Data Analytics and Development of a Wellbore Cleaning Coefficient Model

Abstract

In this study, wellbore cleaning coefficient (WCC) correlations were developed for three conventional coiled tubing sizes (2.375”, 2.625”, and 2.875”). These sizes correspond to roughness to internal (ε/D) ratios of 0.000460828, 0.000510637, and 0.000572517, respectively. Dimensional analysis, applying the Buckingham-π theorem and a database from 150 wells in the Spraberry formation in West Texas, was used. Key performance indicators (KPIs) that influence flow in a cased pipe around an object (coil tubing) were identified and employed in model development. These KPIs are (1) slick water density ( f ñ ), (2) slick water viscosity ( µ f ), (3) hydraulic diameter ( c t d - d ) between casing inner diameter (dc ) and coil tubing outer diameter ( t d ), (4) average annular velocity ( v ) and (5) cleaning pressure gradient(∆P) . The cleaning pressure gradient is the ratio of the circulating differential pressure (pu -pd ) to measured depth (MD). A global model that relates WCC to the Euler number and the inverse of the Reynolds number was attempted at first. A low coefficient of multiple determination R2 of 0.626 was obtained. To better explain the physics of the cleaning process and improve the model fit, data segregation was performed by separating data into three data sets, a set for each ε/D ratio. R2 of 0.974, 0.945, and 0.877 were obtained. It was decided to separate the database further and create models that would be used to identify “clean” and “not clean” wellbores. These equations addressed operational conditions since in data partition threshold values of annular velocity, Euler and Reynolds numbers were applied to describe laminar and turbulent flow conditions. The predictive equations showed excellent degrees of fit with R2 of 0.979, 0.822, and 0.897, for clean wells for the three ε/D ratios, respectively. This study’s findings were also validated using cumulative debris versus elapsed time data from 12 Woodford wells.