A Multiscale Framework for Predicting Reservoir Drainage Dynamics Under Uncertainty

Thesis Abstract

This study addresses the escalating uncertainty in reservoir drainage dynamics arising from multiscale heterogeneities, complex fluid–rock interactions, and stochastic operational conditions that challenge conventional reservoir models. The aim is to develop a multiscale predictive framework that integrates pore-scale processes with continuum-scale behavior to quantify drainage trajectories and associated uncertainty under varying production scenarios. The specific objectives are (1) to quantify the influence of pore-scale heterogeneity on macro-scale drainage rates using upscaling via homogenization and volume averaging; (2) to develop a probabilistic multiscale model that couples stochastic input parameters (permeability, capillary pressure, and oil–water interfacial tension) with deterministic Darcy-based flow, enabling predictions with quantified uncertainty; (3) to implement Bayesian calibration and data assimilation to update model states using historical production data from 12 representative reservoirs; (4) to evaluate the framework against observed drainage metrics (pressure drawdown, cumulative oil production, and water cut) under multiple operational strategies (waterflooding, enhanced oil recovery, and primary depletion); and (5) to propose a decision-support tool for uncertainty-aware optimization of drainage pathways. The methodology adopts a mixed-methods, model-driven research design anchored in hemispherical multiscale theory and stochastic processes. The population comprises reservoir rock-fluid systems characterized by heterogeneous grain-scale features and field-scale drainage behavior. A purposive sampling approach selects 12 well-documented reservoirs across carbonate and sandstone formations with diversified depth, porosity, and heterogeneity indices to ensure generalizability. Data collection relies on (i) petrophysical logs (porosity, permeability, capillary pressure data), (ii) core measurements (pore throat size distributions, wettability indices, relative permeability curves), (iii) production history (time-series data of pressure, rate, oil-water ratio for at least five years per reservoir), and (iv) seismic attributes for spatial heterogeneity context. Instrumentation includes high-resolution micro-CT imaging for representative elementary volume (REV) analysis and standard coreflood experimental rigs to characterize drainage under controlled conditions. The analytical framework comprises three integrated components. First, a multiscale upscaling module employs homogenization and volume averaging to derive effective continuum equations that retain pore-scale drainage signatures, with uncertainty propagation via stochastic permeability fields described by Gaussian random fields. Second, a probabilistic predictive engine uses Bayesian hierarchical modeling to fuse prior information with data and to calibrate parameters such as effective permeability, capillary pressure-saturation relationships, and interfacial tension. Markov Chain Monte Carlo (MCMC) methods, specifically the No-U-Turn Sampler (NUTS), and Sequential Monte Carlo (SMC) data assimilation are applied to update state estimates as new production data arrive. Third, a decision-support layer integrates the calibrated multiscale model with trajectory optimization under uncertainty, using stochastic optimization and Bayesian decision theory to generate production schedules that minimize uncertainty in drainage forecasts while maximizing net present value. Analytical techniques include regression analysis to identify scaling laws across scales, ANOVA to assess the significance of different heterogeneity descriptors, and sensitivity analyses (Sobol indices) to quantify parameter influence. The model specification aligns with a coupled Darcy flow–multiscale transport framework, augmented by a stochastic volatility component to capture operational perturbations. Expected findings include (i) robust quantification of how microstructural traits influence macro-scale drainage rates and uncertainty envelopes; (ii) validated multiscale upscaling schemes with predictive intervals that outperform single-scale models under posterior predictive checks; (iii) demonstrable improvements in reservoir drainage forecasts when integrating data assimilation with history matching across multiple wells; and (iv) actionable recommendations for uncertainty-aware production planning, including threshold-based decision rules for switching drainage strategies. The study contributes to knowledge by bridging pore-to-field scale drainage dynamics under uncertainty through a coherent multiscale, probabilistic framework, advancing theoretical understanding of upscaling under stochastic inputs and providing a practical tool for operators. The main conclusion anticipates that incorporating explicit multiscale heterogeneity and Bayesian data assimilation yields predictive confidence improvements and more resilient drainage strategies, with recommendations emphasizing routine acquisition of high-resolution petrophysical data, integration of seismic-informed heterogeneity metrics, and continuous updating of model states via real-time production data.