The technique of matrix acidification or acid fracturing is commonly utilized to establish communication with natural fractures during reservoir reconstruction. However, this process often encounters limitations due to filtration, which restricts the expansion of the primary acid-etching fracture. To address this issue, a computational model has been developed to simulate the expansion of an acid-etching wormhole by considering various factors such as formation process, injection duration, pressure build-up, and time-varying acid percolation rate. By analyzing the pumping displacement of acid-etching wormholes, this model provides valuable insights into the time-dependent quantities of acid percolation. It has been revealed that the filtration rate of acid-etching wormholes is strongly influenced by pumping displacement, viscosity, and concentration of the acid fluid used in stimulation as well as physical properties of the reservoir itself. Notably, viscosity plays a significant role in determining the effectiveness of acid fracturing especially in low-viscosity conditions. Acid concentration within 15% to 20% exhibits maximum impact on successful acid fracturing while concentrations below 15% or above 20% show no obvious effect. Furthermore, it was found that pumping displacement has a major influence on effective fracturing. However, beyond a certain threshold (> 5.0 m3/min), increased pumping displacement leads to slower etching distance for acids used in construction purposes. The simulation also provides real-time distribution analysis for acidity levels within eroded fractures during matrix-acidification processes and quantifies extent of chemical reactions between acids and rocks within these fractures thereby facilitating optimization efforts for design parameters related to matrix-acidification.