The incubation period preceding "rollover" within a stratified LNG tank involves intensive heat and mass transfers between layers. Numerical integration of equations describing these processes leads to predicted time-history and boil-off characteristics which are in excellent agreement with Sarsten's (1972) even in well-insulated tanks, cause a slow boil-off of the LNG, and this requires removal of some vapor. During this "weathering" process the composition of the LNG changes because the small amount of nitrogen present is much more volatile than the methane and the heavier hydrocarbons are effectively nonvolatile. Obviously the temperature and density of the LNG change as well. Natural convection causes circulation of the LNG within the tank, maintaining a uniform liquid composition. The addition of new liquid, however, can result in the formation of strata of slightly different temperature and density. The energy and mass iransfer between these strata (or cells), given sufficient time, will result in an unstable interface and rapid mixing of the cells. This is called rollover. When the lower, more dense cell is also at a higher temperature, rollover causes the vapor pressure at the top of the LNG to rise very rapidly, and a rapid evolution of a large quantity of vapor results. At best, such a situation results in a loss of valuable fuel. At worst, it could be dangerous.In operating an LNG storage facility it would be helpful to have a reliable method for predicting the occurrence and severity of a rollover and for evaluation of countermeasures to prevent it. This in turn requires a good understanding of the energy and mass transfer between the cells and of the rate of boil-off. A mathematical (computer) model of the dynamics within the tank, with provision for addition and removal of LNG, would be a useful tool.Only one rollover incident, at LaSpezia in Italy, has documentation sufficient for testing a computer model of the rollover process (Sarsten, 1972). Geist (1972, 1976) and Germeles (1975) developed models which omitted the important contribution of nitrogen to the density and volatility of the LNG; they used the thermohaline equations of Turner (1965) and Huppert (1971); and introduced simplifications which required "adjustment" of the data supplied by Sarsten.The present paper gives a more adequate theoretical framework for rollover analysis and presents quantitative computer results for the simulation of the LaSpezia rollover. CONCLUSIONS AND SIGNIFICANCEA model has been developed which closely simulates the LaSpezia incident details using only input data from Sarsten (1972). It contains only two adjustable constants. The first is the fraction of the heat leak into the vapor space which is transferred to the vaporizing film; changing this fraction from 0.95 to 0.85 has no sensible effect on the dynamics of vaporization and rollover. The second is the proportionality constant in the expression for the intercellular heat transfer coefficient. The rollover time is acutely sensitive to this constant. A...

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The available analyses of the conditions for equilibrium in electrochemical systems do not consider the electrostatic field as a possible variable. Since there is a voltage difference between the electrodes in an electrochemical system, an electrostatic field must be present, and this field must be considered in the treatment of equilibrium because it affects the internal energy of the system. This paper presents an analysis in which the electric displacement vector is included as a possible variable. The results show that Poisson's equation is a condition of equilibrium in addition to the usual conditions of uniformity of the electrochemical potential, the pressure, and the temperature.

A method is described for solving the problem: given fixed pressure, temperature, the amounts of the chemical elements, and the chemical potentials of possible chemical species a t the pressure and temperature specified, determine the equilibrium composition. The method requires a minimum of judgment on the port of the user.A modification of Naphtali's method for direct minimization of Gibbs' function provides an estimate of the cornposition of sufficient accuracy to insure convergence of solution, by the Newton-Raphson method, of the nonlinear equations describing the equilibrium.Problems in treating multiple phases of unknown stability and chemical species present i n small amounts are handled by ignoring unstable phases and small quantities i n the direct minimization until the amounts of the major constituents have been a t least approximately determined. To accomplish this, species temporarily ignored are assigned a fictitious mol fraction so that their re-entry into the calculation con be established. Truncation errors in the direct minimization can be tolerated because of the two-step method.Examples of some of the problems solved are given. 6 J J 2 2 aj,ixj's$,bjdM+ + 2 aj,imj'd(logexj) + = 1 j = 1 j=1 J = Ei -2 aj,imjl ( i = l + I ) (30) '.> j=1 J J 2 Xj'S,,bjd(logeXi) 1 1 -2 Xj'S+,+j j = 1 j=1 J J

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