An Upscaling-Based Numerical Simulation Method for Time-Varying Reservoir Properties

Yubo Lan^1,2Sen Deng^1,2Liang Shi^1,2Siyuan Cui^1,2Haoqiang Wu^3*

• ¹Exploration and Development Research Institute of Daqing Oilfield Co Ltd, Daqing, China
• ²Heilong jiang Provincial Key Laboratory of Reservoir Physics & Fluid Mechanics in Porous Medium, Daqing, China
• ³China University of Geosciences, Beijing, China

Both field practices and laboratory experiments in mature, high water-cut oilfields have confirmed that long-term water flooding dynamically alters rock wettability and micro-pore structure, causing shifts in relative permeability curves and reservoir properties. Conventional numerical simulations, by directly applying core-scale dynamic laws, neglect the scale effect from core to grid and inherent reservoir heterogeneity, leading to inaccurate predictions of remaining oil distribution. To address this, we propose an upscaling method for modeling the dynamic evolution of relative permeability. Based on volume averaging theory, the method first establishes a local empirical model from core data and then introduces a Gamma distribution to represent intra-grid heterogeneity. By performing a probability-weighted average, a concise, closed-form analytical model is derived for grid-scale parameter evolution. The model explicitly links the macroscopic dynamic response to log-permeability variance (σk²) and cumulative water injection. Applied to a typical block in the Daqing Oilfield, the new method provides a more accurate history match of water cut and pressure than conventional models. More importantly, it predicts a more dispersed remaining oil distribution, correcting the overestimation of oil in preferential channels. The primary contribution of this work is the derivation of a novel, closed-form analytical model for upscaling time-varying properties. This physically grounded and computationally efficient method provides a rigorous framework to bridge the critical gap between core-scale physics and grid-scale simulation, representing a significant methodological advance for accurately modeling mature reservoirs.