The Experimental and Numerical Modeling Challenges Related to Multiphase Flows in Subsurface Resource Exploitation

1. Introduction

Scientists are continuously seeking new methods to identify and predict multiphase flows in porous media using experimental characterization, modeling, and numerical simulations to improve the efficiency of subsurface industry processes for extraction and storage processes. Due to the complexity involved, creating a digital twin has become a significant challenge for both industry and academic researchers in this field. This article aims to provide an overview of the latest findings in this area, as published in the Special Issue “Pore-Scale Multiphase Fluid Flow and Transport in Porous Media” (2022).

Exploiting subsurface resources that cannot be accessed through open-pit mining requires substantial investments and represents a significant risk. Modeling processes in such configurations—such as reservoir simulation—can aid decision-making, helping to establish optimized goals and reasonably predictable solutions, provided that a set of processes are put in place to characterize the properties and define boundaries based on physics, followed by access via exploratory wells using geology. Additionally, this involves characterizing the physical and sometimes even chemical properties of these inaccessible zones using exploratory wells, wireline logging, and core samples. The predicted data population within the volume of interest—the reservoir—thus becomes a major concern. Understanding and characterizing multiphase flows at the pore scale is therefore a key topic for those who are interested in producing hydrocarbons, storing gases, and envisaging a solution to replacing the classic characterization methods that require core-sized samples and, especially, a period of investigation of six months or more, thus immobilizing the setup and daily staff.

At the beginning of the 2000s, Keehm et al. [1] proposed simulating two-phase flows based on an X-ray microtomographic image using the Lattice Boltzmann Method (LBM) to extract relative permeabilities. Some universities, such as Imperial College, Heriot Watt, Stanford, and ANU, and several spin-offs such as Ingrain (USA) and Numerical Rock (Norway) were pioneers in this new technology [2,3].

The success was swift, and increasingly larger companies became interested in this field—either by acquiring spin-offs or by entering the business themselves. This trend eventually attracted major service companies, large multinationals, and national corporations.

Originally, the goal was to create a digital twin of a specific type of flow, conditioned by a process within a rock sample [4,5,6,7]. It has captivated the entire porous media physics community, with industrial applications currently being in development. However, numerous challenges (experimental and numerical) remain, and overcoming these obstacles to unlock current limitations is critical for any form of industrialization, regardless of the method used.

Today, we can identify four challenges that represent the four essential building blocks for constructing an ideal industrial workflow. The first of these blocks involves microfluidics and managing reference experiments, which are imaged to compare with computational codes [8]. The second challenge concerns data acquisition and processing. These two elements are inseparable, because in understanding the physical tomography system, reconstruction artifacts are closely linked; therefore, adopting an image processing approach that is based on this knowledge (such as physical filters, segmentation, etc.) allows for optimization of this phase, which is strategic in data conditioning. Next comes the digital component, starting with the meshing problem, particularly the alignment of the mesh with the pore space [9], followed by calculation convergence, scalability, and the strengths and weaknesses of the flow simulation methods that can be used: Direct Numerical Simulation [10], Lattice Boltzmann Methods [11], and pore network models [12].

2. Review of Recent Advances

This scientific field therefore requires mastering a set of essential skills to reliably predict effective properties and quantify the propagation of resulting errors. Guibert et al. [13] demonstrated the impact of human inference on error and proposed a machine learning method that achieves high reproducibility and convergence of results regarding the influence of imaging methods on the calculation of effective properties. The authors have previously shown the impact of the voxel size and meshing on the convergence of the simulations with a proposed method to quantify errors [9], and here, they succeeded in finding an efficient method to facilitate image processing with four minerals and brine and CO2 phases, limiting the divergences of five effective properties: the porosity, tensor of permeability, tortuosity, specific surface area, and coordinance. The image quality that is achieved by changing the morphology of the pore space (shape)—in particular the surface roughness and topology (connectedness)—by eliminating the smallest pores is of prime interest and is the main factor affecting in situ analysis or Digital Rock Physics.

Mukherjee et al. [14] proposed a qualitative sensitivity analysis based on a machine learning approach, highlighting the relationship between the fluid–fluid interfacial area, phase saturation, connectivity, and relative permeabilities. This approach aligns with the flow sensitivity in porous media, providing valuable insights into first- and potentially second-order phenomena that are critical for any modeling efforts. It could also pave the way for developing a semi-quantitative method to evaluate relative permeability. In the short term, this study is expected to improve the correlative behaviors of a two-phase flow, but it also offers a methodology that enables us to enhance the predefined configurations of the pore network models by incorporating a set of baseline configurations that better represent two-phase hydraulic conductivities.

Zhang et al. [15] proposed a pore network model to investigate the structure, morphology, and multiphase flow properties of carbonate rocks. Three distinct carbonate rock samples were analyzed, each featuring unique pore and throat distributions, capillary pressures, and normalized permeabilities. High-resolution 3D X-ray microscope and experimental measurements were used to validate the findings. These simulated capillary pressure curves matched well with measured MICP data without requiring parameter adjustments, such as of the contact angle or pore size, emphasizing the importance of a sufficient image resolution. A higher image resolution significantly impacted the accuracy of the relative permeability curves, as it allowed for the identification of the smaller pores and throats that govern multiphase flow. Increasing contact angle variations demonstrated a pronounced effect of wettability on relative permeability in water-wet and oil–water systems. In mixed-wet systems, the fraction of oil-wet pores and throats strongly influenced the permeability curves.

With a two-phase-flow pore network model, Zhang et al. [15] found similar simulated and scaled Mercury Intrusion Pressures for carbonates. The PNM method has also been tested for relative permeability curves and has the advantage of being able to handle very large volumes of data; however, two-phase flow situations are defined in advance. This approach is currently the only one that allows for experimental–theoretical comparisons, making it a highly interesting and effective modeling technique.

