Transient drilling fluid flow in Venturi channels: comparing 3D and 1D models to experimental data

Abstract

In well drilling operations, bottom hole pressure control within a narrow pressure margin has a high risk of influx (kick) and outflux (loss) at greater depths. Kick occurs when the formation pressure is higher than hydrostatic pressure on the borehole. As a consequence of poor bottom hole pressure control, the following adverse effects can happen in the drilling operation: increase of non-productive time, fracturing of the wellbore, loss of drilling fluid, and in a worst-case scenario: blowout. Monitoring the active pit volume and measuring the return flow using a flow paddle in the open channel running to the active pit are the standard kick monitoring methods. These methods have low accuracy, which limits the resolution of kick/loss detection. As a low cost and accurate solution for the return flow measurement, a Venturi flume method was studied in this thesis work. The thesis presents the results of modeling return channel flow under two aspects: 3D computational fluid dynamics (CFD) modeling and 1D numerical modeling. The flow modeling results were validated with experimental laboratory results. The experiments were carried out in a laboratory Venturi rig for water and drilling fluids. Measurement were taken from ultrasonic level sensors, a Coriolis mass flow meter, an Anton Paar rheometer and a density meter, and the channel inclination was measured and taken into account. The model drilling fluid used in the experiment is a water-based drilling fluid, which contains potassium carbonate as a densifying agent and xanthan gum as a viscosifier.

The CFD models are based on the volume of fluid (VOF) model and the Eulerian multifluid VOF method. 3D and 2D CFD open channel flow always can be considered as a multiphase flow because it has an interface (free surface) between the flowing fluid and air above the flowing fluid. The non-Newtonian behavior of drilling fluid, the effect of drill cuttings, gravity flow, hydraulic jump, turbulence, wall and boundary conditions, and unsteady flow were the main factors analyzed from the CFD simulations. The 1D model, which is a version of the shallow water equations, was developed from the fundamental conservation laws by application to a non-Newtonian open Venturi channel flow. The flow depth and mean flow velocity (or flow rate) are the state variables of the developed 1D model. The momentum equation was modified with additional friction slopes for the non-Newtonian drilling fluid. High resolution well balanced numerical schemes were used to solve the developed 1D model because of unsteady hydraulic jumps propagation. The second order accurate total variation diminishing (TVD), flux limiter centered (FLIC) scheme and the fourth-order Runge-Kutta scheme were used to solve the 1D numerical model. The cell interface fluxes, discretized with the finite volume method (FVM), is calculated with a higher order flux and a lower order flux combined with a flux limiter function, still keeping the second order accuracy.

A hydraulic jump, depending on the channel inclination, stands between the inlet and the Venturi contraction. Flow regimes, when there is a standing hydraulic jump, changes supercritical to critical, and critical to subcritical until the Venturi throat; after the Venturi throat, subcritical to critical, and critical to supercritical. An oblique jump propagates, when the flow state is at supercritical flow condition, at the Venturi throat. The wall-reflection pressure-force from the contraction walls significantly changes the flow regimes in open Venturi channel flow. The conventional shallow water equations must be modified to capture the wall-reflection pressure-force effect in irregular geometry. The strictly hyperbolic requirement can be violated in the FLIC scheme, which allows adding additional friction slopes to the Saint-Venant equations. Two friction slopes in the 1D open channel model can be correlated for drilling fluid flow: external friction slope and internal friction slope. The external friction slope covers the wall friction and turbulence behavior, and the internal friction slope covers the non-Newtonian surface friction and laminar behavior. The developed 1D model of the TVD Runge-Kutta scheme can be used for real-time flow measuring in the well return flow using a single level sensor. Drill cuttings effect on the flow depth might be insignificant for low concentrations of drill cuttings, especially in short length open channels.