Model Extension to a Multi-Scale Climate–hydrology Framework. Nairobi-Kenya Case Study

This paper presents the nonlinear operator formulation of a coupled CO₂ sequestration model arising from the mathematical modeling of carbon dioxide concentration dynamics governed by the Reaction-Diffusion-Advection (RDA) equation. Six interacting physical processes are identified and modeled simultaneously: dissolved CO₂ transport, multiphase saturation dynamics, pressure evolution, geochemical reactions, fault activation, and leakage accumulation. These processes are assembled into a unified state vector and reformulated as a single nonlinear evolution operator acting on a Banach space. The governing system of coupled partial differential equations (PDEs) is derived from first principles, including the mass conservation equation, Darcy’s law for subsurface flow, and geomechanical constitutive relations. The resulting nonlinear operator N(U) is explicitly constructed, and well-posedness of the system is established through local existence, uniqueness, and continuous dependence theorems under standard Sobolev space assumptions. The formulation supports a fixed-point interpretation consistent with the Banach Contraction Principle and provides a rigorous mathematical foundation for numerical simulation and stability analysis of CO₂ geological storage systems