Optimal design of matrix acidizing treatments in long horizontal wells represents a technical challenge for stimulation engineers. Acid coverage and distribution are particularly challenging because differences in formation permeability can be a predominant feature in horizontal wells. If acid is not effectively diverted in formations with high permeability anisotropy, some treated zones may become acid sinks while other zones are left with inadequate acid stimulation. Acid coverage and distribution depend on chemical and physical processes at different length scales. In the microscopic or pore scale in carbonate formations, acid creates flow paths of high permeability or wormholes which can affect the further penetration of the acid treatment downhole. In the macroscopic scale, fluid hydraulics in both wellbore and reservoir affect acid distribution as well.
In this paper, we present an integrated model in both the microscopic and macroscopic scale to simulate multistage acidizing treatments in limited-entry and open-hole long horizontal wells. We propose a modified semi-analytical model to describe the wormholing phenomena and chemical diversion by using core flow test data. The reservoir heterogeneity in both vertical and horizontal directions is taken into consideration in this model. In addition, we establish a dynamic wellbore hydraulics model to characterize the fluid mechanics inside the wellbore with considerations for acid distribution, pressure drop due to friction loss, fluid rheology and fluid flow behavior.
The integration of the elements mentioned above makes of this model a powerful tool to optimize critical parameters for matrix treatment design and distribution such as treatment interval length, diverter and acid volume, number of stages, and optimal rates. We present a case study to investigate the effects of chemical diversion, acid injection rate and volume on the performance of the treatment. The results of acid distribution, wormhole length and skin factor for each treatment interval as functions of time are analyzed. The evolution profiles of wellbore hydraulics during the acidizing treatment are also discussed.