Beyond the Damkohler Number: A New Interpretation of Carbonate Wormholing

Abstract

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.

Wormhole Formation in Carbonates Under Varying Temperature Conditions

“…Most of the work has been reported in the works of Schechter and Gidley (1969), Lund et al (1973Lund et al ( , 1975, Williams et al (1979), Hoefner and Fogler (1985, 1988, Daccord (1987), Daccord et al (1989), Hung et al (1989), Hoefner et al (1987), Kurmayr et al (1992, Pichler et al (1992), Schechter (1992), Wang et al (1993), Daccord et al (1993aDaccord et al ( , 1993b, , Bazin et al (1995), Chen et al (1997), Fogler (1998, 1999), Huang et al (1997Huang et al ( , 1999, Gdanski (1999), Bazin and Abdulahad (1999), Bazin (2001), Buijse (2000), Golfier et al (2002), Buijse and Glasbergen (2005), Glasbergen et al (2005), Panga et al (2002Panga et al ( , 2004Panga et al ( , 2005, Tardy et al (2007), Ziauddin and Bize (2007), Cohen et al (2007Cohen et al ( , 2008, Kalia andBalakotaiah (2007, 2009) and Talbot and Gdanski (2008). Most of the work has been reported in the works of Schechter and Gidley (1969), Lund et al (1973Lund et al ( , 1975, Williams et al (1979), …”

HP/HT Carbonate Acidizing—Recent Discoveries and Contradictions in Wormhole Phenomenon

“…1 (Talbot and Gdanski 2008) and this is shown in Table 4. 3 and 4 show the experimental PVBT data for 15% HCl and 1% HCl modeled using Eq.…”

“…The interstitial velocity (and the wormhole growth rate) keeps decreasing as the fluid moves radially outward. Talbot and Gdanski (2008) further modeled wormhole efficiency factor (W eff ) and wormhole beta factor (W B ) of Buijse and Glasbergen (2005) model as a function of acid concentration, system temperature, sample porosity and permeability, and aspect ratio, making the wormhole growth model more generalized in nature. Matrix acidizing treatment design therefore requires use of a simulator to track the wormhole penetration/front.…”

Development of Acid Fracturing Model for Naturally Fractured Reservoirs

“…To estimate the amount of leakoff through the matrix, the effect of wormhole length on leakoff is considered. The wormhole length is calculated using the method presented by Talbot and Gdanski (2008). The etching of the hydraulic fracture and the width increase with time are neglected by the model.…”