Annular Friction and Cuttings Density Effects on Pressure Margins in Belhedan Fractured Carbonate Wells

Abstract

Annular friction and suspended cuttings can consume much of the pressure allowance in fractured carbonate wells even when annular losses are below 4% of standpipe pressure. This study uses actual field operating inputs and WellPlan hydraulic outputs from Belhedan wells V33, V36, and V39 to compare segmented Bingham-flow models and evaluate solids-loading effects against local pressure reserves. Exact concentric-annulus and plane-slot solutions separate curvature error from plug-flow truncation. At fixed flow rate, the relative pressure-gradient error of the linearized slot is ξ³/2 (requiring plug ratio ξ ≤ 0.464159 for a 5% tolerance), whereas a 1,860-state dimensionless survey (0.20 ≤ κ ≤ 0.80, 1 ≤ Bi ≤ 60) finds a maximum slot-to-annulus curvature error of 3.36%. Across the wells, the exact solutions differ by 0.10–0.12 psi, whereas linearization adds 6.97–9.24 psi. At 1 vol% solids, the calculated margin sign differs across models in V39 (+5.78 vs. −3.59 psi, consuming 162% of the concentric reserve; +5.44 psi with micromechanical coupling) at diagnostic specific gravity 2.145, and in V33 (+1.28 vs. −1.75 and −5.79 psi) and V36 (+0.69 vs. −2.83 and −7.37 psi) at calcite reference density 2.71. Model-specific critical formation limits (F_crit,m) delimit where hydraulic model choice changes the margin classification.