Generalized network modelling of two-phase flow in a water-wet and mixed-wet reservoir sandstone: Uncertainty and validation with experimental data

We use a generalized pore network model in combination with image-based experiments to understand the parameters that control upscaled flow properties. The study is focued on water-flooding through a reservoir sandstone under water-wet and mixed-wet conditions. A set of sensitivity studies is presented to quantify the role of wettability, pore geometry, initial and boundary conditions as well as a selection of model parameters used in the computation of fluid volumes, curvatures and flow and electrical conductivities. We quantify the uncertainty in the model predictions, which match the measured relative permeability and capillary pressure within the uncertainty of the experiments. Our results show that contact angle, initial saturation, image quality and image processing algorithm are amongst the parameters which introduce the largest variance in the predictions of upscaled flow properties for both mixed-wet and water-wet conditions

Pore-scale modeling of two-phase flow: a comparison of the generalized network model to direct numerical simulation

Despite recent advances in pore-scale modeling of two-phase flow through porous media, the relative strengths and limitations of various modeling approaches have been largely unexplored. In this work, two-phase flow simulations from the generalized network model (GNM) [Phys. Rev. E 96, 013312 (2017)2470-004510.1103/PhysRevE.96.013312; Phys. Rev. E 97, 023308 (2018)2470-004510.1103/PhysRevE.97.023308] are compared with a recently developed lattice-Boltzmann model (LBM) [Adv. Water Resour. 116, 56 (2018)0309-170810.1016/j.advwatres.2018.03.014; J. Colloid Interface Sci. 576, 486 (2020)0021-979710.1016/j.jcis.2020.03.074] for drainage and waterflooding in two samples-a synthetic beadpack and a micro-CT imaged Bentheimer sandstone-under water-wet, mixed-wet, and oil-wet conditions. Macroscopic capillary pressure analysis reveals good agreement between the two models, and with experiments, at intermediate saturations but shows large discrepancy at the end-points. At a resolution of 10 grid blocks per average throat, the LBM is unable to capture the effect of layer flow which manifests as abnormally large initial water and residual oil saturations. Critically, pore-by-pore analysis shows that the absence of layer flow limits displacement to invasion-percolation in mixed-wet systems. The GNM is able to capture the effect of layers, and exhibits predictions closer to experimental observations in water and mixed-wet Bentheimer sandstones. Overall, a workflow for the comparison of pore-network models with direct numerical simulation of multiphase flow is presented. The GNM is shown to be an attractive option for cost and time-effective predictions of two-phase flow, and the importance of small-scale flow features in the accurate representation of pore-scale physics is highlighted

Automatic measurement of contact angle in pore-space images

A new approach is presented to measure the in-situ contact angle (θ) between immiscible fluids, applied to segmented pore-scale X-ray images. We first identify and mesh the fluid/fluid and fluid/solid interfaces. A Gaussian smoothing is applied to this mesh to eliminate artifacts associated with the voxelized nature of the image, while preserving large-scale features of the rock surface. Then, for the fluid/fluid interface we apply an additional smoothing and adjustment of the mesh to impose a constant curvature. We then track the three-phase contact line, and the two vectors that have a direction perpendicular to both surfaces: the contact angle is found from the dot product of these vectors where they meet at the contact line. This calculation can be applied at every point on the mesh at the contact line. We automatically generate contact angle values representing each invaded pore-element in the image with high accuracy. To validate the approach, we first study synthetic three-dimensional images of a spherical droplet of oil residing on a tilted flat solid surface surrounded by brine and show that our results are accurate to within 3° if the sphere diameter is 2 or more voxels. We then apply this method to oil/brine systems imaged at ambient temperature and reservoir pressure (10MPa) using X-ray microtomography (Singh et al., 2016). We analyse an image volume of diameter approximately 4.6  mm and 10.7  mm long, obtaining hundreds of thousands of values from a dataset with around 700 million voxels. We show that in a system of altered wettability, contact angles both less than and greater than 90° can be observed. This work provides a rapid method to provide an accurate characterization of pore-scale wettability, which is important for the design and assessment of hydrocarbon recovery and carbon dioxide storage

Dynamic fluid configurations in steady-state two-phase flow in Bentheimer sandstone

Fast synchrotron tomography is used to study the impact of capillary number, Ca, on fluid configurations in steady-state two-phase flow in porous media. Brine and n-decane were co-injected at fixed fractional flow, fw=0.5, in a cylindrical Bentheimer sandstone sample for a range of capillary numbers 2.1×10−7≤Ca≤4.2×10−5, while monitoring the pressure differential. As we have demonstrated in Gao et al. [Phys. Rev. Fluids 5, 013801 (2020)], dependent on Ca, different flow regimes have been identified: at low Ca only fixed flow pathways exist, while after a certain threshold dynamic effects are observed resulting in intermittent fluctuations in fluid distribution which alter fluid connectivity. Additionally, the flow paths, for each capillary number, were imaged multiple times to quantify the less frequent changes in fluid occupancy, happening over timescales longer than the duration of our scans (40 s). In this paper we demonstrate how dynamic connectivity results from the interaction between oil ganglia populations. At low Ca connected pathways of ganglia are fixed with time-independent small, medium, and large ganglia populations. However, with an increase in Ca we see fluctuations in the size and numbers of the larger ganglia. With the onset of intermittency, fluctuations occur mainly in pores and throats of intermediate size. When Ca is further increased, we see rapid changes in occupancy in pores of all size. By combining observations on pressure fluctuations and flow regimes at various capillary numbers, we summarize a phase diagram over a range of capillary numbers for the wetting and nonwetting phases, Caw and Canw, respectively, to quantify the degree of intermittent flow. These different regimes are controlled by a competition between viscous forces on the flowing fluids and the capillary forces acting in the complex pore space. Furthermore, we plot the phase diagrams of the transition from Darcy flow to intermittent flow over a range of Reynolds and Weber numbers for the wetting and nonwetting phases to evaluate the balance among capillary, viscous, and inertial forces, incorporating data from the literature. We demonstrate that pore geometry has a significant control on flow regime

