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

Abstract

Summary Matrix-acidizing models have traditionally underpredicted acid-stimulation 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 wormhole-growth 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.

The Accuracy of Carbonate Matrix-Acidizing Models in Predicting Optimum Injection and Wormhole Propagation Rates

“…Semi-Empirical models (Buijse and Glasbergen 2005;Furui et al 2012) also do not predict dissolution structures. Dominant wormholes are assumed for these models in calculating the propagation rate of the acid in the treated formation.…”

“…Péclet number theory based models such as the ones by Daccord (1989) and Frick et al (1994), and semi empirical based models such as the ones from Buijse and Glasbergen (2005) and Furui et al (2012) do not predict optimum injection rate.…”

“…To model fluid distribution and wormhole growth in a heterogeneous formation, this model must be embedded into a more comprehensive near-wellbore simulator. Furui et al (2012) extended the semi-empirical correlation model by Buijse and Glasbergen (2005) and combined it with the earlier described capillary tube model (Hung et al 1989), which is based on acid transport and fluid loss from a single wormhole. This model improves on the previous semi-empirical one by accounting for the effect of core size used in the coreflood test, from which the parameters used in the model are obtained.…”

“…Furui et al (2012) improved on the original semi-empirical model by Buijse and Glasbergen (2005) to account for the effects of core size used in the coreflood tests. The Furui et al (2012) model combines the Buijse and Glasbergen model with the Hung et al (1989) mechanistic model for wormhole propagation earlier described. The scale up technique developed by the authors extends linear coreflood tests to radial-flow observed in field applications, eliminating the core-size dependency and flow translation limitations.…”

“…The Furui et al (2012) modified semi-empirical equation to calculate wormhole growth rate, v wh , is given by Eq. (8):…”