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A global energy minimization criterion based on Griffith's theory is introduced for the node-splitting lattice spring model. The fracture criterion is computed by both direct numerical simulations of energy release rate G and through a J-integral formulation for comparison and validation. For mode I fractures, the standard implementation of J-integral formulation yields very good estimations of the energy release rate, but for mixed mode fracture the estimations deviates from the direct calculated energy release rate. The reasons for this discrepancy are elucidated and an approach to best approximate the J value is given. This method is compared with the more standard maximum tip stress threshold crack criterion, and shows a much better prediction of the energy release rate and is more robust under grid refinement. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. Article highlights: A level set approach to Ostwald ripening that handles arbitrary pore geometries and gas-ganglia configurations. The role of a disconnected liquid phase in Ostwald ripening is to stabilize more bubbles and prolong bubble lifetime. During coarsening in sandstone spherical bubbles dissolve while large ganglia grow and develop a more ramified structure. [ABSTRACT FROM AUTHOR]

Multiphase flow simulations on imaged porous rock structures require numerical methods that are accurate and robust when applied on complex geometries. A key element in this context is to investigate how simulations behave under grid refinement. In this work, we couple an existing software for structured adaptive mesh refinement (AMR) and parallelism to a previously developed level set method for capillary-controlled displacement on the pore scale. The level set method accounts for wettability by using different evolution velocities in pore and solid space rather than implementing it as a boundary condition on the pore walls. We perform simulations with up to three nested refinement levels on idealized pore geometries to validate the AMR technology. Based on simulations, we identify suitable cell refinement criteria for our applications. We demonstrate effects of AMR in simulations relevant for drainage in porous media, such as in the computation of capillary entry pressures in pore throats with different shapes and wetting states, and obtain excellent agreement with analytic results. Finally, we investigate the effects of AMR during simulation of quasi-static drainage on sandstone. The comparison of capillary equilibrium fluid configurations, capillary pressure, and specific fluid/fluid interfacial area–saturation relationships for drainage with and without AMR shows differences that diminish for less water-wet states. The general behavior is that the capillary pressure and interfacial area for a given saturation increase in simulations with AMR. The largest deviation occurs for small water saturations, suggesting AMR can be an important component in simulation tools to describe more accurately capillary behavior in the low water saturation regime where interface curvature is high. [ABSTRACT FROM AUTHOR]