A Computer Model for Hole-Cleaning Analysis
Authors: Iyoho A.W. , Horeth II J.M. , Veenkant R.L. 
Published: December 2007

Summary
This paper describes a unique computer modeling capability for hole-cleaning analysis in the total drilling system context. The New Material Balance (NMB) model uses standard drilling data - rate of penetration (ROP), pump rate, bit size, wellbore geometry, and mud properties - to generate a wellbore profile of hole-cleaning parameters. To accomplish this, the model calculates wellbore constituent velocities and concentrations by solving a set of finite-difference equations representing material transport throughout the wellbore. The current version of the NMB model is for straight holes-i.e., hole angles not exceeding 10 degrees [0.17 rad] from vertical. Work is in progress to extend the model to high-angle wells.
Results obtained from the model include:cuttings concentration and cuttings-size distribution in the annulus degreescuttings settling velocity, net transport velocity, and transport ratio;effects of mud weight and mud rheology on hole cleaning,effects of ROP and pump rate on hole cleaning degrees andequivalent mud weight, considering cuttings loading for various drilling scenarios.
The model has been tested successfully against a variety of laboratory and field data. One direct application of the model is to perform analytical hole-cleaning studies; but it is also a vital link in total drilling system simulation for ROP and solids-control studies.

Introduction
The study of hole-cleaning problems has been a major concern for years in the drilling industry because inadequate hole cleaning can lead to stuck pipe, fractured formations, high rotary torque, and decreased ROP.
This paper discusses the development, testing, and applications of the NMB model used for hole-cleaning studies in the context of a total drilling simulator. We refer to it as the "material balance model" because it is based on the physical principle of mass conservation in the wellbore. This is a new hydraulics transport model that replaces an earlier unpublished version. it is tightly coupled to a hydraulics pressure model. The NMB model will soon be implemented into a second-generation drilling simulator that eventually will replace the Engineering Simulator for Drilling described by Millheim and Huggins. Millheim also presented a comprehensive discussion of the role of simulators in drilling operations.
The drilling-system simulator is an attempt to improve conventional analysis techniques by modeling the drilling process as a complete system. The NMB model is one of several models that represent the whole drilling process (geology, drill bit. wellbore, drillstring, rig equipment, mud system. and solids-control equipment). Refer to Figs. 1 and 2 for "causality diagrams" i.e, schematics of how the models coexist and interact in the simulator. Fig. 3 depicts the total drilling system modeled by the simulator.
The NMB model should be particularly useful and interesting because, to the best of our knowledge, there has been no previous comparable model and it provides a quantitative, analytical basis for addressing certain drilling design concerns for the first time. The major concerns in designing drilling hydraulics areobtaining good bit cleaning and ROP (by removal of cuttings from under the bit);circulating drilled cuttings up the annulus effectively for removal by the solids-control equipment to avoid stuck pipe, lost circulation, excessive torque and reduced ROP; andaccomplishing the first two with minimum wellbore erosion.
Previously in drilling a well, however, the hydraulics design was based mostly on experience and a few local system criteria-horsepower at the bit or jet impact force. Examples in Refs. 4 and 5 make the point that because of interactive system effects, an optimized total-system design does not necessarily correspond to the local nile of maximum horsepower at the bit.