# A New Compound Staged Gelling Acid Fracturing Method for Ultra-Deep Horizontal Wells
## 1 Introduction  
Sichuan carbonate gas reservoir is rich in natural gas resources. The reservoir has the characteristics of high temperature, low porosity, and low permeability [1, 2, 3]. The formation temperature can reach 160 \({}^{\circ}\)C, and the reservoir lithology is mainly dolomite. The gas production of vertical wells after fracturing is low, which cannot support the economic development of gas reservoirs [4, 5]. Staged acid fracturing of horizontal wells is a favorable means to improve the development effect of gas reservoirs [6, 7, 8]. Staged fracturing technologies mainly comprise double-pack single-slip multistage fracturing [9], packer-sliding sleeve fracturing [10], and hydraulic jetting multi-stage fracturing [11]. Staged acid fracturing of ultra-deep horizontal wells faces many problems, such as fracture parameter optimization, staged fracturing process optimization, and acid corrosion fracture length improvement. Productivity simulation and fracture parameter optimization of horizontal wells are the basis of staged acid fracturing of horizontal wells [12, 13, 14]. Simple analytical solutions are derived on the basis of the assumption of infinite drain hole conductivity. These models are widely adopted because they are easy to use. However, they are not able to produce an accurate prediction of productivity because they ignore the pressure drop in the wellbore [15, 16, 17, 18]. [PERSON] et al. [19] conducted a series of studies about the productivity of fractured horizontal wells in a uniform sandstone reservoir. [PERSON] et al. [20]established the productivity-prediction model, which was suitable for the acid fracturing horizontal well in the fracture-cavity reservoir, by comprehensively considering primary factors, wellbore pressure drop, cracks for supporting liquid, and connected fracture system. The reaction rate of acid liquid rises sharply at high temperatures, which seriously affects the acid fracturing effect of ultra-deep reservoirs [21; 22; 23]. [PERSON] [24] developed a comprehensive acid fracturing model that solved for 2D/pseudo-3D fracture geometry, leakoff, heat transfer, and acid transport. [PERSON] et al. [25] developed a 3D acid fracturing model to compute the rough acid fracture geometry induced by multi-stage alternating injection of pad and acid fluids, they investigated the effects of viscous fingering, perforation design, and stage period on the acid etching process. [PERSON] et al. [26] investigated the stability of immiscible viscous fingering in Hele-Shaw cells with spatially varying permeability, providing an efficient, high accuracy scheme to track the interfacial displacement of immiscible fluids. [PERSON] et al. [27] developed an improved VOF interface-sharpening method on the general curvilinear grid for two-phase flows. [PERSON] et al. [28] developed a modeling framework for the coupled thermal-hydro-mechanical chemical processes during acid fracturing in carbonatite geothermal reservoirs. [PERSON] et al. [29] developed a pore-scale numerical model to analyze the impact of acid-rock interaction on multiphase flow behavior, and the pore-scale model in this research provides the fundamental knowledge of the physical and chemical phenomena of acid-rock interactions and their impact on acid transport. [PERSON] et al. [30] studied the final fracture conductivity during acid fracturing. [PERSON] et al. [31] studied the influences of rock microstructure on acid dissolution on a dolomite surface. [PERSON] et al. [32] used a cohesive zone method (CZM)-based finite element model to obtain the fracture closure pressure and minimum horizontal principal stress of the major fracture and the branch fracture based on pressure fall-off analysis. Deep high-temperature vuggy naturally fractured formations where tools are not reliable and costive [33], and diverted fracturing with temporary plugging has become an option [34]. Degradable fiber is another commonly used diverter. It can bridge on the fracture, or fill the gap between particulate diverters to form a tight barrier.