Mathematical Development for Analysis of Gravel Packing Using 3-D Numerical Simulation
Authors: Nguyen P.D. , Fitzpatrick H.J. , Woodbridge G.A. , Reidenbach V.G. 
Published: October 2008

ABSTRACT
Numerical simulators have proven to be viable tools for studying dynamic systems and providing accurate predictions. When combined with the advanced capability of modern computers, the flexibility of the numerical approach allows a wide array of variables to be investigated that otherwise would be limited by time, safety, or cost. Previous attempts at simulating gravel packing have yielded less than desirable results. This paper provides a comprehensive review of previous models and describes the mathematical development of a full scale, three-dimensional, gravel pack simulator.

INTRODUCTION
A significant portion of the most attractive petroleum reserves exists in reservoirs which require sand production control if these reserves are to be produced efficiently and economically. Often the environment and location of these reservoirs dictate that they must be tapped via deviated, extended reach, or horizontal wellbores. Various parameters of the reservoir itself and the welhore equipment utilized to access the reservoir present additional challenges. While sand control is but one aspect of the overall petroleum production system, the optimum producing system will be the product of effective integration of all the system parts.
Gavel packing has been recognized as an effective practice for controlling movement of sand particles from an unconsolidated reservoir into the wellbore during production of oil and gas. During the last few decades much research and field studyl-10 have been performed to improve completion techniques with the purpose of enhancing productivity and life span of the well. Voids or incomplete packs am known to occur more often in directional and horizontal wells. 10,11 Case histories1,12of wells with poorly designed gravel pack treatments all led to conclusions that incomplete packing would decrease the production rate, and in certain cases, would also result in equipment damage.
To determine causes of incomplete packing, physical and numerical models4–17 of gravel placement have been used to simulate the gravel packing process downhole by examining formation conditions, fluid properties, wellbore parameters, and operating procedures. However, the currently known numerical grovel pack modelsls15–17can only simulate the gravel placement in a two-dimensional reamer, which results in a number of Imitations. The development techniques of past numerical models therefore were reviewed to study their merits and distinct features in implementing applicable criteria for an alternate approach of simulating the gravel placement process. This paper for the first time presents a three-dimensional, mathematical analysis to simulate the complete process of a gravel pack treatment, and thus facilitates planning and optimizing treatment designs. A simple yet powerful numerical method, equipped to handle complex boundary conditions of the grovel pack transport system, is illustrated in this paper.

LITERATURE REVIEW

Background Work
Fluid mechanics of slurry tmnaport can be dated back to the early 1900's. Binstein was the first who theoretically examined the effect of suspension concentration on the apparent viscosity of monomodal sphere slurry. 18 Blatch developed the first correlation for predicting pressure drop in slurries. 19 These studies and numerous others since then have provided solid background for the current slurry transport investigations.