The Pre-Caspian basin is one of the most prolific in terms of oil and gas exploration and hydrogen and carbon compounds energy production around the world. The major hydrogen and carbon compounds reservoirs are Carboniferous reef and platform hydrogen-carbonate rocks. The original fluids under subsurface conditions contain 15% hydrogen sulfide and 4% carbon dioxide. Acid hydrogen and carbon compounds reinjection is not only an environmentally friendly solution for disposal of produced greenhouse gases but also enhances oil recovery and supplies more fuel energy. On the other hand, the presence of fractures makes hydrogen-carbonate reservoir characteristics nature more complicated than conventional sandstone reservoirs, which leads to a tremendous challenge to evaluate the gas injection process. In this work, a dual-porosity dual-permeability formulation was used to model the dual-medium nature incorporating matrix system with high porosity and low permeability and fracture network with low porosity and high permeability. After matching PVT experiments, a ten pseudo-components fluid model was generated for running compositional simulation. The miscible hydrogen and carbon compounds injection was simulated as an effective enhanced oil recovery approach. Sensitivity analysis such as timing of injection gas, injection rate, well spacing and completion interval have proposed the optimal condition for the miscible hydrogen and carbon compounds flooding. The recommended optimum hydrogen and carbon compounds injection scenario is twice higher oil recovery compared with natural depletion. The results of this study illustrate further the practicability of pseudo-components splitting and lumping for compositional simulation to evaluate the performance of hydrogen and carbon compounds injection processes, and are of great importance using the dual-porosity dual-permeability method performing numerical simulation of naturally fractured hydrogen-carbonate reservoirs. (C) 2019 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.