A numerical model of two-phase flow at the micro-scale using the volume-of-fluid method

This study presents a simple and robust numerical scheme to model two-phase flow in porous media where capillary forces dominate over viscous effects. The volume-of-fluid method is employed to capture the fluid-fluid interface whose dynamics is explicitly described based on a finite volume discretization of the Navier–Stokes equations. Interfacial forces are calculated directly on reconstructed interface elements such that the total curvature is preserved. The computed interfacial forces are explicitly added to the Navier–Stokes equations using a sharp formulation which effectively eliminates spurious currents. The stability and accuracy of the implemented scheme is validated on several two- and three-dimensional test cases, which indicate the capability of the method to model two-phase flow processes at the micro-scale. In particular we show how the co-current flow of two viscous fluids leads to greatly enhanced flow conductance for the wetting phase in corners of the pore space, compared to a case where the non-wetting phase is an inviscid gas

The impact of bimodal pore size distribution and wettability on relative permeability and capillary pressure in a microporous limestone with uncertainty quantification

Pore-scale X-ray imaging combined with a steady-state flow experiment was used to study the displacement processes during waterflooding in an altered-wettability carbonate, Ketton limestone, with more than two orders of magnitude difference in pore size between macropores and microporosity. We simultaneously characterized macroscopic and local multiphase flow parameters, including relative permeability, capillary pressure, wettability, and fluid occupancy in pores and throats. An accurate method was applied for porosity and fluid saturation measurements using greyscale based differential imaging without image segmentation. The relative permeability values were corrected by considering the measured saturation profile along the sample length to account for the so-called capillary end effect. The behaviour of relative permeability and capillary pressure was compared to other measurements in the literature to demonstrate the combined effects of wettability and pore structure. Typical oil-wet behaviour in resolvable macropores was measured from contact angle, fluid occupancy and curvature. The capillary pressure was negative while the oil relative permeability dropped quickly as oil was drained to low saturation and flowed through connected oil layers. Brine initially largely flowed through water-wet microporosity, and then filled the centre of large oil-wet pore bodies. Thus, the brine relative permeability remained exceptionally low until brine formed a connected flow path in the macropores leading to a substantial increase in relative permeability. Overall, this work demonstrates that not only wettability but also pore size distribution and microporosity have significant impact on displacement processes

Pore-scale imaging and analysis of low salinity waterflooding in a heterogeneous carbonate rock at reservoir conditions

X-ray micro-tomography combined with a high-pressure high-temperature flow apparatus and advanced image analysis techniques were used to image and study fluid distribution, wetting states and oil recovery during low salinity waterflooding (LSW) in a complex carbonate rock at subsurface conditions. The sample, aged with crude oil, was flooded with low salinity brine with a series of increasing flow rates, eventually recovering 85% of the oil initially in place in the resolved porosity. The pore and throat occupancy analysis revealed a change in fluid distribution in the pore space for different injection rates. Low salinity brine initially invaded large pores, consistent with displacement in an oil-wet rock. However, as more brine was injected, a redistribution of fluids was observed; smaller pores and throats were invaded by brine and the displaced oil moved into larger pore elements. Furthermore, in situ contact angles and curvatures of oil–brine interfaces were measured to characterize wettability changes within the pore space and calculate capillary pressure. Contact angles, mean curvatures and capillary pressures all showed a shift from weakly oil-wet towards a mixed-wet state as more pore volumes of low salinity brine were injected into the sample. Overall, this study establishes a methodology to characterize and quantify wettability changes at the pore scale which appears to be the dominant mechanism for oil recovery by LSW

Preferential Paths of Air-water Two-phase Flow in Porous Structures with Special Consideration of Channel Thickness Effects.

Accurate understanding and predicting the flow paths of immiscible two-phase flow in rocky porous structures are of critical importance for the evaluation of oil or gas recovery and prediction of rock slides caused by gas-liquid flow. A 2D phase field model was established for compressible air-water two-phase flow in heterogenous porous structures. The dynamic characteristics of air-water two-phase interface and preferential paths in porous structures were simulated. The factors affecting the path selection of two-phase flow in porous structures were analyzed. Transparent physical models of complex porous structures were prepared using 3D printing technology. Tracer dye was used to visually observe the flow characteristics and path selection in air-water two-phase displacement experiments. The experimental observations agree with the numerical results used to validate the accuracy of phase field model. The effects of channel thickness on the air-water two-phase flow behavior and paths in porous structures were also analyzed. The results indicate that thick channels can induce secondary air flow paths due to the increase in flow resistance; consequently, the flow distribution is different from that in narrow channels. This study provides a new reference for quantitatively analyzing multi-phase flow and predicting the preferential paths of immiscible fluids in porous structures