The success in matrix acidizing carbonate-formations depends entirely on the ability to create long wormholes that bypass the damaged near-wellbore region. Recently, much work has been performed to understand the wormhole propagation. This has led to various criteria and models to optimize matrix-acid treatment design for volumes, fluids, and flow rates. In many publications, the existence of an optimum flow rate for wormhole propagation has been described and efforts have been made to design treatments around these criteria. This paper will discuss several of the criteria and models that can be used to determine the optimum flow rate in both radial and linear flow and will introduce a new and simple criterion for both radial and linear flow that is based on diffusivity, reactivity, porosity, and surface area. Most of the criteria have been developed based on laboratory results or simulations in controlled and idealized environments. Under field conditions, many additional factors must be considered. Because of certain parameters such as significant heterogeneities in the formation, uncertainties in formation data, uncertainties in fluid placement, and operational constraints, the environment is neither controlled nor ideal. This paper will discuss the impact of these field conditions on the criteria and models to determine the optimum injection rate and verify their validity under field conditions. Examples and a case history are included to emphasize the need for consideration of these parameters. In addition, constraints are given to the validity of the criteria for the optimum flow rate under field conditions. This paper will further discuss the best practices and recommendations for cases where these constraints cannot be easily met or in cases where the data is uncertain. Introduction The major goal of acid stimulation under matrix conditions into carbonate formation is to create conductive flow channels known as wormholes that bypass the damage in the formation. These flow channels make the connection between the hydrocarbon-containing formation and allow the hydrocarbons to flow into the wellbore when the well is put back on production. The wormholes are formed when the matrix of the porous and permeable rock is dissolved by reactive fluids, such as hydrochloric acid (HCl). In contrast, during sandstone stimulation, only the damage inside the pores can be removed and typically wormholes are not formed. The practical implications are that matrix stimulation in sandstones can only restore a well's natural productivity (skin = 0) by removing damage if the damage skin is acid-soluble; whereas, matrix stimulation in carbonates can truly stimulate the productivity in a well because the highly conductive wormholes can penetrate beyond the damaged zone and result in a negative skin. To obtain this negative skin, the treatment must be performed in such a way that deep penetrating wormholes are generated. Three important parameters that can be controlled need to be considered: fluid volume, injection flow rate, and fluid type. The fluid volume is an import consideration because more volume will generally lead to deeper fluid invasion and to potentially deeper wormhole penetration. The second important aspect is the injection flow rate. Under some conditions, typically when the injection flow rate is too low, wormholes are not formed. Instead, only some of the permeable rock is dissolved in the vicinity of the wellbore. At the other end of the spectrum, when the injection flow rate is extremely high, one consequence could include the development of very thick wormholes that do not penetrate deep enough. The results of these two flow extremes have been observed in core tests and led to the observation that there is an optimum flow rate. The third parameter that can be controlled is the fluid type. Some fluids will behave better for wormhole propagation under known reservoir conditions, such as temperature, mineralogy, and permeability. Variations in acid types, concentrations, additives such as gelling agents, and emulsions affect the wormhole propagation.

Optimizing matrix acidizing is important to obtain the most effective stimulation treatment. Finding the optimum flow rate has been the subject of many papers and several of those focus on finding an optimum Damkohler number. This approach finds a unique solution only for a given linear core aspect ratio. Additionally, the pore volumes to breakthrough at the optimum Damkohler number are different between different laboratories and only scale to a master curve. This paper bridges the gap between data sets from different laboratories that have been performed using different aspect ratios. This paper uses the approach of minimizing the pore volumes to breakthrough as a function of interstitial velocity. To use the Damkohler number, the reactivities of all the rocks would need to be known, and they are generally not available from published work. Therefore, temperature is used in this model instead of reactivity. This paper analyzes many plain hydrochloric acid test results and takes into account differences in temperature, acid concentration, core aspect ratio, porosity, and permeability. Having obtained a global function to describe all the data, the data can be collapsed to form a master curve. From this master curve, one can predict the optimum pump rate given a set of experiments conducted on a given rock regardless of aspect ratio. The new methodology allows improved optimization of acid wormholing using linear core test data from various laboratories by taking into account acid concentration, core aspect ratio, test temperature, and rock morphology in a single mathematical description. Introduction Several investigators have put forth theories and equations to describe carbonate wormholing. Fredd and Miller (2000) and Tardy et al. (2007) have summaries of the previous work in this area. The general theme for most of these papers is to find an optimum injection rate when performing matrix acidizing. The goal is to find a surface injection rate that creates a network of highly conductive wormholes with the least possible amount of acid used. A flow rate too low leads to compact or face dissolution and a flow rate too high leads to inefficient tip splitting and side branching or uniform dissolution. In this paper, the concepts originally published by Buijse and Glasbergen (2005) will be used to further develop the understanding of how hydrochloric acid (HCl) reacts with the calcite rock matrix at flow rates that correspond to pressures less than fracture initiation pressure. Several authors have observed that the core length, diameter, or aspect ratio can have an impact on the optimum injection rate (Bazin et al. 1995, Bazin 2001, and Buijse 1997). Some authors have performed experimental series at different temperatures and acid concentrations. Further, many different types of rocks with different permeability and porosity have been used. By combining all of this data, a global model of the wormholing behavior of HCl and calcium carbonate (CaCO3) is proposed.