LNG 저장 탱크내 증발가스 발생 예측 프로그램 개발

박철수, 박 영, 최성희, 김영수*, 김 효*

한국가스공사 연구개발원, 서울시립대학교 화학공학과*

Predictions of Boil-Off Gas Generation Rate in LNG Storage Tanks

Chul-soo Park, Young Park, Sung-hee Choi, Young-soo Kim*, Hyo Kim*

Research and Development Center, Korea Gas Corporation

Department of Chemical Engineering, University of Seoul*

Introduction

Because of the large liquid-to-gas density ratio (about 600), natural gas is liquefied at a production site by compression and cooling, transported by ship to our Receiving Terminal, and stored under a pressure slightly above atmosphere in large tanks.  In real design process of such LNG (liquefied natural gas) storage tanks, several factors control the tank capacity, construction requirements, consequently, the unit storage price.  Among those parameters, predictions of boil-off gas generated in LNG tank often require special details.  Since, under a variety of storage or tank operational conditions, total amounts of heat energy of LNG by steady state approach determines corresponding design boil-off generation rates (BOR), its correct evaluation is very important for both insulation requirements and the capacities of vapor recovery system. On the other hand, appropriate predictions of unsteady release rate of heat energy accumulated in LNG, will suggest tank operational procedures optimized for the safety and BOR.

This work presents a general computer program, 'KOBOR', developed for BOR predictions covering from design BOR calculations to unsteady BOR under various tank operational modes, focussing to the economic, thermal designs and the operations of LNG tanks.

Outline of Program 'KOBOR'

KOBOR consists of two main stages (Fig 1); Stage-I (Fig 2) calculates external heat leaks, under several storage conditions or tank specs, giving output of a steady-state BOR such as the design value of storage BOR and average temperature distribution.  An additional routine includes to check the validity of designer's  guaranteed storage BOR from the results of BOR Test at Real Site.  Under tank operational modes such as unloading and pump-out of LNG, a computation routine closely simulating heat accumulations in LNG due to any density stratifications and mixing calculates a real-time BOR at stage-II assuming psuedo-steady heat flux from stage-I, and additional calculations of steady design BOR at different operational modes are also calculated for determining allowable capacity of tank vapor system.(Fig 3).

Calculation Models

Heat Gains By LNG

Total thermal overfill of homogeneous LNG at storage ([eqn: TRIANGLE H_E]) is the sum of all excess enthalpy elements over[eqn: H_0], the enthalpy values of LNG-vapor in thermodynamic equilibrium at a isobaric storage condition, and[eqn: TRIANGLE H_E] will depend on real operational and thermophysical properties at a specific time:

[eqn: TRIANGLE H_E`=` SUM `(`H`-`H_0`)]                                 (1)

Due to a poor mixing or any change of the thermodynamic conditions,  overall heat accumulation of LNG is

[eqn: { PARTIAL TRIANGLE H_E}over { PARTIAL t } `=`Q prime`-`M prime`` lambda]                                 (2)

where[eqn: `M prime``]is BOR, [eqn: lambda] is the latent heat of vaporization at saturated LNG, [eqn: Q prime] is the total heat-input rate to LNG including external heat leak rate [eqn: Q_T prime] and[eqn: mol_out/input`TRIANGLE H prime] due to other heat sources under operational conditions.

The external heat leak [eqn: Q_T prime] involves several different heat transfer processes, e.g. solar radiation, convection (via boundary layers within and on the outside surfaces of the tank), and conduction through the insulation layers occur simultaneously, depending on the site's topography and latitude, as well as the time of day and the year.  For a simplicity, average external heat-in leaks,[eqn: Q_T] (instead of[eqn: Q_T prime]) by steady-state approach can be approximated:

[eqn: Q_T``=``Q_base`+`Q_shell `+`Q_roof`]                          (3)

To estimate a steady external surface temperature ([eqn: T_surf]) of the tank under a design ambient condition, both solar radiation and convective heat flow should be applied to the shell or roof area.  The net solar radiation([eqn: alpha ``I_T]) to each area is :

