Carbon capture and storage (CCS) has been identified as an area of research interest due to its potential for reducing the global greenhouse effect. CCS typically involves injection of supercritical CO2 into abandoned oil and gas reservoirs or saline aquifers with sufficient porosity and permeability. CO2 is trapped by a number of mechanisms which differ in security with storage in carbonate minerals (geological carbon storage) being the most secure long term mechanism. Consequently, it is important to understand the behaviour of reactive flows and what influences the mineralisation process to occur so that the CCS process can be optimised as a tool for reducing the greenhouse effect. In this work, we present a novel methodology based on 3D models of connected pore structures extracted from micro computed tomography (microCT). The pore geometry is used to build a representative volume in which fluid flow and mineral precipitation takes place. We numerically solve the governing equations of coupled advection-diffusion-reaction using Finite Element Discretisation. The performed simulations describe advection and diffusion of an injected CO2 brine as well as reaction of this fluid phase with the pore walls to form carbonate minerals. A series of different Damköhler (Da) and Péclet (Pe) numbers are employed to investigate the effect on mineralisation and brine migration of differing advective, diffusive and reactive strengths in the system. We complement our microscale model of porous flow with a regional scale model taking into account geological structures relevant to the subsurface of the UK Geoenergy Observatories Cheshire Energy Research Facility Site, UK.