Johan Olav Helland

We present a workflow, based on level-set and lattice-Boltzmann methods, for numerical estimation of relative permeability and capillary pressure curves with hysteresis in capillary-dominated flow on segmented 3D rock images. Calculation of relative permeability from rock images has commonly been limited to studies of the bounding hysteresis loop and conventional porous media. Here, we demonstrate the workflow on an almost unexplored case, a consolidated sandstone with low pore-to-throat aspect ratio, and obtain a complex relative permeability hysteresis behavior, consistent with the few studies available for such media. The pore-scale simulations include primary drainage, followed by the main bounding hysteresis loop and scanning curves for secondary drainage and secondary imbibition. We also explore the impact of initial saturation after primary drainage on hysteresis and phase trapping. The relative permeability hysteresis is larger for the non-wetting phase than for the wetting phase, yet the extent of both decreases with increasing initial wetting-phase saturation. For the non-wetting-phase relative permeability, imbibition and drainage curves may cross, while scanning curves cross each other and exhibit a more significant hysteresis than the bounding loop. The role of trapped ganglia makes secondary processes different from primary. The behavior complies with hysteresis in phase connectivity, in which snap-off/coalescence breaks/recovers pathways. The results deviate significantly from the nested hysteresis loops seen for unconsolidated media and show that hysteresis in scanning curves cannot be neglected, indicating that flexible machine learning methods are better suited approaches than standard hysteresis models to implement this complex relative permeability behavior in reservoir simulators.

Underground natural gas storage (UNGS) is a means to store energy temporarily for later recovery and use. In such storage operations, carbon dioxide (CO₂) can be injected as cushion gas to improve the operating efficiency of the working gas and then be permanently stored in the same reservoir. A potential obstacle for widespread use of this technology is that the mixing of the different gases can lead to undesired CO₂ production. Herein, we use a two-component flow model to simulate injection and withdrawal periods of methane (CH₄) in idealized reservoirs containing CO₂. First, we simulate cases with a single well for both CH₄ injection and production. From 1200 simulations with systematic variation of reservoir temperature, porosity, permeability, height, and injection time, we find that the reservoir height and permeability have the most significant impact on the production time until the well stream reaches 1% mole fraction of CO₂. In another set of simulations, we investigate the impact of well spacing in seasonal gas storage scenarios with separate wells for CH₄ injection and production, while CO₂ injection occurs from a third well. Based on the simulated data we construct artificial neural networks (ANNs) that describe the relations between the varied input parameters and the production time of CH₄, well-block mole fraction and pressure. We conclude that trained and validated ANN models are useful tools to optimize important parameters for UNGS operations, including well positioning, with the aim at maximizing the amounts of delivered gas.

Multiphase flow in porous media often occurs with the formation and coalescence of fluid ganglia. Accurate predictions of such mechanisms in complex pore geometries require simulation models with local mass conservation and with the option to improve resolution in areas of interest. In this work, we incorporate patch-based, structured adaptive mesh refinement capabilities into a method for local volume conservation that describes the behaviour of disconnected fluid ganglia during level set simulations of capillary-controlled displacement in porous media. We validate the model against analytical solutions for three-phase fluid configurations in idealized pores containing gas, oil, and water, by modelling the intermediate-wet oil layers as separate domains with their volumes preserved. Both the pressures and volumes of disconnected ganglia converge to analytical values with increased refinement levels of the adaptive mesh. Favourable results from strong and weak scaling tests emphasize that the number of patches per processor and the total number of patches are important parameters for efficient parallel simulations with adaptive mesh refinement. Simulations of two-phase imbibition and three-phase gas invasion on segmented 3D images of water-wet sandstone show that adaptive mesh refinement has the highest impact on three-phase displacements, especially concerning the behaviour of the conserved, intermediate-wet phase.

Ostwald ripening of gas bubbles is a thermodynamic process for mass transfer, which is important for both foam enhanced oil recovery and geological CO₂ storage. We present a methodology for simulating Ostwald ripening of gas ganglia surrounded by liquid in arbitrary pore geometries. The method couples a conservative level set model for capillary-controlled displacement and a ghost-bubble technique that calculates mass transfer based on difference in chemical potentials. The methodology is implemented in a software framework for parallel computations. As a validation of the model, we show that simulations of bubble ripening in a pore throat connecting two pore bodies are consistent with previously reported trends in similar geometries. Then we investigate the impact of gas type, compressibility factor, and local capillary pressure on gas-bubble ripening in various water-wet pore geometries. The results confirm that gas solubility and compressibility factor are proportional to the rate of mass transfer. Our simulations suggest that Ostwald ripening has largest impact in heterogeneous or fractured porous structures where differences in gas-bubble potentials are high. However, if the liquid separating the gas bubbles is also a disconnected phase, which can happen in intermediate-wet porous media, the resulting local capillary pressure can limit the coarsening and stabilise smaller bubbles. Finally, we simulated Ostwald ripening on a 3-D pore-space image of sandstone containing a residual gas/water configuration after imbibition. Characterization of gas-bubble morphology during the coarsening shows that large ganglia get more ramified at the expense of small spherical ganglia that cease to exist.

We present a discrete‐domain approach to three‐phase displacements and hysteresis in porous media. In this method, constrained energy minimization leads to evolution equations for local saturations that describe a wide range of three‐phase displacements, including pressure‐ and saturation‐controlled displacement with or without preservation of one of the defending phases. Under action of global saturation constraints, irreversible displacements lead to significant fluid redistribution, as well as abrupt fluctuations of both the three‐phase saturation paths and the corresponding capillary pressures. These features are a consequence of Haines jumps with cooperative behavior that occur at pore scale in three‐phase systems. The method is a fast and convenient way to investigate hysteresis behavior of three‐phase displacement in porous media. As free energy is an extensive property, the framework links pore and core scales and provide a means to achieve upscaled three‐phase displacements for higher‐order hysteresis loops, which rarely is obtained in time‐consuming three‐phase measurements or pore‐scale simulations.