In this paper, we study the dissolution process in carbonates for the design of acidizing jobs. The difficulty is the modelling of the formation and the propagation of the dissolution patterns (the wormholes) which result from an instability very similar to viscous fingering.
In reservoir simulators, the flow equations must generally be written at a scale larger than the standard Darcy equations in order to incorporate the heterogeneities of the formation (upscaling). In multiphase displacements without acidizing, the upscaled properties such as relative permeabilities and capillary pressure, are derived from properties on homogeneous core samples by numerical simulations using the standard Darcy's equation ("Kyte and Berry" methods). For acidizing, the upscaling process must also incorporate the effect of the dissolution which is similar to heterogeneity which change with time. To derive the upscaled properties, we will use a similar approach based on numerical simulations. However, we need a numerical simulator that can account for worm-hole formation at Darcy scale.
We have built a 2D numerical simulator which calculates the dissolution pattern in a core. The originality of the simulator is the introduction of the physics at the pore scale:
The flow equation takes into account Darcy flow in the matrix and Stokes law in the wormhole.
The dissolution equation is derived from a volume averaging of the diffusion and reaction equations written at the pore scale.
Comparison between the numerical simulations and experimental results demonstrates that adequate physics is introduced in the model:
The various dissolution regimes observed in experiments are also obtained in numerical simulations: compact, wormholing and homogeneous
An optimum flow rate corresponding to the maximum penetration of the wormhole is also reproduced with the simulator.
For the effect of concentration and core length, the simulations exhibit the same trends as those observed with the experiments
In addition, the simulator as been used to study the effect of parameters which are difficult to change experimentally. The larger number of "numerical experiments" will be used to build the upscaled model for reservoir simulations.
Acid injection is a process widely used for stimulation of petroleum wells to increase rock permeability1,2. The dissolution of the porous matrix is an unstable process similar to viscous fingering that leads to the formation of dissolved channels called wormholes. Many experimental and theoretical studies have tried to describe the roles of the various factors on the formation of the wormholes: injection rate, acid volume, permeability, reaction kinetics, etc…. Today, most of the mechanisms can be considered as understood but the models available in literature are still qualitative.
The dissolution kinetics at the level of the solid walls of the grains is well understood. The dissolution process can be separated into three successive steps: the acid transport by diffusion and advection to the solid surface, the chemical reaction at the solid surface, and the transport of the products of the reaction away from the surface. If the chemical reaction characteristic time is very short compared to the mass transfer kinetics, the process is called mass transfer limited. This is the case for limestone dissolution with HCl at temperatures larger to 0°C3. On the other hand, if mass-transfer kinetics is slow, then the process is reaction rate limited. It is the case for dolomite dissolutions with HCl at temperatures inferior to 50°C4. In this paper we will study only the case of mass transfer limited dissolution processes.