The recent advancements in imaging techniques have allowed quantifying the transport and fluid flow inside the complex rock pores at the microscopic scale. Specifically, micro-computed tomography (micro-CT) can reconstruct the three-dimensional pore-space geometry with micron-scale resolution. In this work, a numerical investigation of single-phase fluid flow is conducted on micro-CT images of carbonate core-plug subsamples. The presented numerical model studies the fluid flow and transport inside the rock pores at the pore-scale. The flow dynamics is modeled using the Darcy-Brinkman formulation to consider the wide pore size distribution in carbonate rock samples. The simulation model takes into account pores at the micro-CT image resolution as well as the unresolved pores (microporosity) that are smaller than the micro-CT voxel sizes. These unresolved pores are usually categorized as microporosity, which is a parameter in the simulation model. The microporosity is quantified based on the micro-CT gray-scale intensity. Simulation results show that direct pore-scale simulation on micro-CT images can characterize the permeability, porosity, and microporosity. As a result, pore-scale simulation can supplement conventional core analysis as well as provide detailed information of the primary fluid flow paths inside the carbonate rock pores. It is also shown that the microporosity has a first order effect on the rock permeability. Neglecting the microporosity regions alters the pore connectivity, which is essential to compute the permeability and rock petrophysical properties accurately. The novelty of this study lies in solving the Darcy-Brinkman simulation model in a finite-volume framework to capture the effect of microporosity on carbonate rock samples in full three-dimensional space. The new findings shed light on the fluid flow and transport inside highly heterogeneous carbonate formations, which becomes an important first step to understand the fundamentals of oil recovery in advanced waterflooding process at the microscopic level.