The depletion of oil reserves and higher oil prices has made chemical enhanced oil recovery (EOR) methods more attractive in recent years. Because of geological heterogeneity, unfavorable mobility ratio, and capillary forces, conventional oil recovery (including water flooding) leaves behind much oil in reservoir, often as much as 70% OOIP (original oil in place). Surfactant/polymer flooding targets these bypassed oil left after waterflood by reducing water mobility and oil/water interfacial tension. The complexity and uncertainty of reservoir characterization make the design and implementation of a robust and effective surfactant/polymer flooding to be quite challenging. Accurate numerical simulation prior to the field surfactant/polymer flooding is essential for a successful design and implementation of surfactant/polymer flooding. A recently developed unified polymer viscosity model was implemented into our existing polymer module within our in-house reservoir simulator, the Implicit Parallel Accurate Reservoir Simulator (IPARS). The new viscosity model is capable of simulating not only the Newtonian and shear-thinning rheology of polymer solution but also the shear-thickening behavior, which may occur near the wellbore with high injection rates when high molecular weight Partially Hydrolyzed Acrylamide (HPAM) polymers are injected. We have added a full capability of surfactant/polymer flooding to TRCHEM module of IPARS using a simplified but mechanistic and user-friendly approach for modeling surfactant/water/oil phase behavior. The features of surfactant module include: 1) surfactant component transport in porous media; 2) surfactant adsorption on the rock; 3) surfactant/oil/water phase behavior transitioned with salinity of Type II(-), Type III, and Type II(+) phase behaviors; 4) compositional microemulsion phase viscosity correlation and 5) relative permeabilities based on the trapping number. With the parallel capability of IPARS, commercial scale simulation of surfactant/polymer flooding becomes practical and affordable. Several numerical examples are presented in this dissertation. The results of surfactant/polymer flood are verified by comparing with the results obtained from UTCHEM, a three-dimensional chemical flood simulator developed at the University of Texas at Austin. The parallel capability and scalability are also demonstrated. / text

This thesis presents a framework for history matching and model calibration of surfactant-polymer (SP) flooding. At first, a high-fidelity mechanistic SP flood model is constructed by performing extensive lab-scale experiments on Berea cores. Then, incorporating Sobol based sensitivity analysis, polynomial chaos expansion based surrogate modelling (PCE-proxy) and Genetic algorithm based inverse optimization, an optimized model parameter set is determined by minimizing the miss-fit between PCE-proxy response and experimental observations for quantities of interests such as cumulative oil recovery and pressure profile. The epistemic uncertainty in PCE-proxy is quantified using a Gaussian regression process called Kriging. The framework is then extended to Bayesian calibration where the posterior of model parameters is inferred by directly sampling from it using Markov chain Monte Carlo (MCMC). Finally, a stochastic multi-objective optimization problem is posed under uncertainties in model parameters and oil price which is solved using a variant of Bayesian global optimization routine. <br>

Understanding flow and transport in porous media is critical as it plays a central role in many biological, natural, and industrial processes. Such processes are not limited to one length or time scale; they occur over a wide span of scales from micron to Kilometers and microseconds to years. While field-scale simulation relies on a continuum description of the flow and transport, one must take into account transport processes occurring on much smaller scales. In doing so, pore-scale modeling is a powerful tool for shedding light on processes at small length and time scales.<br><br>In this work, we look into the multi-phase flow and transport through porous media at two different scales, namely pore- and Darcy scales. First, using direct numerical simulations, we study pore-scale Eulerian and Lagrangian statistics. We study the evolution of Lagrangian velocities for uniform injection of particles and numerically verify their relationship with the Eulerian velocity field. We show that for three porous media velocity, probability distributions change over a range of porosities from an exponential distribution to a Gaussian distribution. We thus model this behavior by using a power-exponential function and show that it can accurately represent the velocity distributions. Finally, using fully resolved velocity field and pore-geometry, we show that despite the randomness in the flow and pore space distributions, their two-point correlation functions decay extremely similarly.<br><br>Next, we extend our previous study to investigate the effect of viscoelastic fluids on particle dispersion, velocity distributions, and flow resistance in porous media. We show that long-term particle dispersion could not be modulated by using viscoelastic fluids in random porous media. However, flow resistance compared to the Newtonian case goes through three distinct regions depending on the strength of fluid elasticity. We also show that when elastic effects are strong, flow thickens and strongly fluctuates even in the absence of inertial forces.<br><br>Next, we focused our attention on flow and transport at the Darcy scale. In particular, we study a tertiary improved oil recovery technique called surfactant-polymer flooding. In this work, which has been done in collaboration with Purdue enhanced oil recovery lab, we aim at modeling coreflood experiments using 1D numerical simulations. To do so, we propose a framework in which various experiments need to be done to quantity surfactant phase behavior, polymer rheology, polymer effects on rock permeability, dispersion, and etc. Then, via a sensitivity study, we further reduce the parameter space of the problem to facilitate the model calibration process. Finally, we propose a multi-stage calibration algorithm in which two critically important parameters, namely peak pressure drop, and cumulative oil recovery factor, are matched with experimental data. To show the predictive capabilities of our framework, we numerically simulate two additional coreflood experiments and show good agreement with experimental data for both of our quantities of interest.<br><br>Lastly, we study the unstable displacement of non-aqueous phase liquids (e.g., oil) via a finite-size injection of surfactant-polymer slug in a 2-D domain with homogeneous and heterogeneous permeability fields. Unstable displacement could be detrimental to surfactant-polymer flood and thus is critically important to design it in a way that a piston-like displacement is achieved for maximum recovery. We study the effects of mobility ratio, finite-size length of surfactant-polymer slug, and heterogeneity on the effectiveness of such process by looking into recovery rate and breakthrough and removal times.