A comprehensive model of high-rate matrix acid stimulation for long horizontal wells in carbonate reservoirs

Matrix acidizing models have traditionally under-predicted acid stimulation benefits due to under-prediction of wormhole penetration and corresponding completion skin factors in vertical wells. For long horizontal wells drilled in carbonate reservoirs, productivity enhancement is a function of acid placement and effective wormhole penetration. However, prediction of wormhole penetration requires more effective analysis than provided by current industry models. This paper presents results of matrix acid modeling work for horizontal wells and describes a practical engineering tool for analyzing the progress of matrix acid stimulation for cemented and un-cemented horizontal well completions typically employed in carbonate reservoirs. An integrated flow model has been developed to predict the wellbore pressure profile and wormhole distribution by tracking the movement of the acid in the wellbore and the formation. Analysis of injection rates and pressures during acid treatment provides engineers with a way to determine the varying injectivity and tubing friction as stimulation proceeds. The model presented here can be used as a forward model for analyzing real-time treatment rate and pressure histories and can also be used to review past treatments to improve future treatment designs. The wormhole growth model is based on Buijse and Glasbergen's empirical correlation augmented by the effect of formation heterogeneity and scale-up procedures that extend the wormhole geometry and penetration from laboratory flow tests on small cores to field-size treatments. Application of this modeling shows acid wormholing through carbonate formations can provide significant stimulation resulting in post-stimulation skins as low as -3.5 to -4.0 vs. previously predicted values in the -1.0 to -2.0 range. Using actual field stimulation data, we also discuss key elements to successful stimulation planning and the diagnosis of matrix acid treatments to achieve effective wormhole coverage for horizontal completions in carbonate formations.