On the Application of Morison's Equation to Fixed Offshore Platforms
Authors: Wade Bruce G. , Dwyer Mike G. 
Published: October 2008

ABSTRACT
Several methods are presented for calculating wave forces acting on tubular members of fixed offshore platforms. Each is within the guidelines set forth in American Petroleum Institute's RP 2A. The formulation of the methods considered are based upon several interpretations of the application of Morison's equation to randomly oriented tubular members. This paper presents a comparison of these various methods with identical design conditions and demonstrates significant differences between the methods. Horizontal and vertical water particle motions of a design wave were determined by Stokes Fifth Order Wave Theory. These kinematic vectors were used in calculations with each of the wave force methods on two deep water platforms, four pile and eight-pile template structures, to compare the horizontal base shears and overturning moments. Comparisons between the methods are made using numerous crest locations and several wave approach directions with respect to the global axes of the platforms. Variation of base shears and overturning moments between the methods considered were found to exceed 22% despite the fact that all the methods are within procedures generally accepted by industry. Exclusion of vertical water particle velocities in any method resulted in small changes in base shear and overturning moment whereas the method of calculation was found to produce significant differences in these quantities.

INTRODUCTION
Numerous technical papers, texts, and offshore design codes (Refs. 1 to 7) have referenced Morison's equation for determining hydrodynamic forces on small tubular structural elements. The Morison equation (8) includes terms for both drag and inertial forces. The drag term includes a drag coefficient, CD, and water particle velocity, while the inertia term involves an inertial coefficient, Cm, and water particle acceleration. This equation is applicable to small objects (compared to the wave length) where wave kinematics do not change appreciably over a distance equal to the width of the structural element. Morison's equation is more nearly correct when used to determine the hydrodynamic force on a small cylindrical body that is in a vertical attitude. However, when a cylinder is randomly orientated with respect to the mudline, there is considerable question concerning the application of the Morison equation.
Borgman (9), Ippen (2), and Bursnall, et. al. (12), and more recently Chakarbrati, et. al. (10) and Morgan, et. al. (11) have shown how Morison's equation for a vertical cylinder may be applied to a cylindrical member orientated in a random manner with respect to the mudline. A review of these papers reveal that there are a variety of methods for calculating wave forces acting on tubular members of fixed offshore platforms. Four different methods are presented in this paper, each of which is within procedures generally used by industry (4), for computing wave forces on a randomly oriented cylindrical member. The formulation of the methods considered are based upon various interpretations of the application of Morison's equation. Many of the wave force calculation methods presented herein have been presented previously by other authors.