A Semi-Empirical Model To Calculate Wormhole Growth in Carbonate Acidizing

Abstract

Abstract The success in matrix acidizing carbonate formations depends entirely on the ability to create long wormholes that bypass the damaged near wellbore region. During the last decade, much progress has been made in the understanding of the physical and chemical processes that determine the final wormhole structure.Several different wormhole models have been proposed in literature. These models are usually successful in predicting wormhole growth under idealized conditions in the laboratory: linear core flow tests, one main wormhole, simple fluids like HCl with known rheology and reactivity, etc. In the design of an acid treatment, however, these models are less useful because they cannot handle the complex field conditions such as: radial flow, multiple wormholes, complex fluids such as emulsified acids or foams, etc. In this paper, we describe an alternative approach to model wormhole growth. A relatively simple wormhole growth model is developed, that still captures the essential physics and chemistry, and is therefore qualitatively correct. The model is semi-empirical, in the sense that the accuracy depends on two parameters that can be measured in a simple (linear) core flow test. Alternatively, the value of these two parameters can be taken from literature data. In developing the model, the intend was to create a relatively simple tool that can be used by the field engineer to design and optimize an acid treatment, and answer basic questions such as: what type of acid must be used and what is the optimum acid volume and pump-rate? The paper will describe the details of the wormhole growth model. The wormhole model was embedded in a comprehensive near wellbore flow simulator to analyze wormhole behavior in more complex environments, such as multi-layered reservoirs and long horizontal wells.The model has been used with good success in the design of many carbonate acid treatments. Several examples will be discussed in the paper. Introduction In matrix acidization of carbonate formations, the acid generates highly conductive channels, or "wormholes", that bypass the damaged near wellbore region and lower the skin. Creation of wormholes and optimization of the wormhole length is one of the main goals in acid treatment design.A proper understanding of the parameters that affect wormhole growth is therefore important.Acid wormholing has been the subject of numerous studies and many papers[1–17]. These studies revealed the complexity of the wormholing process. Moreover, although much insight has been gained into the fundamental chemistry and physics underlying the wormholing process, gaps in the knowledge still remain. For example, the mechanism behind the wormhole density is only poorly understood. Modeling wormholing has proven to be equally difficult. Many published models start with basic chemistry and physics[9–16]. Acid flow in a pore, or in a network of pores, is coupled with acid diffusion and reaction at the pore wall. Some models exploit the fractal behavior of wormhole patterns and use diffusion limited aggregation (DLA) equations to describe wormhole growth. See e.g. Fredd et al.[13] for a recent overview of the existing models. Parameters that are used in most models are:mineralogy, porosity and permeabilityacid concentration and (effective) acid diffusionacid-rock reaction rateacid injection rate These modeling exercises invariably lead to complex models, that are sometimes difficult to understand and difficult to implement. The models are generally successful in predicting wormhole growth in well defined (idealized) conditions in which acid and rock properties are accurately known. For example, the results of linear core flow tests are usually well reproduced. In reality, however, conditions are more complex with wormhole growth depending on many parameters that are not present in the current models, for example:rock heterogeneity, natural fractures, wetted surface areaacid rheology, dissociation constant (weak acids)acid types: emulsified, foams, in-situ viscosified acidsacid additives and the effect on properties such as wettability and reaction rate