Mathematical Prediction and Experimental Verification of Deep Water Accumulator Capacity
Authors: Good Craig A. , McAdams James P. 
Published: October 2008

Abstract
As drilling and subsea production move to ever-deeper waters, gas charged accumulator capacity calculations must become more sophisticated than the traditional ideal gas law methods. This paper describes a mathematical model of high-pressure accumulators and the extensive laboratory tests carried out to verify its accuracy when using both nitrogen and helium as the precharge gas.

Introduction
As drilling and subsea production moves to ever-deeper waters, gas charged accumulator capacity calculations must become more sophisticated than the traditional ideal gas law methods, since the ideal gas law becomes highly inaccurate at pressures exceeding 5000 psi.
Typical discharge times allow enough heat to flow between the gas and the accumulator to cause serious deviations from both isothermal and adiabatic models. The need to limit the number of bottles in these large systems, while still supplying enough fluid, demands the use of new models that deliver a high level of accuracy.
This paper describes a mathematical model of highpressure accumulators and the extensive laboratory tests carried out to verify its accuracy when using both nitrogen and helium as the accumulator precharge gas. The model includes both gas compressibility and the effects of heat transfer between the gas and the accumulator bottle. The tests were carried out at temperatures, pressures, and flow rates typical of those encountered in today's deep water drilling and production systems.
The results presented are particularly helpful in the design of any accumulator system operating at pressures of 5000 psi and higher.

History of Accumulator Use and Calculations
Since the 1960's gas charged accumulators have been placed on subsea blowout preventers (BOP's) to reduce hydraulic response times and provide a local hydraulic power supply in case of interruption of surface communication. Accumulators are also used in subsea production control systems to provide local storage that allows smaller line sizes in control umbilicals. For drilling systems, the accumulator output capacity is mandated by various regulatory agencies, chiefly API (specification 16D) and NPD. These regulations provide direction as to the nominal output requirements based on the BOP actuator requirements and some guidance as to the location of the accumulators, whether surface or subsea.
Traditionally subsea accumulator capacities have been calculated using Boyles Law: P1V1 = P2V2 (also known as the isothermal model). The name isothermal indicates that this method does not take into account the temperature (and thus pressure) changes that occur temporarily in the accumulator while charging and discharging. This method has given adequate accuracy in surface and relatively shallow subsea systems, partially due to the generous safety margins that are built into the mandated capacities.
Another, more accurate accumulator model is the adiabatic method which is stated P1V1n = P2V2n where n is an exponent based on the physical properties of the precharge gas. This model calculates the pressure that the accumulator initially contains after a rapid charge or discharge. This method gives smaller useable fluid volumes and has not been used extensively because, after a period of time, the temperature (and thus the pressure) recovers to the level predicted by the isothermal method.