Optimum Conditions for Wormhole Formation in Carbonate Porous Media: Influence of Transport and Reaction
- C.N. Fredd (U. of Michigan) | H.S. Fogler (U. of Michigan)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- September 1999
- Document Type
- Journal Paper
- 196 - 205
- 1999. Society of Petroleum Engineers
- 4.3.4 Scale, 4.2.3 Materials and Corrosion, 3.2.4 Acidising, 1.8 Formation Damage, 1.6.9 Coring, Fishing, 4.1.2 Separation and Treating, 5.1 Reservoir Characterisation
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The effects of transport and reaction on the phenomenon of wormhole formation were investigated for a wide range of fluid systems including strong acids, weak acids, and chelating agents. These fluid systems are influenced by a variety of transport and reaction processes such as the transport of reactants to the surface, the reversible surface reactions, and the transport of products away from the surface. When these transport and reaction processes are taken into account, a common dependence of the dissolution phenomenon on the Damko¨hler number is observed. There exists an optimum Damko¨hler number at which a minimum number of pore volumes are required for channel breakthrough. This optimum Damko¨hler number occurs at approximately 0.29 for all the fluid/mineral systems investigated in this study. In addition, an optimum kinetic parameter exists at which wormhole formation is most efficient. This optimum kinetic parameter occurs at a value of about 130. Together, the Damko¨hler number and the kinetic parameter provide a complete description of the dissolution phenomenon.
The flow and reaction of reactive fluids in carbonate porous media results in the formation of highly conductive flow channels, commonly referred to as wormholes. These wormholes form because of rapid rates of dissolution and a large percentage of the mineral being dissolvable in the reactant. The structure of the wormhole channels is strongly dependent upon the rates of mass transfer and the kinetics of the surface reaction, which may vary considerably among different fluid/mineral systems. Typical dissolution structures range from face dissolution (or complete dissolution of the medium starting from the inlet flow face) at low injection rates to ramified wormhole structures and uniform dissolution at high injection rates. Single dominant wormhole channels are obtained at intermediate injection rates. The formation of these single dominant wormhole channels represents the most effective means of matrix stimulation because these structures minimize the volume of fluid required to obtain a given depth of wormhole penetration.
The importance of wormhole formation on the effectiveness of matrix stimulation treatments has led many investigators to study the dissolution phenomenon.1-9 These studies have focused on either mass-transfer or reaction-rate limited systems, but do not account for the combined effects of transport and reaction processes. Recent studies have shown that alternative fluid systems such as chelating agents and weak acids are effective stimulation fluids.10 These alternative fluid systems are influenced by both transport and reaction processes11,12 and, therefore, cannot be described by results from previous studies. The combined influence of transport and reaction processes has been included in a generalized description of the dissolution phenomenon.13 A common dependence on the Damko¨hler number was demonstrated and an optimum Damko¨hler number for wormhole formation was observed for a wide range of fluid/mineral systems.
This paper extends the study of the influence of transport and reaction on the phenomenon of wormhole formation by varying the pH and temperature of a wide range of fluid systems, including HCl, acetic acid, and chelating agents. The importance of mass transfer and surface reaction on wormhole formation is demonstrated, and the existence of an optimum Damko¨hler number is substantiated under a variety of conditions. The dissolution phenomenon is fully described by including an additional kinetic parameter. Optimum conditions for wormhole formation are demonstrated for a wide range of fluid/mineral systems.
Optimum Stimulation Conditions
Several investigators have studied the phenomenon of wormhole formation in a variety of fluid/mineral systems and have reported the existence of an optimum injection rate. The optimum injection rate represents the conditions at which a minimum volume of fluid is required for the wormhole channel to breakthrough, or percolate, a porous medium. Daccord et al.1 investigated the water/plaster of Paris system and reported the optimum injection rate to occur at a Peclet number just above unity. (The water/plaster of Paris system is limited by the rate of transport of products away from the surface at ambient temperature.14) The Peclet number is defined as the ratio of the rate of transport by convection to the rate of transport by diffusion. A similar dependence on the Peclet number was observed for the HCl/limestone system,2-4 which is limited by the rate of transport of reactants to the surface above 0°C.15 Daccord et al.3 and Frick et al.5 combined the concepts of fractal geometry with the dependence on the Peclet number to describe wormhole formation in the HCl/limestone system. Bazin et al.6 studied the HCl/limestone system and reported efficient wormhole formation to occur at a transition between convection and mass-transfer limited regimes. Wang et al.7 and Huang et al.8 investigated HCl/limestone and HCl/dolomite systems and proposed that the optimum injection rate occurs at a transition between reaction-rate and fluid-loss limited regimes. (The dissolution of dolomite by HCl is reaction-rate limited below about 50°C.16) Despite mass transfer having a major influence on wormhole formation, diffusion plays only a minor role in their theory.
Hoefner and Fogler9 investigated the HCl/carbonate systems and found that the phenomenon of wormhole formation is governed by the Damko¨hler number for flow and reaction. The Damko¨hler number is defined as the ratio of the net rate of dissolution to the rate of transport by convection, where the net rate of dissolution is the rate of mass transfer or the rate of surface reaction for mass-transfer or reaction-rate limited systems, respectively. They varied the Damko¨hler number over several orders of magnitude and observed most efficient wormhole formation at intermediate values. Because the Damko¨hler number is inversely proportional to the injection rate, this observation is consistent with the existence of an optimum injection rate for constant fluid/mineral properties.
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