A Comprehensive Model for Carbonate Matrix Acidizing in Complex Horizontal Well Completions
Authors: Ali Mahmoud T. , Zakaria Ahmed , Wang Jiliang , Chaudhary Saleem 
Published: February 2024

Abstract
Thousands of horizontal wells are completed around the globe in carbonate formations. Those long laterals are usually stimulated with acids to improve/restore productivity. Most horizontal wells are equipped with orifices/valves to uniformize production. Comprehensive modeling of wellbore hydraulics, flow through valves/orifices, annular flow, and wormhole growth in the formation is necessary to accurately model acid distribution in those wells.
This study introduces a detailed model to capture the physics and chemistry of acid flow in complex horizontal wells completed in carbonate formations. The pipes and annuli hydraulics are handled by accounting for the change in the hydrostatic head and the friction losses. A friction formula that accounts for fluid rheology is derived from flow-loop experiments. Mathematical models are implemented to account for the pressure drop across valves and orifices presented in complex lower completions, e.g., Limited Entry Liners (LEL), Inflow Control Devices (ICDs), and Inflow Control Valves (ICVs). The acid is distributed in the openhole-liner annulus based on the flow rate through the orifice/valve, annulus flow area, packers location, and formation injectivity. The flow distribution from the current model agrees with results from a widely accepted, advanced completions-flow modeling software.
An improved wormhole growth model was implemented to simulate acid flow in the formation. The linear model was validated using core flow experiments with a wide range of temperatures, acid concentrations, acid types, rock types, mineralogy, and core sizes. An upscaling scheme based on radial experiments and simulations was adopted. The skin values from the radial model developed in this work was found to be in excellent agreement with the post-stimulation field measurements.
Two case studies with the model application are presented. In the first case study, the new model was used to evaluate a stimulation treatment in an openhole extended reach horizontal well. An excellent match between calculated and observed bottomhole pressures was achieved with the model. This allowed investigating many scenarios (i.e., advanced fluids, chemical diversions) to improve acid placement designs and zonal coverage in those wells. In the second case study, the model was used to design a stimulation treatment in a well equipped with 16 ICDs and openhole packers that divide the well into seven compartments. The advanced model has shown that the 4,300 ft. lateral can be stimulated successfully by bull-heading using only 25 gal/ft. of low viscosity retarded acid system without diverters. The agreement between model predictions and post stimulation increase in well productivity confirms the model accuracy.
This paper presents an extensively validated model to simulate acid flow from the wellhead to the wormhole tip in carbonate formations. The model accounts for upper and lower completion wellbore hydraulics, pressure-drop across valves, annular flow, and wormhole growth. The comprehensive model introduced in this work provides stimulation engineers with a reliable tool to design successful acid stimulation jobs in complex horizontal well completions.