A quantitative in situ characterization of the impact of surface roughness on wettability in porous media is currently lacking. We use reservoir condition micrometer-resolution X-ray tomography ...combined with automated methods for the measurement of contact angle, interfacial curvature, and surface roughness to examine fluid/fluid and fluid/solid interfaces inside a porous material. We study oil and water in the pore space of limestone from a giant producing oilfield, acquiring millions of measurements of curvature and contact angle on three millimeter-sized samples. We identify a distinct wetting state with a broad distribution of contact angle at the submillimeter scale with a mix of water-wet and water-repellent regions. Importantly, this state allows both fluid phases to flow simultaneously over a wide range of saturation. We establish that, in media that are largely water wet, the interfacial curvature does not depend on solid surface roughness, quantified as the local deviation from a plane. However, where there has been a significant wettability alteration, rougher surfaces are associated with lower contact angles and higher interfacial curvature. The variation of both contact angle and interfacial curvature increases with the local degree of roughness. We hypothesize that this mixed wettability may also be seen in biological systems to facilitate the simultaneous flow of water and gases; furthermore, wettability-altering agents could be used in both geological systems and material science to design a mixed-wetting state with optimal process performance.
We present an application of deep generative models in the context of partial differential equation constrained inverse problems. We combine a generative adversarial network representing an a priori ...model that generates geological heterogeneities and their petrophysical properties, with the numerical solution of the partial-differential equation governing the propagation of acoustic waves within the earth’s interior. We perform Bayesian inversion using an approximate Metropolis-adjusted Langevin algorithm to sample from the posterior distribution of earth models given seismic observations. Gradients with respect to the model parameters governing the forward problem are obtained by solving the adjoint of the acoustic wave equation. Gradients of the mismatch with respect to the latent variables are obtained by leveraging the differentiable nature of the deep neural network used to represent the generative model. We show that approximate Metropolis-adjusted Langevin sampling allows an efficient Bayesian inversion of model parameters obtained from a prior represented by a deep generative model, obtaining a diverse set of realizations that reflect the observed seismic response.
•A new method for the extraction of contact angle from micro-CT images is presented.•This method is applied to the CO2–brine–water system at 10MPa and 50°C.•A distribution of contact angles is seen, ...ranging from 35° to 55° with a mean of 45°.•The range arises from surface roughness variation and contact angle relaxation.•Measurement error is analysed and found to be small for this system.
Contact angle is a principal control of the flow of multiple fluid phases through porous media; however its measurement on other than flat surfaces remains a challenge. A new method is presented for the measurement of the contact angle between immiscible fluids at the pore scale at reservoir conditions (10MPa and 50°C) inside a quarry limestone through the use of X-ray microtomography. It is applied to a super-critical CO2–brine–carbonate system by resampling the micro-CT data onto planes orthogonal to the contact lines, allowing for vectors to be traced along the grain surface and the CO2–brine interface. A distribution of contact angles ranging from 35° to 55° is observed, indicating that the CO2–brine–carbonate system is weakly water-wet. This range of contact angles can be understood as the result of contact angle hysteresis and surface heterogeneity on a range of length scales. Surface heterogeneity is examined by comparison of micro-CT results with optical thin sections and SEM images.
To evaluate the variability of multiphase flow properties of porous media at the pore scale, it is necessary to acquire a number of representative samples of the void-solid structure. While modern ...x-ray computer tomography has made it possible to extract three-dimensional images of the pore space, assessment of the variability in the inherent material properties is often experimentally not feasible. We present a method to reconstruct the solid-void structure of porous media by applying a generative neural network that allows an implicit description of the probability distribution represented by three-dimensional image data sets. We show, by using an adversarial learning approach for neural networks, that this method of unsupervised learning is able to generate representative samples of porous media that honor their statistics. We successfully compare measures of pore morphology, such as the Euler characteristic, two-point statistics, and directional single-phase permeability of synthetic realizations with the calculated properties of a bead pack, Berea sandstone, and Ketton limestone. Results show that generative adversarial networks can be used to reconstruct high-resolution three-dimensional images of porous media at different scales that are representative of the morphology of the images used to train the neural network. The fully convolutional nature of the trained neural network allows the generation of large samples while maintaining computational efficiency. Compared to classical stochastic methods of image reconstruction, the implicit representation of the learned data distribution can be stored and reused to generate multiple realizations of the pore structure very rapidly.
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The change of wettability toward more water-wet by the injection of low salinity water can improve oil recovery from porous rocks, which is known as low salinity water flooding. To ...simulate this process at the pore-scale, we propose that the alteration in surface wettability mediated by thin water films which are below the resolution of simulation grid blocks has to be considered, as observed in experiments. This is modeled by a wettability alteration model based on rate-limited adsorption of ions onto the rock surface.
The wettability alteration model is developed and incorporated into a lattice Boltzmann simulator which solves both the Navier-Stokes equation for oil/water two-phase flow and the advection-diffusion equation for ion transport. The model is validated against two experiments in the literature, then applied to 3D micro-CT images of a rock.
Our model correctly simulated the experimental observations caused by the slow wettability alteration driven by the development of water films. In the simulations on the 3D rock pore structure, a distinct difference in the mixing of high and low salinity water is observed between secondary and tertiary low salinity flooding, resulting in different oil recoveries.
