8Studies of the rock matrix acidizing for enhanced recovery of oil or gas have entirely focused on the 9 fully water saturated conditions. In fact, matrix acidizing can be conducted in low-water-cut oil-10 production wells without pre-flushing of water or in high water production by injecting gas or oil 11 ahead of the acid injection. These conditions yield a multiphase system, where the dynamics of acid 12 transport and reactions can be altered by the presence of an immiscible phase. Against this backdrop, 13we present an investigation of the impact of initial saturation of an immiscible phase in the damaged 14 zone on the efficiency of wormhole generation and growth in acidizing operations. We present a 15 dimensionless two-phase reactive transport modelling tailored for studying the processes associated 16 with rock acidizing. For a case study of acid injection into calcite with random porosity and 17 permeability distribution, we show that an initial two-phase condition has positive feedback on the 18 generation of wormholes. The results, however, indicate that the relative magnitude of reduction in 19 the amount of pore volume of injected acid to produce effective wormholes depends on the mobility 20 ratio, so that a higher mobility ratio facilitates a faster wormhole generation process. Under the 21 conditions of modelling study presented, we demonstrate that in addition to the commonly used pair 22 of Péclet-Damköhler regime identification, the mobility ratio of the displacing/displaced fluids, the 23 * Corresponding author: Telephone +44 (0)161 306 4554,