Optimum Conditions for Wormhole Formation in Carbonate Porous Media: Influence of Transport and Reaction

Abstract

Summary 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 Damköhler number is observed. There exists an optimum Damköhler number at which a minimum number of pore volumes are required for channel breakthrough. This optimum Damköhler 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 Damköhler number and the kinetic parameter provide a complete description of the dissolution phenomenon. Introduction 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 Damköhler number was demonstrated and an optimum Damköhler 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 Damköhler 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 Damköhler number for flow and reaction. The Damköhler 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 Damköhler number over several orders of magnitude and observed most efficient wormhole formation at intermediate values. Because the Damköhler 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.

Microemulsion Applications in Carbonate Reservoir Stimulation

“…(Fluids were injected from left to right during linear coreflood experiments.) The top four images are neutron radiographs of dissolution structures formed during the dissolution of limestone by hydrochloric (HCl) and ethylenediaminetetraacetic acid (EDTA) [11,22,23]. The bottom image is a Wood's metal casting of a dissolution structure formed during the dissolution of dolomite by aqueous HCl [10].…”

“…Early investigators recognized the significant influence of mass transfer on wormhole formation in limestone [12,13]. This influence has served as a basis for many of the theories describing wormhole formation and has led to models of wormhole formation that depend on dimensionless terms such as the Peclet number (ratio of rates of transport by convection to transport by diffusion) [14][15][16] and the Damköhler number (ratio of the overall rate of dissolution to the rate of transport by convection) [10,11]. Both dimensionless terms depend on the effective diffusion coefficient and successfully predict wormhole formation for at least a few types of dissolution structures.…”

“…This dependency is illustrated in Figure 2 where the type of dissolution structure and corresponding normalized number of pore volumes to breakthrough is shown as a function of the Damköhler number for a wide range of fluid/rock systems (adapted from Ref. [11]). The data includes aqueous HCl, organic acids [acetic acid (HAc) and formic acid (HFc)], and chelating agents [ethylenediaminetetraacetic acid (EDTA), 1,2-cyclohexanediaminetetraacetic acid (CDTA), and diethylenetriaminepentaacetic acid (DTPA)], which have varying effective diffusion coefficients and are influenced by reversible or irreversible surface reactions.…”

“…The dissolution removes resistances to flow and creates highly conductive flow channels, thereby allowing oil or gas to flow more readily. The key parameter governing channel formation is the Damköhler number which is the ratio of the rate of reaction of the acid with the porous medium to the rate of convective transport of the acid through the rock [9][10][11]. When the Damköhler number is high, such as would be the case for low acid flow rates or high acid reaction rates, the acid will not penetrate very deep into the rock, resulting in face dissolution and little if any penetration and dissolution into the formation.…”

“…However, the treatments are often constrained by the very rapid rate of reaction between HCl and carbonate rock, which results in limited depth of live acid penetration and ineffective flow capacity of the acid-dissolution channels [9][10][11][12][13][14][15][16][17]. The rapid HCl-carbonate rock reaction is limited by the rate of mass transfer of acid to the rock surface (diffusion limited) under common reservoir conditions [18,19].…”