The Analysis of Drilling Barge Motions in a Random Sea

Burke, Ben G., Member AIME, Chevron Oil Field Research Co., La Habra, Calif. Abstract The theory of random processes has been shown to be an effective means of describing real ocean waves. This paper illustrates the application of the theory to the prediction of drilling barge motions due to waves. Measured data from a drilling barge in the open ocean are presented to verify the results. The theoretical model permits a means for computing the power spectra of drilling vessel motions from the directional power spectrum of the ocean waves and the wave response functions of the vessel. (The wave response functions are obtained by determining the motions of the vessel in simple, sinusoidal waves of all frequencies and directions.) Statistical properties of vessel motions, such as the rms motions, the "significant" amplitude, or the expected largest motion over the duration of a storm, may then be computed from the power spectra of the motions and a probability law. power spectra of the motions and a probability law. The theoretical model is adequate for many practical engineering problems and can be applied feasibly within the present state of the art. An example of results from the theoretical model is presented using a sample of data obtained from a drilling barge offshore Oregon during operations by Standard Oil Co. of California, in the summer of 1965. The data was analyzed by computing auto spectra and cross spectra from the measured time series of vessel motions and waves and by estimating the directional wave spectrum with a least-squares fit to the measured wave spectra. Power spectra of vessel motions were then computed from the random vibration model using the estimated directional wave spectrum and wave response functions; the results are compared with the vessel motion spectra obtained from the measured data. Average and extreme values from the measured data are compared with corresponding values predicted from the theoretical probability law. Results from the comparisons support the validity of the theoretical model as a practical engineering tool. Introduction Floating drilling vessels are presently in operation on continental margins throughout the world in the search for petroleum reserves. Experience has shown that drilling vessel motions caused by particular wave conditions can significantly impair or halt drilling operations and that the capability for operating in a particular wave environment varies considerably among available drilling vessels. In the past, information from various sources has served as a basis for selection of a drilling vessel and drilling equipment for an operation in a particular area; results from model test data, theoretical studies, and actual experience sometimes gained at considerable expense have all served as a basis for selection. Requirements continue to arise for conducting floating drilling operations in new areas, and in more severe wave and weather environments than have been experienced previously. As these requirements increase, the need for more accurate means to predict vessel motions in particular wave environments increases; and as more complete oceanographic data becomes available, the use of more complete theoretical models for calculating vessel motions becomes practical. This paper presents a theoretical model for predicting the motions of drilling vessels in waves predicting the motions of drilling vessels in waves that can serve as an engineering tool for the selection of drilling vessels and drilling equipment for operations in prospective wave environments. The paper is presented in two parts. The first part describes the theoretical model and discusses several considerations pertinent to an intelligent application of the model. The second part describes the analysis of measured data used to verify several aspects of the theoretical model and presents results from one data record to support the validity of the model. THEORETICAL MODEL The theoretical model for predicting the motions of a drilling vessel in waves is based on elements of small-amplitude rigid body mechanics, small-amplitude wave theory and the theory of random vibrations. The variables and relationships that constitute the theoretical model are described and several practical aspects of applying the model to engineering problems are discussed. SPEJ p. 541