Fluid flow through porous materials is critical for understanding and predicting the behavior of systems as diverse in function and scale as hydrocarbon reservoirs, aquifers, filters, membrane separators and even catalytic converters. Recently, there have been calls to incorporate more physics in oil reservoir simulations, as well as to enhance computational capability through the use of High Performance Computing (HPC), in order to improve reservoir management. Accurate prediction of reservoir behavior depends on the physical properties of not only the fluid but also the underlying rock formation. Contemporary approaches to solving these flows involve simulation of only a single physical scale. We are currently developing HiMuST (Hierarchical Multiscale Simulator Technology), an integrated multiscale simulation system for flow through heterogeneous porous materials. HiMuST uses a hierarchy of simulation codes to address the issue of rock property characterization at the pore scale and can self-adjust according to available input data. At the microscopic scale, HiMuST employs the Lattice Boltzmann Method, based on magnetic resonance digitizations of actual rock samples. At the mesoscopic scale, a stochastic model represents a pore network as a randomly generated skeleton of cylindrical pipes, based on physical characteristics determined by the microscopic simulation. We present computational and computer science issues involved in the HPC implementation of the codes and in integrating them into a seamless simulation system. Issues such as portability, scalability, efficiency and extensibility of the final product are also discussed, as well as the numerical methods implemented at each scale. Example simulation results are presented.