We study compositional, thermal and reactive flow in porous media and the numerical simulation of those processes, with a focus on laboratory scale In-Situ Combustion (ISC) cases. We discuss the governing equations and models, our numerical framework and its implementation, as well as a two-step verification process using state-of-the-art industrial codes and a grid convergence study. First, we go over a numerical verification process using two industrial codes as well as internal grid-convergence studies. We illustrate that our framework is robust and accurate on complex thermal, compositional and reactive cases. We then investigate the appropriateness and performance (in terms of both runtime and non-linear iterations) of some of the models typically used for compositional and isothermal simulation. We illustrate that in the presence of strong thermal effects, we need to make sure that we can capture the relevant physics using those models. More specifically, we discuss our findings on compositional and thermal models for heat capacity, enthalpy and phase behavior in the context of laboratory scale in-situ combustion. We show that a free-water flash captures the right behavior for our low pressure, high temperature conditions, even in a K-value form. The computational cost is three times lower than using a full flash and two times lower than using a regular K-value flash. Using a temperature-independent heat capacity model, as is often done in the thermal literature, will lead to issues to capture the ignition by overestimating heat capacity at low temperature. We discuss the different options to compute enthalpy in a compositional, thermal setting and show some possible unphysical behavior.

Polymer flooding is one efficient EOR technology by overcoming non-uniform and unstable displacement caused by water injection. Polymer flooding in reservoirs is a complicated process that involves strongly nonlinear physics, e.g., non-Newtonian rheology in porous media with retention and adsorption. In the presence of multi-scale heterogeneity, high-fidelity simulations are usually required to capture such nonlinear behavior, which is a time-consuming process for conventional reservoir modelling.
In this study, we extend an advanced linearization strategy, called the Operator-Based Linearization (OBL) approach, to simulate non-Newtonian polymer flooding with retention and adsorption mechanisms using the fully implicit method. A velocity-dependent viscosity multiplier compliments the operator form of governing equations to represent the non-Newtonian rheology of the high-molecular-compound polymer. The retention of polymer, reducing the porosity, is represented by a Langmuir-type adsorption model. Several simplified models have been used for validation of the developed numerical framework. The numerical results show good agreement with both the analytical solutions and the coreflood experimental data though some negligible discrepancies can be observed in simulation results.
A highly resolved near-well model is used to test the performance of polymer flooding in realistic reservoir conditions. Both shear-thinning and thickening regimes, depending on the injection velocity and polymer concentration, are recognized in the near-wellbore zone. The injected polymer concentration and brine salinity significantly affect the shear viscosity, and consequently, polymer injectivity. Polymer retention and adsorption have a substantial effect on the rate of polymer propagation through porous media. Overall, polymer flooding shows its advantages to mitigate water fingering in field-scale operations and improves the ultimate sweep of the reservoir. However, optimal injectivity is one essential factor that affects the performance of polymer flooding. The computational superiority of the proposed model allows us to optimize the parameters of polymer flooding in realistic reservoirs and operational settings.

In the past years, foam flow in porous media has increased research interest due to several applications associated with this complex nonlinear process. Examples of foam applications include the petroleum industry (Enhanced Oil Recovery) and soil contamination recovery. The primary usability is connected to the control of gas mobility, which allows fingering and improves sweeping efficiency. As the foam is created in the presence of surfactant solution in the water phase, this technique's applicability is connected to the surfactant adsorption to the surrounding matrix. Several experiments reported saturation and foam texture profiles moving through the porous medium as traveling waves, motivating searching for the solution in such form.

In previous works, we investigated and classified possible analytical solutions for a simplified version of the foam bubble population model, considering surfactant solution to be homogeneously distributed in the water phase. We followed the literature and neglected the apparent gas viscosity dependence on gas velocity to allow mathematical analysis. The present paper extends this analysis by including the surfactant concentration as a tracer in the water phase and surfactant dispersion. Using phase space geometric analysis (a standard tool in Dynamical Systems), we investigate the existence and uniqueness of the traveling wave solutions for the original system of the partial differential equation for different injection conditions. In the present work, we model the situation with low surfactant concentration and mathematically investigate how surfactant dispersion can affect the traveling wave solutions applied to the foam displacement in porous media. We classify the parameter space into ten regions according to the traveling wave type and investigate the solution existence in two of these regions, which are more attractive from the experimental point of view. Direct numerical simulations support all analytical estimates for parameter values corresponding to real experimental data.

In enhanced oil recovery (EOR) processes, foam injection reduces gas mobility and increases apparent viscosity, thus increasing recovery efficiency. The reliability of simulators in the oil industry depends on the sensitivity of the outputs when subjected to input uncertainty. In this context, uncertainty quantification (UQ) is a key procedure while studying these physical systems. This work evaluates the influence of the prior distribution's choice for the apparent viscosity variance during the inverse uncertainty quantification of foam model parameters.

To model the two-phase flow for foam, the CMG-STARS mathematical model was used. In this model, the foam effects are modeled considering a reduction factor in the mobility of the gas phase. The mobility reduction factor term can describe the effects of surfactant concentration, water and oil saturations, shear-thinning, and other effects. This work uses a Bayesian inference process to perform parameter estimation. It allows obtaining the best estimation of parameters (as an optimization method) together with an estimation of the uncertainty of each one. Using a Bayesian technique for a regression problem requires the definition of prior distributions for the parameters of interest and the variance parameter of the normal distribution assumed for the data distribution. The latter is the main focus of the investigation in this work. In particular, the Half-t distribution is evaluated due to its more conservative form built on the standard Normal distribution. We also assess a strategy based on the vectorization of the variance parameter as a form of weighting the data points, considering the errors obtained from the experiments at each point. The data from a foam quality-scan experiment was considered to estimate parameters describing the foam's apparent viscosity.

The results demonstrate that a proper choice of the prior for the variance of the apparent viscosity has a significant impact on the obtained posterior distribution of the parameters values. More importantly, when properly chosen and supported with data available from the experimental setting at each foam quality, the prior of the variance can significantly improve the estimation of key parameters while reducing the propagation of uncertainties to the quantities of interest.