LNG 탱크 내 Rollover현상 예측 프로그램 개발

박 영, 박철수, 최성희, 최건형, 김 효*

한국가스공사 연구개발원, 서울시립대학교 화학공학과*

Predictive Models for the Rollover Phenomenon in LNG Tanks

Young Park, Chul-Soo Park, Sung-Hee Choi, Keun-Hyung Choi, Hyo Kim*

Research and Development Center, Korea Gas Corporation

Department of Chemical Engineering, Seoul City University*

Introduction

An addition of LNG (liquefied natural gas) of different thermophysical properties to partially filled LNG tanks can lead to temporary formation of strata of slightly different temperature and density.  These strata gradually become unstable and enter mixing processes as the stratified layer densities approach equality due to heat leak into the tank and energy/mass transfer between strata (Fig 1).  After sufficient time, the cells equilibrate in density and eventually a rapid mixing of strata (termed as "rollover") can occur, possibly accompanied by a sharp increase of boil-off gas rate.  Rollover usually results venting large scale of valuable methane gas for preventing the consequent overpressurization of the tank, and it may be dangerous as reported in the La Spezia case of 1971 [1].  A reliable methodology to predict the occurrence or the severity of rollover and prevent a possible threat would be necessary in safety operation of LNG storage facilities.  This work presents the preliminary models and computer simulations developed for predicting the rollover phenomenon and its physical behavior in stratified LNG tank.

Formulation of Model

Consider a tank (diameter: d) with n homogeneous convection cells of LNG of given heights Li, surface area A, and physical properties (density[eqn: rm rho_i] and temperature[eqn: rm T_i]) separated by a sharp interface (Fig 1), where the stratification may be induced either by an insufficient mixing during the cargo loading or by a preferential evaporation on the top liquid surface.  While external heat leaks from into the tank ([eqn: rm q_E =q_b +q_w +q_t]) and the evaporation[eqn: rm □_V] on the top surface take places, turbulent heat/mass transfer across the cells occurs until the density equilibration is approached by adjacent cells to break up cells to mix.

evaporation on the top liquid surface

Hashemi-Wesson model [2], derived on the assumption of turbulent heat transfer between two horizontal plates with heat flux upwards, can be applied for computing LNG boil-off flux,

[eqn: rm □_V =c_1 TRIANGLE T_s^{3/4}]                                  (1)

where[eqn: rmc_1] can be calculated from the thermodynamic properties of the top cell, and[eqn: RM TRIANGLE T_s] is the difference between temperatures of bulk[eqn: rm T_n] and surface[eqn: RM T_s].

VLE(vapor-liquid equilibrium) calculations

For properly accounting for correlations between the evaporation flux, the composition and temperature, it is assumed that the vapor evolved is in equilibrium with an arbitrarily thin film of liquid on the surface (Fig. 2).  Thus, the surface temperature[eqn: rm T_s] should be in accordance with a saturation temperature to pressure in the vapor space above the film.  With the Rayleigh flow[eqn: rm□], the evaporation flux[eqn: rm □_v], enthalpies (;[eqn: rmH_n] for the bulk,[eqn: rmH_s] for the liquid-side, and[eqn: rmH_v] for the vapor-side film), the film compositions of liquid and the vapor-side film for j=m components[eqn: rmx_s (j)] and[eqn: rmy_s (j)], the energy and mass balance for the surface film is formulated as,

[eqn: & rm (□ +□_v )` H_n - □` H_s - □_v `H_v + q' = 0 #& rm (□ +□_v )~x_n (j) - □~ x_s (j) - □_v ~y_s (j) = 0]                     (2)

where[eqn: rmq'] represents heat transmitted to the film from the vapor space.  The the Rayleigh flow

[eqn: rm □= c_2 {[TRIANGLE rho/<rho> ]}^1/3],                             (3)

where again[eqn: rmc_2] can be calculated from a thermodynamic properties of the top cell, and the difference and the average of densities between the liquid film and the bulk and the average are [eqn: rmTRIANGLE rho] and[eqn: rm<rho>], respectively [3].

Intercellular transfer rates: DDC (double-diffusive convection)

The DDC(double-diffusive convection), which has been studied extensively for heated salt solutions [4], is used in our model to determine the cellular transfer coefficients.  Taking the methane as a solvent (j=1) and other components as solutes Sj (j=2 to m) for adjacent cells, the stability parameter for LNG system,

[eqn: rmR_i,~j =LEFT | { beta_i,j DELTA S_i,j / alpha_i DELTA T_i } RIGHT |],                           (4)

where the expansion coefficients with respect to temperature and solute are

[eqn: rm & alpha_i = - 1/rho_i{ (PARTIAL rho_i/ PARTIAL T_i)_S_ i,j} rm #&beta_j =1/ rho{ (PARTIALrm rho/PARTIAL S_j )_T} }].                           (5)

The intercellular coefficients for heat[eqn: rm h_i] and mass[eqn: rm k_i (j)] are calculated from Tuner and Huppert's correlations [4, 5]:

[eqn: &rm h_i =` c_i LEFT ( DELTA T_i)^1/3`/R_i,j^2#& rm R_i,~j ~k_i,~j /h_i`=`f_i,~j (R, Pr, L`e`)],                    (6)

where function f for each solutes are constructed from the values of the stability, Prandtl, and Lewis number [6] (Fig 3).

