During the matrix acidizing of carbonate formations, channels with high permeability are created, known as wormholes. The effectiveness of this type of treatment depends primarily on the structure, geometry, and the depth of penetration of the wormholes beyond the damaged zone. This should be ensured by a properly developed acidizing fluid, which in the case of carbonate formations most often consists of solutions of hydrochloric acid and/or organic acids such as acetic or formic acid. Additionally, in the case of high-temperature formations, additives are used to reduce the reaction rate of acid with the reservoir rock. The Damköhler number (Da) is an important factor that influences the model of the wormholes created. It represents the ratio of the rate of the reaction between the acid and the rock to the rate of its convection along the wormhole. The aim of the study was to determine the Damköhler number for four selected acidizing liquid–rock systems and to confirm that the structure of the wormholes depends on this variable. As part of the work, rheological tests of gelled acidizing liquids using a viscoelastic surfactant were conducted. The reaction rate tests were carried out on core plugs cut from Pińczów limestone and Guelph dolomite, which are characterized by relatively low permeability and porosity coefficients: 9.11–14.23 × 10−15m2 and 28.51%–29.10%, respectively, in the case of Pińczów limestone and 3.69–7.48 × 10−15m2 and 7.67%–9.38%, respectively, for Guelph dolomite. A rotating disk apparatus was used to determine the kinetics of the reaction of these rocks with two types of acidizing liquids. Then, core flow tests were performed on the core plugs using the AFS-300 system for the same types of rocks and liquids. The core plugs of Pińczów limestone used in these tests had a permeability coefficient ranging from 9.65 to 26.27 × 10−15m2 and a porosity coefficient ranging from 28.78% to 31.29%. On the other hand, samples of the Guelph dolomite had permeability coefficients of 7.48 to 61.52 × 10−15m2, while the porosity was much lower, ranging from 7.63% to 10.60%. After the core flow tests, the Damköhler number was calculated for each identified wormhole, using X-ray computed microtomography combined with an analysis of the geometric parameters. The types of structures that are formed in carbonate rocks as a result of matrix acidizing and their impact on the effectiveness of treatment are described in the theoretical part of this publication. Seven models of carbonate acidizing, which are used to estimate the influence of the parameters of the treatment and the properties of the liquid and rock on the efficiency of the acidizing process, are also discussed. Particular attention was paid to the theory of the Damköhler number, the value of which determines the formation of wormholes. The tests showed that at 80°C the overall reaction rate for each of the four acidizing liquid–rock systems was controlled by the mass transport rate. It was found that a gelled 15% HCl solution using TN-16235 viscoelastic surfactant reduced the overall reaction rate by reducing the mass transport rate. In the case of Pińczów limestone, the addition of 7.5% TN‑16235 surfactant reduced the De value from 4.45 × 10−6cm2/s to 3.53 × 10−6cm2/s; for Guelph dolomite De decreased from 2.25 × 10−6cm2/s to 1.97 × 10−6cm2/s. The values of the acidizing liquid pore volumes required to break through the core plug (PVbt) were determined based on the core flow tests. The lowest values of this parameter for Pińczów limestone were 0.26 for a 15% HCl solution and a velocity of 2.93 cm/min and 0.28 for a gelled 15% HCl solution and a velocity of 0.30 cm/min. For the Guelph dolomite rock, they were 0.88 for a 15% HCl solution and a velocity of 3.68 cm/min and 0.25 for a gelled 15% HCl solution and a velocity of 1.00 cm/min. Gelling a liquid with TN-16235 viscoelastic surfactant thus enables efficient matrix acidizing of carbonate formations with lower pumping rates. It was also found that the model of dissolution of the porous medium by a given acidizing liquid depended on the value of the Damköhler number. For wormholes created in the plugs of Pińczów limestone using the 15% HCl solution, the calculated values of Da were in the range of 0.244 to 0.026 (optimal value: 0.031); for the gelled 15% HCl solution it ranged from 0.145 to 0.008 (optimal value: 0.097). The optimal value for Da was considered to be the value for which wormholes were able to penetrate the entire length of the core with minimal acid spending described by PVbt. For wormholes etched in the Guelph dolomite rock by the 15% HCl solution, the calculated values of Da ranged from 0.104 to 0.030 (optimal value: 0.066), and for the gelled 15% HCl solution they ranged from 0.188 to 0.030 (optimal value: 0.069). The research methodology presented in this paper allows the Damköhler number to be determined for acidizing liquid–rock systems, and thus facilitates the preparation of technology for matrix acidizing of carbonate formations in such a way as to make these treatments as effective as possible. Keywords: matrix acidizing, Damköhler number, viscoelastic surfactant
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