Unified Framework for Multiphase Flow Uncertainty in Reservoir Simulations

Thesis Abstract

The increasing complexity of reservoir heterogeneity and operating conditions renders conventional deterministic reservoir simulations insufficient for reliable uncertainty quantification in multiphase flow predictions. This study addresses the gap by developing a unified framework that integrates probabilistic, mechanistic, and data-driven approaches to quantify and propagate uncertainty across multiphase flow models, with specific emphasis on relative permeability, capillary pressure, and phase behavior under varying reservoir conditions. The aim is to establish a cohesive methodology that links geological uncertainty, bed-scale upscaling, and experimental measurement error to forecast ranges of oil, water, and gas saturations and production metrics under project-wide scenarios. The objectives are (i) to synthesize a consolidated theoretical structure that combines Bayesian inference, stochastic upscaling, and physics-informed machine learning for multiphase flow; (ii) to formulate a generative uncertainty model for key petrophysical properties and boundary conditions; (iii) to implement a modular software framework enabling seamless integration with existing reservoir simulators; (iv) to evaluate the framework on benchmark synthetic reservoirs and a real-field dataset; and (v) to propose robust decision-support metrics for field development planning under uncertainty. A mixed-methods research design is employed, integrating quantitative stochastic simulation experiments with qualitative expert elicitation to calibrate and validate the uncertainty models. The population includes petroleum reservoirs with heterogeneous carbonate and clastic lithologies, for which field data from 15 development blocks and corresponding core and log data are collected. The sample comprises 20 representative conditioning realizations drawn from a hierarchical Bayesian prior over porosity, permeability, and relative permeability curves, supplemented by capillary pressure data from laboratory core floods. Data collection instruments consist of core plug measurements, mercury injection capillary pressure tests, wireline and formation tester logs, production history, and high-frequency production data. Model calibration uses Markov Chain Monte Carlo (MCMC) to update posterior distributions of uncertain parameters, and a physics-informed neural network (PINN) to learn subgrid-scale multiphase flow relationships while honoring conservation laws. Methodologically, the study advances a unified uncertainty framework through four components. First, a probabilistic upscaling module translates core-scale uncertainties to grid-block-scale parameters using a Bayesian hierarchical model with priors informed by laboratory experiments and geological statistics. Second, a physics-constrained surrogate modeling module employs PINNs trained on high-fidelity multiphase flow simulations to interpolate and extrapolate relative permeability and capillary pressure across rock types and saturation ranges. Third, a stochastic sensitivity analysis module applies Sobol indices and then variance-based decomposition to identify dominant uncertainty sources and quantify their impact on predicted production profiles. Fourth, a decision-support module integrates probabilistic forecasts into scenario-based optimization for field development planning, using stochastic programming and risk measures such as value-at-risk (VaR) and conditional value-at-risk (CVaR). Expected findings include (i) reduced predictive uncertainty in oil-water-gas saturation trajectories by 25–40% across tested scenarios, (ii) identification of the most influential sources of uncertainty—relative permeability hysteresis and capillary pressure-saturation relationships—under varying pore-scale conditions, and (iii) demonstration of the effectiveness of a minimal set of measurements to constrain forecasts. The study anticipates that the unified framework will outperform traditional deterministic simulations and ad hoc uncertainty treatments in both accuracy and decision-support value, with quantifiable improvements in production forecast intervals and risk-adjusted project metrics. Contributions to knowledge comprise (i) a novel theoretical synthesis integrating Bayesian inference, stochastic upscaling, and physics-informed learning for multiphase reservoir flow, (ii) a practical, modular computational framework adaptable to industry-standard simulators, and (iii) an empirically validated methodology for end-to-end uncertainty quantification that links core-scale measurements to field-scale outcomes. The main conclusion is that a unified approach to multiphase flow uncertainty significantly enhances confidence in reservoir performance predictions and decision-making under uncertainty. Recommendations emphasize routine integration of probabilistic parameter estimation in reservoir workflows, expansion of physics-informed surrogates for other flow regimes, and the maintenance of transparent uncertainty disclosure in field development plans, with future work targeting real-time updating of posteriors using new production data.