[eqn: `alpha```I_T``=`` epsilon ```sigma``` LEFT [ LEFT ( { 273+T_surf} RIGHT )^4`- LEFT ( 273 +T_ INF )^4 RIGHT ]``+``h_c``(T_surf`-`T_inf`)]         (4)

where total solar radiation[eqn: I_T] includes direct and diffuse solar radiation, and [eqn: alpha_s], [eqn: epsilon] is the absorptivity, the emissivity of surface, [eqn: sigma] is the Stefan-Boltzman constant, and[eqn: `h_c] is the convective heat transfer coefficient of air at ambient temperature[eqn: T_INF].  With use of[eqn: T_surf],, the total external heat leak can be calculated for the volumes of LNG stored at a specific design specs and conditions (Table 1).

Steady BOR

For thermal design of large cylindrical LNG tanks whose capacities are usually more than 10kM3,[eqn: { PARTIAL H_E}/{ PARTIAL t } `=`0] in (2) is assumed to easily calculate a steady BOR ([eqn: `M``]) for a time period (ie, on daily bais) and at a specific design conditions (Table 1). In case of static LNG storage ([eqn: Q prime`=`Q_T]), the calculations of daily storage BOR ([eqn: Q_T prime`=`M_d`` `lambda]) under an appropriate design conditions is most useful technique estimating design insulation requirements. These calculations also demonstrate an optimal tank shape (eg, aspect ratio) of tanks for less BOR, which must necessarily meet any construction requirements.

In case of unloading LNG from ship tanker, a maximum possible BOR should be estimated from total heat input including any super or sub-saturation of incoming LNG([eqn: Q prime`=`Q_T`+ mol_input`TRIANGLE H prime]) and a equation of state in the vapor volume.  BOR calculations varying unloading design parameters such as the pressure difference between tanker and tank and initial vapor volume, will give sensitivity of BOR for economic capacity of vapor recovery and pressure safety systems.

Unsteady BOR

In actuality, external heat entering LNG in tank is absorbed by a boundary layer flow caused by natural convection, and its most of superheat is puffed away by the evaporation on liquid surface.  Simple assumptions that an arbitrary films of LNG-vapor interface [2] is at equilibrium while underlying bulk is in somewhat superheated.  The correlations for turbulent heat transfer between horizontal fluid layer heated from below and cooled by surface evaporation can be used for the surface heat transfer rate[eqn: &Q_s], (instead of [eqn: Q prime] in (2)) and unsteady BOR [eqn: M_U] :

[eqn: N`u `=`0.13`{Ra }^{1/3 }]                                     (5)

[eqn: &Q_s `=h prime`` TRIANGLE T_s` #& ~~`=M_U`lambda`]                                        (6)

where[eqn: TRIANGLE T_s] is a degree of supersaturation-the difference between temperatures of bulk and surface (in accordance with a thermodynamic state of the LNG-vapor film).  Rayleigh circulation flow[eqn: F_Ra] enters the surface film flashing the BOR[eqn: M_U] and the non-flashed liquid returning to bulk [2]:

[eqn: & F_Ra```H_bulk - (`F_Ra`-`M_U`)``` H_0`(l) - M_U `H_0`(v) + a``Q_roof = 0 #&F_Ra```x_n (j) - (`F_Ra`-`M_U`)``` x_s (j) - M_U ~y_s (j) = 0]               (7)

While the above considerations may apply to a static homogeneous storage, LNG as multicomponent mixture usually experiences density stratifications induced by an incomplete mixing, preferential evaporation, and auto-stratification conditions, whose physical nature has been in very active research area [1,2,4,5].  For filling-induced initial n stratified cells (;its numerical predictions of stratifications are elsewhere [1]), the energy/mass balances are in the following:

