Hydro-pneumatic tension systems have been widely used to support production and drilling risers on floating production systems (such as Spars and TLPs). A hydro-pneumatic tension system utilizes several hydro-pneumatic piston-cylinders (typically four) filled with a working gas (such as nitrogen) to provide the riser it supports with a tension. When the riser experiences strokes with respect to its supporting vessel caused by vessel motion (e.g. due to environmental change), the tensioner will accommodate most of the strokes by changing the volume and pressure of the cylinders. The riser tension will accordingly fluctuate with the pressure change about its design value. Such tension variation directly affects riser design and the vessel’s performance. Therefore, in the design of a hydro-pneumatic tension system, the stiffness of the tensioner, which describes the tension and stroke relationship of the tensioner, is one of the key design parameters to be concerned of. Since it is difficult to perform full-scale tests to determine the relationship for a tensioner, a theoretical model, which considers the tension’s stroke motion as a polytropic process, has been used to simulate the tension-stroke behavior of the tensioners. A polytropic process is well defined by a single parameter, the exponent. For nitrogen as the working gas, an exponent of 1.1 to 1.3 has been adopted in the offshore industry without theoretical or experimental verification.

The objective of this study is to theoretically predict the pressure-stroke relationship of the hydro-pneumatic tension systems and to determine proper values of the exponent for the polytropic process used in the offshore industry. The study uses the first law of thermodynamics and the knowledge of heat transfer to predict status change of the working gas with piston stroke and then to calculate the pressure-stroke relationship of the tensioner. The status of the gas is determined from the work exchange induced by piston strokes and heat transfer through the outer surfaces of piston rods and cylinder barrels. As a numerical example, a tension system similar to those used in the Gulf of Mexico is analyzed for 100-year hurricane environments. The predicted pressure time traces are compared with those given by a polytropic process with a series of exponents (or gas constants). The comparisons show that an exponent of 1.3 or 1.4 is a proper value for the polytropic process.

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