## 1 Introduction  
Phosphogypsum leachate significantly accelerates carbonate rock dissolution in karst regions [1, 2, 3]. Despite global reliance on landfill disposal for phosphogypsum waste management, frequent leakage incidents from storage sites have been documented to accelerate carbonate rock dissolution [4, 5, 6], thereby compromising the geological integrity of karst terrains [7]. This process fundamentally arises from the evolution of geotechnical structures and hydrochemical compositions [8, 9], which alter water-rock interaction mechanisms by exacerbating heterogeneity in both hydrodynamic parameters (e.g., flow rate, velocity) and -solute transport processes (chemical component distribution) [10; 11; 12]. To systematically investigate these phenomena, this study integrates experimental investigations with numerical simulations, which in recent years have proven effective in characterizing a range of geological dynamics [13]. The evolution of carbonate rock dissolution constitutes a complex, multi-process coupled system involving fluid percolation, solute transport and diffusion, and multiphase chemical reactions at mineral-fluid interfaces [14]. Extensive research has been conducted through static and dynamic dissolution experiments to investigate macro-/microstructural evolution and physico-mechanical property alterations in rocks under varying chemical and coupled field conditions [15; 16]. In this field, researchers employ diverse methodologies: Scanning Electron Microscopy (SEM) [17; 18], computed tomography with digital image processing (CT) [19; 20; 21], Raman spectroscopy [22; 23], and nuclear magnetic resonance (NMR) techniques [24; 25]. These investigations have yielded insights into acetic acid-carbonate reaction dynamics [26], fractal characteristics of karst morphologies [27], dissolution rate quantification [28], and kinetic model development [29]. Notably, most existing carbonate dissolution experiments [30; 31; 32] under reservoir conditions employ plug-flow [33] or rotating disk reactors [34]. These setups primarily replicate surface-mediated reactions. However, these surface-focused approaches fail to replicate the intrinsic petrogenic processes in which acidic fluids migrate through pore networks characterized by hydrodynamically constrained pathways or conditions. Extensive research on factors influencing chemical dissolution processes has demonstrated that carbonate rock dissolution rates exhibit strong dependencies on solution pH, chemical composition [35; 36], lithology (mineralogical constitution) [37], structural characteristics, CO\({}_{2}\) partial pressure [38], temperature, and hydrodynamic conditions. Experimental studies [39; 40] demonstrate that pH critically controls carbonate dissolution rates. Kinetic analysis of dolomite dissolution [41] reveals limestone's faster reaction kinetics compared to dolomite, necessitating strict mineralogical control in this study. Acetic acid-based dissolution experiments on four carbonate types show inverse temperature dependence and positive pressure correlation for dissolution efficiency, with temperature exerting greater influence than pressure [42]. Consequently, our experimental design incorporates pressure modulation while maintaining temperature constraints. Building upon previous experimental findings, this study combines physical experimentation and numerical simulations to investigate the mechanism of interaction between phosphogypsum leachate and fractured carbonate rock. Unlike conventional surface reaction simulations, our approach incorporates critical factors influencing dissolution (e.g., fracture aperture variations) while systematically quantifying phosphogypsum-carbonate dissolution characteristics under different geochemical conditions. This methodology thereby provides more realistic representations of subsurface reactive transport processes compared to idealized surface reaction models.