We have investigated the effect of wettability of carbonate rocks on the morphologies of remaining oil after sequential oil and brine injection in a capillary‐dominated flow regime at elevated ...pressure. The wettability of Ketton limestone was altered in situ using an oil phase doped with fatty acid which produced mixed‐wet conditions (the contact angle where oil contacted the solid surface, measured directly from the images, θ=180°, while brine‐filled regions remained water‐wet), whereas the untreated rock (without doped oil) was weakly water‐wet (θ=47 ± 9°). Using X‐ray micro‐tomography, we show that the brine displaces oil in larger pores during brine injection in the mixed‐wet system, leaving oil layers in the pore corners or sandwiched between two brine interfaces. These oil layers, with an average thickness of 47 ± 17 µm, may provide a conductive flow path for slow oil drainage. In contrast, the oil fragments into isolated oil clusters/ganglia during brine injection under water‐wet conditions. Although the remaining oil saturation in a water‐wet system is about a factor of two larger than that obtained in the mixed‐wet rock, the measured brine‐oil interfacial area of the disconnected ganglia is a factor of three smaller than that of oil layers.
Key Points
Mixed‐wet conditions were obtained by chemical treatment of the carbonate rock
X‐ray micro‐tomography was used to resolve oil layers in oil‐wet pores and throats
In situ contact angle, brine‐oil curvatures and local capillary pressure were measured
•Novel finite volume simulation of two-phase flow on microCT images of porous media.•Novel upscaling method for obtaining viscous pressure drops from pore-scale forces.•Relative permeability curves ...are validated against experimental measurements.
Pore-scale forces have a significant effect on the macroscopic behaviour of multiphase flow through porous media. This paper studies the effect of these forces using a new volume-of-fluid based finite volume method developed for simulating two-phase flow directly on micro-CT images of porous media. An analytical analysis of the relationship between the pore-scale forces and the Darcy-scale pressure drops is presented. We use this analysis to propose unambiguous definitions of Darcy-scale viscous pressure drops as the rate of energy dissipation per unit flow rate of each phase, and then use them to obtain the relative permeability curves. We show that this definition is consistent with conventional laboratory/field measurements by comparing our predictions with experimental relative permeability. We present single and two-phase flow simulations for primary oil injection followed by water injection on a sandpack and a Berea sandstone. The two-phase flow simulations are presented at different capillary numbers which cover the transition from capillary fingering at low capillary numbers to a more viscous fingering displacement pattern at higher capillary numbers, and the effect of capillary number on the relative permeability curves is investigated. Overall, this paper presents a new finite volume-based methodology for the detailed analysis of two-phase flow directly on micro-CT images of porous media and upscaling of the results to the Darcy scale.
Residual non‐wetting phase saturation and wetting‐phase permeability were measured in three limestones and four sandstones ranging in porosity from 0.13 to 0.28 and in absolute permeability from 2 × ...10−15 to 3 × 10−12 m2. This paper focuses on the residual state established by waterflooding at low capillary number from minimum water saturation achieved using the porous plate technique, which yields the maximum residual under strongly water‐wet conditions. The pore coordination number and pore body‐throat aspect ratio of each rock were estimated using pore networks extracted from X‐ray microtomography images of the rocks. Residual saturation decreases with increasing porosity, with no apparent difference in magnitude between the limestones and sandstones at a given porosity. Thus intraparticle/intra‐aggregate microporosity does not significantly alter the efficiency of capillary trapping in the rocks considered presently. Residual saturation broadly decreases as conditions become less favorable for snap‐off, i.e., with decreasing pore aspect ratio and increasing coordination number. The measured residual saturations imply that capillary trapping may be an effective mechanism for storing carbon dioxide in both sandstones and carbonates provided that the systems are strongly water‐wet.
Key Points
Maximum residual saturation was measured in sandstones and limestones
High initial saturations were achieved using the porous plate method
Impact of microporosity, pore aspect ratio, and coordination number are studied
We apply an accurate numerical scheme to solve for Stokes flow directly on binarized three-dimensional rock images, such as those obtained by micro-CT imaging. The method imposes no-flow conditions ...exactly at the solid boundaries and employs an algebraic multigrid method to solve for the resultant set of linear equations. We compute the permeability of a range of consolidated and unconsolidated porous rocks; the results are comparable with those obtained using the lattice Boltzmann method and agree with experimental measurements on larger core samples. We show that the Kozeny–Carman equation can over-estimate permeability by a factor of 10 or more, particularly for the more heterogeneous systems studied. We study the existence and size of the representative elementary volume (REV) at lamina scale. We demonstrate that the REV for permeability is larger than for static properties—porosity and specific surface area—since it needs to account for the tortuosity and connectedness of the flow paths. For the carbonate samples, the REV appeared to be larger than the image size. We also study the anisotropy of permeability at the pore scale. We show that the permeability of sandpacks varies by less than 10 % in different directions. For sandstones, permeability changes by 25 % on average. However, the anisotropy of permeability in carbonates can be up to 50 %, indicating the existence of connected pores in one direction which are not connected in another.
X‐ray microtomography was used to image the shape and size of residual ganglia of supercritical CO2 at resolutions of 3.5 and 2 μm and at representative subsurface conditions of temperature and ...pressure. The capillary pressure for each ganglion was found by measuring the curvature of the CO2‐brine interface, while the pore structure was parameterized using distance maps of the pore space. The formation of the residual clusters by snap‐off was examined by comparing the ganglion capillary pressure to local pore topography. The capillary pressure was found to be inversely proportional to the radius of the largest restriction (throat) surrounding the ganglion, which validates the imbibition mechanisms used in pore‐network modeling. The potential mobilization of residual ganglia was assessed using a reformulation of both the capillary (Ncmacro) and Bond numbers (Nbmacro), rigorously based on a balance of pore‐scale forces, with the majority of ganglia remobilized at Ncmacro around 1. Buoyancy forces were found to be small in this system (Nbmacro << 1), meaning the gravitational remobilization of CO2 after residual trapping would be extremely difficult.
Key Points
In situ capillary pressure was found by measuring interfacial curvature
Trapping was examined by comparing local pore shape to capillary pressure
We present a new formulation of capillary number based on pore‐scale physics
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