The transport and reaction of fluids in porous media

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.

No abstract

No abstract

Introduction Acidizing treatments are commonly used to remove near-wellbore damage and create artificial flow channels in carbonate formations. Matrix acidizing treatments are most useful when fracture acidizing is undesirable, such as when a shale break or other natural boundary must be maintained to prevent water or gas production, or where fracture acidizing is ineffective, such as in soft chalk formations. Unfortunately, matrix treatments often require low injection rates to prevent fracturing the formation rock or are required in heterogeneous formations with zones of low-conductivity (which need stimulation the most) that accept acid at low rates. It is at these low injection rates that the problem of rapid acid spending severely limits the acid penetration distance. The injection of hydrochloric acid into carbonate formations at low rates results in face dissolution, or complete dissolution of the carbonate matrix near the wellbore This face dissolution requires large volumes of acid and provides negligible increases in the conductivity of the formation. Various acid systems have been used to reduce the limitations of rapid acid spending at low injection rates. A few of the acids include:weak acids, such as acetic and formic acid, which have relatively low H+ concentrations and therefore react with carbonates at a slower rate than HCl,chemically retarded acids, such as oil external microemulsion systems containing HCl, that retard acid diffusion to the carbonate surface and thus allow deeper penetration of live acid, andfoamed acids (nitrogen gas and aqueous HCl) that prevent acid from spending outside the primary dissolution channel thereby promoting the growth of wormholes. Although retarded and foamed acid systems can stimulate carbonate formations at lower injection rates, strong acids such as HCl induce the precipitation of asphaltic sludge from crude oil. This sludge can plug the formation and restrict production after an acidizing treatment. When ferric ions are present, this problem is even more severe. Thus, adequate corrosion protection becomes more essential. Acetic acid, an iron chelating agent, does not reduce sludging tendencies in the presence of ferric and ferrous iron. A variety of acid additives (anti-sludging agents, corrosion inhibitors, and iron reducing agents) have been used to prevent the sludging problem. However, their effectiveness is limited by the need to obtain a compatible combination of additives and a lack of understanding of the complex chemistries involved in the precipitation reactions. These limitations demonstrate the need for an alternative stimulation fluid that combines the ability to stimulate at low injection rates with fluid properties that are not conducive to asphaltic sludge precipitation or corrosion problems. Ethylenediaminetetraacetic acid (EDTA) is an alternative fluid that is capable of stimulating carbonate porous media. EDTA is a chelating agent that stimulates by means of sequestering the metal components of the carbonate matrix. The dissolution mechanism is different from HCl in that hydrogen ions are not required.