Acid-wormholing in a carbonate formation is the result of several chemical and physical processes, including acid diffusion, reaction kinetics and dynamics of fluid flow in porous media. A proper understanding of the combined effect of these processes is essential for the design of acid treatments below and above fracturing pressure. In matrix acid treatments wormholes are favourable. Depending on the interaction of the driving mechanisms, compact dissolution, a few dominating flow channels or a branched network of thin wormholes may emerge. A sound understanding of these mechanisms is the basis for treatment optimization and development of new stimulation strategies. This extended abstract summarizes some results of a study on the mechanisms behind wormholing. These results will be used to build a wormhole evolution model that can aid in the design of acid-fracturing and matrix-acid treatments in carbonate formations. Such a model will be described in a future paper.
Acid flow and reaction in a wormhole was studied by modelling the wormhole as a cylinder and numerically solving the mass balance equation that describes acid transport by convection and diffusion. The acid-rock reaction rate enters the equations as a boundary condition. Often the mathematical problem is simplified when an infinite acid-rock reaction rate is assumed or, similarily, a completely mass-transport controlled acid spending rate is assumed. The boundary condition is in that case: C(x,r=rw)=0. However, this assumption excludes the study of situations in which the acid spending rate is (partly) reaction-rate controlled, such as low-temperature dolomites or low-reactivity acids. Furthermore, the spending rate control mechanism is a function of pore diameter. In the smaller pores near the wormhole tip, acid spending is often limited by the reaction rate. Precisely this area is important for wormhole growth. In this work, a finite acid-rock reaction rate was assumed, given by the power relation J=kCn.
The parameters that define the acid concentration profile in the wormhole (Q, D, rw, C0, krate and n) can be grouped into dimensionless numbers. These dimensionless numbers follow naturally when the diffusion-convection and reaction-rate boundary equations are expressed in terms of normalized variables for acid concentration and axial and radial position (CN=C(xN,rN)/C0,xN=x/rw, and rN=r/rw):
The dimensionless numbers Npe and Nki are the Peclet and kinetic number respectively and are given by:
The Peclet number describes the relative importance of mass transport by convection and diffusion, while the kinetic number describes the relative importance of reaction rate and diffusion rate. A third dimensionless number that is sometimes used is the Damkohler number, equal to the ratio Nki/Npe.
If Nki»1, the spending rate is controlled completely by mass transport processes and the acid concentration profile in the wormhole is a function of Npe only. For this situation, Levich derived an approximate solution of equation (1) in terms of a mass-transport coefficient KMT.