Acid bullheading is a well-known treatment for removing downhole scale and formation damage in oil and gas fields. The treatment is performed by using a controlled percentage of hydrogen chloride, and is normally operated under restricted wellhead pressure for health, safety, and environment (HSE) and well integrity purposes. These constraints sometimes prevent the treatment to be more effective in removing formation damage and improving injectivity and/or productivity of oil and gas wells. The present work is related to a fundamental study of fluid invasion in different types of formation with regard to the designed acid bullheading setups. The results are compared and analyzed based on a numerical investigation for the same geometrical and dynamical parameters to assess the efficiency of the fluid invasion designed process. The new treatment design utilizes the concept of cyclic pressure by fluctuating the injection velocity. In this paper, a mathematical formulation of fluid flow invasion in a porous medium is presented using a lattice Boltzmann numerical analysis. This method uses a mesoscopic approach to solve the flow problem instead of using Navier-Stokes equations and giving good numerical accuracy. It mimics different formation porosities, injection velocities, and procedures over time. A qualitative comparison between constant and variable injection velocities was performed under a fixed period of time. The new simulation code visually demonstrates the growth of fluid invasion in the investigated domains and highlights clear differences between the two cases of continuous and cyclic injections. This approach presents a new design in matrix stimulation that could effectively optimize oil and gas treatment operations.