Also focusing on two-phase flows, Ait Abderrahmane et al. [16] conducted a study using a radial geometry to model instabilities in this configuration corresponding to a well and to prioritize the mechanisms that occur sequentially in this geometry. The goal was to explore the impact of inertia on the onset and propagation of fingering instability in a circular Hele-Shaw cell using miscible fluids. The analysis explored how inertia affects the finger morphology, displacement efficiency, and mixing area under varying log-mobility–viscosity ratios and Reynolds and Peclet numbers, based on a modified Darcy’s model. The obtained results demonstrated that an instability occurs when the log-mobility–viscosity ratio (R) becomes consequent. The authors discussed the inertia of the Reynolds and Peclet numbers and mixing effects for dimensionless numbers, as well as the impact on the displacement efficiency of different mobility–viscosity ratios. The simulations suggested that inertia improves fingering instability at low R values but reduces it at high R values. Additionally, using Darcy’s model, the authors showed that it might impact recovery factors in Enhanced Oil Recovery operations.

Gong et al. [17] examined the geometric and topological properties of sandstone samples, focusing on several topological and morphological properties such as the pore size, shape factor, coordination number, connectivity density, and tortuosity, which were derived from the representative elementary volume (REV) of each sample. The sandstones were categorized into two groups based on their porosity: a high-porosity group (including Bentheimer, Berea, Boise, Doddington, and Gildehauser sandstones) and a low-porosity group (including Clashach, Fontainebleau, and Stainton sandstones).

Both groups displayed highly triangular pores and a high degree of isotropy. However, the high-porosity sandstones exhibited a broader range of pore sizes compared with the low-porosity group. In contrast, the low-porosity group showed a higher global aspect ratio, suggesting the presence of bottleneck-like pores.

The topological properties demonstrated a strong dependence on porosity. High-porosity sandstones are characterized by larger coordination numbers, higher connectivity densities, and lower tortuosities compared to their low-porosity counterparts. A hierarchy of the impact of Minkovski’s functionals on effective transport properties has been highlighted. In addition to the Minkovski’s functionals of a sandstone based on X-ray microtomography images, Gong et al. [17] also calculated the pore and pore throat distributions and the shape factor, as defined by Mason et al. [18], with a good ability to correlate certain pore types.

The striking parallel that was observed by Su et al. [19] highlights the relationship between pore network heterogeneity and sandstone storage and transport capabilities, providing valuable insights into the storage and transport properties of tight reservoirs. The fractal dimensions demonstrated that pore network heterogeneity negatively correlates with storage capacity: less heterogeneous networks exhibit higher storage potentials. However, the impact of heterogeneity on transport capability is more nuanced. Weak correlations between fractal dimensions and transport-related parameters suggest a more complex interplay, indicating that transport efficiency is not only determined by pore network uniformity between MICP results. In addition, laws that are indexed to the fractal dimensions of porous surfaces in tight reservoirs lead to complex morphological considerations.

The study analyzed the pore structure of tight reservoirs in the Lucaogou Formation (Junggar Basin) using Mercury Intrusion Capillary Porosimetry (MICP) and X-ray Computed Tomography (X-ray µ-CT). Tight reservoirs exhibited diverse lithologies with varying porosities and permeabilities. The MICP analyses revealed a unimodal distribution of pore sizes, with significant variations in peak radius. The fractal dimensions, calculated using Swanson’s parameter, ranged from 2.05 to 2.37 for pores with radii below the apex radius. µ-CT images showed pores that were mostly smaller than 5 µm and throats below 1 µm, characterized by irregular shapes and unimodal size distributions. Networks with high coordination numbers and low tortuosity displayed pore volumes that were skewed toward larger sizes. Pores that were connected by throats with radii that were larger than Rapex accounted for up to 50% of the storage volume and dominated the flow pathways. For reservoirs with porosities >5%, the transport capacity increased with the storage capacity. Pore network heterogeneity (fractal dimension) negatively correlated with storage capacity, while its impact on transport capacity was complex and weakly correlated.

Vega et al. [20] explored using the analysis of a fracture network in shales from an Image-Based Fractal Dimension Estimation.

The fractal analysis demonstrated that the connectivity decreases with the system scale when fractures are caused by hydraulic or natural fracturing. In contrast, thermal maturation leads to a completely different process, showing a predominance of connectivity in larger fractures over smaller ones. This effect increases with the scale of the system. In the long term, this study could help improve the understanding and modeling of the connectivity between matrices and fractures through a highly localized approach. The distribution and amount of organic matter in shale significantly influence the formation and clustering of fracture networks when the rock matures, naturally or artificially. In this study, samples with high organic content showed large fractures that were concentrated within their laminations.

3. Conclusions

The articles contributing to this Special Issue, “Pore-Scale Multiphase Fluid Flow and Transport in Porous Media”, contribute to the recent progress in Digital Rock Physics.

The articles contribute to various technical and scientific aspects of Digital Rock Physics (DRP), including image processing and the analysis of geometric properties to establish effective transport or geomechanical property rules in porous media, starting from the pore-scale level. The modeling demonstrates its reliability in primary drainage sequences, including intermediate wettability, thereby addressing challenges to the analytical or modeling capabilities in the physics of porous media.

The reader of this Special Issue can find a description of methods for enhancing the knowledge, characterization, and modeling of multiphase flows in porous media. The collected articles will allow the reader to enhance their understanding of the underlying mechanisms and the quantification of the transport properties connecting certain experimental and numerical methods.