Using Dimensional Analysis to Develop Mathematical Model of Horizontal Well Cleaning

Abstract

    Cleaning the directional and horizontal sections of the horizontal well could be considered the most complex process during well construction, and the main limiting factor of horizontal elongation of the well. This is due to many factors that affect on cutting transportation toward the wellhead, such as, the tendency of drilling string to rest on the lower side of the hole, drilling hydraulic (mud flow rate and flow regime), properties of drilled rocks (cutting weight, size and shape), drilling fluid properties (weight, viscosity and other rheological properties), hole geometry (hole and drill pipes diameters), drill string movements (type and speed of movements), penetration rate (quantity of cutting to be moved out of the hole) and others.

Studying horizontal well cleaning process needs the full understanding of the combination effects of all above mentioned factors, taking in consideration that some of them affect each other. This understanding did not exist

yet, neither through theoretical nor experimental studies.

The effect of some of individual above mentioned factors have been studied which lead to form an acceptable description about cutting particles transportation while horizontal drilling. It is well proved that insufficient cleaning leads to form a bed of cutting on the lower side of the hole.

This study tried to analyze most the affecting factors on cutting transportation through the horizontal well sections using the dimensional analysis method to get some dimensionless factors which controlling hole cleaning process.

A mathematical model has been developed, relating the cleaning efficiency (the ratio of annulus section area equipped by cutting bed) as a function of some dimensionless numbers consisting from the affecting factors mentioned above. Relations for both laminar and turbulent flow regimes have been introduced.

These relations were applied on some previous published

experimental works and found that the most controlling dimensionless items affecting on cleaning process is that items which are referring to the fluid flow rate (Fraud Number) and to drilling string movement (Taylor Number). While the secondary controlling factors are the items referring to drilling fluid and cutting properties, and hole           inclination. This model may give a good tool for the drilling engineers to modify the drilling parameters to get the most suitable hole cleaning.

Further work is recommended to develop these functions to logical equilibrium equations to be instantaneously used in practical engineering.