A comprehensive model of high-rate matrix-acid stimulation for long horizontal wells in carbonate reservoirs: Part i-scaling up core-level acid wormholing to field treatments

Matrix-acidizing models have traditionally underpredicted acidstimulation benefits because of underprediction of wormhole penetration and the corresponding magnitude of 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 that 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 in carbonate reservoirs. The wormhole-growth model is based on the Buijse and Glasbergen empirical correlation. Combining with the mechanistic model of the wormhole propagation based on acid transport and fluid loss from a single wormhole, a modified Buijse-Glasbergen wormholegrowth model is developed that relates the wormhole growth rate to the in-situ injection velocity at the tip of the dominant wormhole. The wormhole constitutive model developed in this study also accounts for core-size dependencies seen in laboratory acid-flood experiments. A semianalytical flow correlation is derived for estimating interstitial velocities at the tip of the dominant wormholes based on a number of 3D FEM simulation analyses, accounting for more realistic flow regimes (radial and spherical flow) typically observed in field application. The scaleup procedure developed in this study extends the wormhole geometry and penetration from laboratory flow tests on small cores to field-sized treatments. The scaleup procedure developed in this work can be applied to cemented and uncemented horizontal wells, including barefoot and perforation-cluster completions typically employed in carbonate reservoirs. Application of this modeling shows that 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.