Experimental Determination of Interfacial Friction Factor in Horizontal Drilling With a Bed of Cuttings
Authors: Martins A.L. , Sa C.H.M. , Lourenco A.M.F. , Freire L.G.M. , Campos W. 
Published: December 2007

Abstract
The study of stratified solid-liquid annular flow is relevant in several areas, e.g., mining and oil industries. A typical application is in the study of the removal of the rock formation cut by the bit during the drilling of a horizontal or highly inclined well. Several theoretical models have been proposed for the description of this phenomenum. In these models, some empirical parameters are required, such as the shear stresses at the interface between the fluids and the cuttings bed and the maximum cuttings-wall friction factor which avoids bed movement. This work shows the results of an experimental work developed on a large scale flow loop aiming at the quantification of these empirical parameters. The tests consisted on the visualization of a sandstone bed erosion by different polymeric solutions flowing through an annular section. Pressure losses and steady state bed heights were recorded for several input parameters, such as fluid flow rate, rheology and density, annular geometry, eccentricity and particle size.

Introduction
The drilling of horizontal wells is already a common practice worldwide, and considerable effort is being spent now at reducing costs and increasing safety for these operations. One way of pursuing these objectives is through the use of computer simulators, which are of great help on designing and troubleshooting.
One important aspect of drilling high angle wells is the removal of the cuttings that tend to deposit on the lower part of the horizontal annular section. The description of the complex solid-liquid flow taking place during this removal, in which non-Newtonian drilling fluid is used, requires information about the interactions among the different materials involved, namely, fluid, rock cuttings, rock formation and pipe. These properties are necessary inputs for mechanistic models, developed to characterize the phenomena. It very often occurs that, due to a lack of experimental data, researchers use information from the mining industry, i.e., data obtained from pipe flow of water and mineral grains. This practice, naturally, is questionable, because those flows do differ considerably from the flow of drilled cuttings and non-Newtonian fluids in an eccentric annulus.
In order to overcome this lack of information, an extensive experimental work has been performed in relation to cuttings transport. In this paper, the data have been used to quantify the friction at the interface between the stream and the cuttings bed, as well as the static force between cuttings bed and bore hole wall, which prevents the bed from moving. The procedure used is an adaptation of the one proposed by Torres in the context of gas-liquid stratified flows.

Experimental Program
Experiments have been conducted on a pilot scale flow loop built at the PETROBRAS research center (Martins et al.). The test section consists of a 12m long 0.127 m diameter acrylic pipe where 0.0508m and 0.0635 m PVC internal pipes are introduced to represent two typical annular geometries of horizontal wells. A solids injection system is coupled at the entrance of the test section. Fig. 1 shows a schematic view of the flow loop.
The tests consisted of the following steps:Build up of a constant height solids bed along the test section;Interruption of the solids injection and increase of the fluid flow rate: the bed is eroded until a new equilibrium height is obtained;Measurement and recording of the pressure drop and bed perimeter.
Experimental data have been obtained for different annular geometries, and different values of solid/fluid properties and operational variables. Hence, variables such as eccentricity, particle diameter, rheology, fluid density and flow rate have been changed. The mass flow rate of the polymeric solution has been measured by a Coriolis type equipment, while pressure drop has been determined by a differential pressure transducer. The sandstone bed perimeter has been recorded by direct length measurements.
Test Matrix. A total of 55 different tests were performed using solutions of Xhantam Gum, at different concentrations, to represent the drilling fluids and particles of sandstone of different diameters.
P. 39