The governing differential equations of conservation of energy and material on n convective cells for solutes j=2 to m,

Bottom Cell (i=1):

[eqn: rm &d/dt [ C_1 L_1 x_1 (rm j)] = ({barM}_1 /A) {barx}_1 (j) - ({barM}_R1 /A)`x_1 (j) + k_1`(j) [x_2 (j) - x_1 ( j) ]# rm &d/dt [C_1 L_1 C_P1 (T_1 - T_0 )] = ({barM}_1 /A) {barC}_p1 ({barT}_1 - T_0 ) + q_b + (q_w pi d L_1 /A ) + h_1 (T_2 - T_1 )] (7)

Cells i=2 to N-1:

[eqn: &rmd/dt [ C_i L_i x_i (rm j)] = k_i-1 (j) [x_i-1 ( j) rm - x_1 (j) ]+ k_i (j) [x_i+1 ( j) - x_i (j) ] #&rmd/dt [C_i L_i C_{P i} (T_i - T_0 )] = (q_wL pi D L_i/A )+h_i-1 (T_i-1 - T_i )]            (8)

Top Cell:

[eqn: rm&d/dt [ C_n L_n x_n (j)] =({barM}_n /A){barx}_n (j) -□_v A y_s (j)+ ({barM}_Rn) /A)~x_Rn (j)# rm&~~~~~~~~~~~~~~~~~`+k_n-1 (j) [x_n-1 (j) - x_n (j) ] #rm&d/dt [C_n L_n C_Pn (T_n - T_0 )] = (q_WL pi DL_n /A) + h_n-1 (T_n-1 - T_n )+ q'#rm&~~~~~~~~~~~~~~~~~~~~~~~~~``- □_v H_V +({barM}_n/A) {barC}_Pn ({barT}_n - T_0 )]   ,         (9)

where Ci is the concentration, CPi is the heat capacity of each cell, T0 is the reference temperature for liquid-phase of zero enthalpy, and[eqn: rm{barM}_i,n] and[eqn: rm{barM}_R,1,n]are the flow rate of cargo loading and recirculation.  Similarly, equations are

for the Vapor-space (j=1 to m),

[eqn: rm &d/dt left[M_vs `y_vs (j) right] = □_v A y_s (j)`-{barM} _ vent y_vs (j) # rm&d/dt [T_vs ] = [□_v AT_vs ( T_vs - T_s )-{barM}_Flash (T_Flash - T_vs ) +(q_t -q'rm) A]/M_vs C_Pvs],   (10)

where Mvs is moles of vapor in vapor-space with composition yvs(j), Tvs is the temperature in the vapor-space. [eqn: rm{barM}_vent] and[eqn: rm{barM}_Flash] are the molar venting rate from the surface film and molar rate of addition of flash vapor in the film to vapor-space when the tank pressure decreases, and (qt-q') is the heat transfer rate to the vapor space, the difference between external heat leak rate into vapor dome and heat transfer rate to the surface film.

A computer program was written to integrate equations over time from given initial conditions such as the number of cells, the cell thickness and the initial values of pressure, temperatures and composition for each cell (Fig 4).  For each time step, all thermodynamic properties of multicomponent mixture of LNG such as the density, enthalpy, VLE(;used modified SRK equation of state) relation, and so forth are unambiguously calculated using computation subroutines of LNG/NG thermodynamic properties previously developed [7], which are continuously directed to the main program.  In addition, the values of on-site operating parameters such as cargo loading, recirculation with or without flashing, and LNG withdrawal from the trank can be started and stopped at any specific times.  Final output gives the values of all temperatures, compositions, densities, and boil-off rate at hourly intervals (Fig 4).

Conclusions

A model is developed for closely simulating the physical behavior of LNG in tanks to establish guidelines for minimizing the chances for stratification and for mitigating the problems associated with rollover.  In the model, most of components of LNG mixture as separate species are incorporated with accurate VLE and thermophysical calculation to analyze "weathering process" as well as rollover on site operation.  The validity of the simulation results have been confirmed by comparing predictions and observations for two known cases[1, 8] as well as our LNG terminal site data.

References

1. Saraten J. A., Pipeline and Gas J., 199, 37 (1972).

2. Hashemi, H. T. and Wesson, H. R., Hydrocarbon Processing, 50,

117 (1971).

3. Heestand, J., Shipman, C. W., and Meader, J. W., AIChE J., 29, 199 (1983).

4. Turner, J. S., Inter. J. Heat Mass Transfer, 8, 759 (1965).

5. Huppert, H. E., Deep-Sea Res., 18, 1005 (1971).

6. Germeles, A. E., Advances in Cryogenic Eng., 21, 326 (1975).

7. Kim, H. and Kim, S. Y., "Computation of Thermophysical

Properties of LNG", Annual Research Report, Korea Gas Corporation (1993)

8. Bates, S. and Morrison, D. S., Int. J. Heat and Mass Transfer, 40,

1875 (1997).

Fig 1. Stratified LNG storage tank	Fig 4. Flow diagram of the program
Fig 2. Evaporation from the surface film
Fig 3. Correlation of function f with R