Abstract: Geothermal wells often suffer from production difficulties such as disappointing injectivity/productivity right from the start or declining injectivity/productivity during long-term operation, Acid fracturing, as a soft stimulation technology, is becoming the preferred technology to stimulate the carbonate geothermal reservoir of low permeability in large depth. The basic mechanism of acid fracturing is to inject acid into the carbonate geothermal reservoir through geothermal wells, and then the matrix porosity and fracture apertures can be significantly improved through acid corrosion. Since the acid fracturing technology in geothermal reservoirs is mainly based on the experiences obtained from oil and gas fields, a complete technical system has not yet been established. To be specific, its design method and field implementation process lack theoretical guidance. In this paper, two correction coefficients are proposed to describe the acid etching induced changes in fracture normal stiffness and the maximum closure, based on which a nonlinear fracture constitutive model considering the coupled mechanical-chemical mediations on fracture apertures is developed. The developed nonlinear fracture constitutive model is incorporated into the theoretical framework of coupled thermal-hydraulic-mechanical-chemical processes in fractured rock mass, and a numerical modeling method suitable for acid fracturing in deep carbonate geothermal reservoir is developed. Based on the field test of acid fracturing in the geothermal well D22 in Xiong’an New Area, Hebei, China, the accuracy of the developed modeling method is verified, and the influences of human-controlled parameters including perforation position, acid concentration (mass fraction) and injection rate on the stimulation efficiency of acid fracturing is investigated though sensitivity analysis. The results show that acid fracturing mainly occurs within the fractures with high initial apertures in the carbonate geothermal reservoir of low permeability in large depth. The acid-etched fractures gradually propagated into the surrounding reservoir rocks with high permeability, and a stimulated network is formed after acid fracturing. Stimulation efficiency of acid fracturing is dependent on not only the increase in fracture apertures induced by acid etching and hydraulic pressure, but also the closure path of fractures after stimulation. The closer the perforation position is to the reservoir rocks with high permeability, the better stimulation efficiency of acid fracturing. The high acid concentration and injection rate are helpful to stimulate long fractures, by which the reservoir rocks with high permeability may be connected, and thus the better stimulation efficiency of acid fracturing is obtained.