[eqn: &partial/partial t``[`mol_i` x_i` (j)`]` =`mol_input``x_i (j) - mol_output`x_i (j)`-`M_U ``y_s(j)`+ #&`~~~~~~~~~~~~~~~~~~~k_i-1 (j) `[x_i-1 ( j) - x_i (j) ] (i != n)+ k_i (j) [x_i+1 ( j) - x_i (j) ]`, #& #&partial/partial t``` [`mol_i` C_{P i}` TRIANGLE T_i `]`=`Q_base(i=1)` +`Q_shell(i)`+`Q_roof(i=n)`+`mol_b`TRIANGLE H_b(i=1) `+`mol_t`TRIANGLE H_t(i=n)`+ #&~~~~~~~~~~~~~~~~~~~~~~h_i-1 (T_i-1 - T_i )`(i != n)+`h_i-1 (T_i-1 - T_i )~-~M_U`lambda]    (8)

Thus, the mass and energy on the surface heat is determined from [8], depending inter-cellular transfer rates,[eqn: h_i] [eqn: k_i] , to satisfy the relations of (7).

In the modelling inter-cellular transfer rates, the program KOBOR implements Turner's DDC (double-diffusive convection) correlations [3] being dependant on interfacial stability,

[eqn: rmR_i,~j =LEFT | { beta_i,j DELTA S_i,j / alpha_i DELTA T_i } RIGHT |]                                             (9)

[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`)]                                    (10)

as well as a combination of usual turbulent heat transfer correlation in (10) and  Reynolds analogy for inter-cellular boundary layer being independent of any interfacial stability:

[eqn: {h_i } over {k_i `C_p }`` =``1]                                         (11)

Recent comparisons of above two models for a specific Real Site data (eg, rollover) [6] shows that, the DDC case predicts much later time to roll-over (especially in the mass transport), which might be due to the restriction of sharp interface in the application of DDC to LNG tank.  Incorporated with those preliminary correlations above, another physical model for intermediate density layers and its stratification development due to external heat leak and filling has been derived from experiments using a small mock-up tank [6].  Besides, KOBOR is implemented with several different calculation routines for thermophysical properties of  multi-component LNG/NG system needed for all simulation processes under a variety of tank operations.

Conclusions

A computer program 'KOBOR' was developed for predicting BOR (boil-off rate) in LNG storage tanks under a wide variety of design conditions of tank as well as tank operation modes.  KOBOR can calculate a design BOR by steady-state approach to estimate economic thermal designs and to determine insulation requirements and capacity of vapor recovery system.  KOBOR, in addition, predicts unsteady BOR in which LNG filling-induced stratifications and corresponding inter-cellular transfer relations are closely simulated from the results of a small mock-up tank experiment.  The validity of BOR simulation results have been confirmed by comparing predictions and our LNG terminal site data.

References

1. Park, C., Park, Y., and Choi, S., 'Mixing Storage of LNG of Different Sources and Standardization of Heating Value', Final Research Report, Korea Gas Corporation (1997)

2. Park, Y., Park, C., Choi, S, and Kim, H., *Predictive Models for the Rollover Phenomenon in LNG Tanks", KIChE Conference Nov., 1997

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

4. Bates, S. and Morrison, D. S., Int. J. Heat and Mass Transfer, 40, 1875 (1997).

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

6. Park, C., Park, Y., Choi, S., and Hong, S., 'Applicable Source Program Development to Calculate BOR with LNG Tank Design Specs and Storage Dynamics', Final   Research Report in preparation, Korea Gas Corporation  (1998)

Fig 1. Flow diagrams of the program 'KOBOR	Fig 3. Real-time BOR calculation (Stage-II)
Fig 2. steady-state BOR calculation (Stage-I)	Table 1. Typical Design conditions for LNG tanks ____________________________________ Temperatures -Ambient (Day/Night) [eqn: T_INF] = 35 ¸C -Soil (Day/Night) 16 -LNG stored [eqn: T_L] = -162 ¸C Latent Heat of vaporization 121 kcal/kg Wind velocity 5 - 10 m/sec Reflectance of Ground 30% ________________________________________