pollution from spatially isolated source locations cause the mixing of chemical pollutants from different source origins due to fracture–fracture flux across two or more intersecting fractures. Here, the authors present a framework for determining the exact solution of the reactive groundwater transport model by the coupling of the homogeneous and non-homogeneous model sub-components. The solution of the homogeneous sub-component is obtained using the Laplace transform. The exact solution of the proposed non-homogeneous equation is obtained analytically using Green’s function method. Further, the two equations are numerically discretized using the Crank–Nicolson scheme and their stability conditions are also established. Instead of presenting the specific solution of a particular case study scenario, a general model to approximate the contribution of reactive processes in the system is presented. It is found that the fate and contribution of each species within the system is captured by the model for which the reaction kinetics and equilibrium partitioning between liquid and solid phases are all assumed to be linear first order.

The paper presents a model for two-phase flow, where liquid and gas are treated as one fluid with variable density. A one-component fluid and the diffuse-interface model for two-phase flow are assumed at pore level. The wetting properties of the fluid are described by the Cahn theory. Macroscopic equations are deduced in the framework of the Marle formalism. It is shown that two-phase flow in porous media can be described by the Cahn–Hilliard equation for the mass density. The concept of relative permeability is not needed. For non-neutral wetting, it is shown that a capillary pressure exists but that it is not a function of state. Two numerical illustrations are presented, one of them showing that the model is, at least in a simple steady-state situation, compatible with the generalized two-continuum model.

This work reviews the transient two-phase flow in porous media with engineering applications in Geotechnics. It initially overviews constitutive relationships, conventional theories, and experiments. Then, corresponding limitations are discussed according to conflicting observations and multiphase interfacial dynamics. Based on those findings, the dynamic nonequilibrium effects were so defined, which could also be abbreviated as dynamic/transient effects. Four advanced theories have already been developed to resolve these effects. This review collects them and discusses their pros and cons. In addition, this work further reviews the state-of-art in terms of experimental methods, influential factors in dynamic/transient effects, and modelling performance, as well as micromodel and numerical methods at pore-scale. Last, the corresponding geotechnical applications are reviewed, discussing their applicability in effective stress, shear strength, and deformation. Finally, the entire review is briefed to identify research gaps in Geotechnics.

Monte Carlo simulation of two-phase flow in porous media: Invasion with two invaders and two defenders