... modeling of phase transitions, gas-liquid interactions, and complex interfacial dynamics. The framework reduces computational complexity by consolidating eight governing variables into three through auxiliary relationships for mole fractions, saturations, and capillary pressures. The EG discretization...

... architecture to auto-regressively predict state variables and well outputs of a reservoir for an ensemble of cases with varying well configurations. This new approach constructs a Graph Neural Network (GNN) model to predict hyperbolic variables (i.e. saturations and compositions), a Fourier Neural Operator...

... 's sum to the total reservoir pore volume, then V p , i 0 's also sum to the total pore volume. As it will become much clearer later pressure and saturation equations to be solved, between the nodes i and j are characterized mainly by two parameters; transmissibilities at time...

... Abstract Adaptive Implicit Method (AIM) is widely considered as the state-of-the-art numerical scheme for reservoir simulation. It seeks the middle-ground between IMplicit Pressure Explicit Saturation (IMPES) and Fully Implicit Method (FIM) by dynamically selecting the implicitness of each...

... that water plays a critical role in decreasing CO2 sorption capacity, which in turn influences residual gas saturation. These findings were integrated into continuum-scale modeling, capturing the impact of water on CO2 transport and storage dynamics. Our integrated approach highlights the importance...

... p , i k , j 0 ’s also sum to the total pore volume. As it will become more clear in Sections 2.1 and 2.2 where we present the pressure and saturation equations to be solved, flow between the nodes i k and j is characterized mainly by two parameters; transmissibilities at time...

... does not affect the solution accuracy. united states government fluid dynamics pvt measurement saturation artificial intelligence reservoir simulation dissipation operator hydraulic fracturing iteration journal equation of state modeling & simulation convergence upstream oil...

... with specific loss functions and structure to transform the nonlinear equation and frame it as a bilinear system with constant matrices over time. In such a way, it forces the states (pressures and saturations) to evolve in time by simple matrix multiplications in the lifted manifold. We also adopt a "guided...

... Abstract Saturation distributions that ensue when supercritical CO 2 is injected into heterogeneous porous sedimentary rocks depend on the local balance between viscous, gravitational, and capillary forces. This balance varies among different constituent rock types, and there is mounting...

... , 2020b ). The compositional wellbore model consists of four sets of governing equations, namely, component mass conservation equation, momentum conservation equation, composition conservation equation, and energy balance equation. Fractional flow theory is used to correlate the phase saturation and phase...

.... Adaptive fully implicit multi-scale finite-volume method for multi-phase flow and transport in heterogeneous porous media . Journal of Computational Physics , 217 ( 2 ): 627 – 641 , 2006 . JW Watts . A compositional formulation of the pressure and saturation equations . SPE Reservoir...

..., which is also coupled with a discrete fracture model. The strategy involves coupling of the SV method and reconstructed CVD-MPFA fluxes at the faces of the spectral volume, to obtain an efficient finer scale higher resolution finite-volume method which solves for both the saturation and pressure...

..., and it ensures continuity of transport characteristics at solubilization changes in phase composition. fluid dynamics composition quantity saturation flow in porous media concentration relative permeability water relative permeability formulation reservoir simulation phase state discontinuity...

... with infinitesimal transformation assumed. Specifically, the plastic fluid content, i.e., the total residual (or irrecoverable) saturation, is also additively decomposed into constituents due to the two irreversible processes: the geomechanical plasticity and the capillary hysteresis. The additive decomposition...

... initial condition permeability field algorithm loss function equation machine learning partial differential equation deep learning resolution iteration saturation architecture Introduction Earth systems predictions largely rely upon the modeling of complex fluid dynamics in the porous...

... the displacement fronts more accurately. As a result, the regions that experience significant concentration and saturation gradients are more confined, and that leads to improvements in the computational efficiency of the adaptive scheme. The robustness of the approach is demonstrated using a highly heterogeneous...

... capillary pressure model that is only a function of saturation with hysteresis between inhibition and drainage processes and model three-phase flow as a combination of two 2-phase flow. As we examine only the capillary diffusion (spontaneous imbibition), the transport equation for the water phase can...

.... Capillary-gravity equilibrium is then used to initialize the model with the primary drainage capillary pressure curves at the paleo-contact, which gives the minimum water saturation for each grid-block. From this, an imbibition scanning curve is generated for a second initialization based on the current oil...

...., well rates) of the reservoir and not only the states (e.g., pressure and saturation) matching. A Combination of data-driven model reduction strategies and machine learning (deep- neural networks – NN) will be used here to achieve state and input-output matching simultaneously. In Jin, Liu...

... for the saturation equation of two-phase flow in porous media in two space dimensions. The keys to high order accuracy are to use WENO reconstruction in space (which handles shocks and steep fronts) combined with a two-stage Radau-IIA Runge-Kutta time integrator. The saturation is approximated by its averages over...