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3D computer simulation of Artificial Ground Freezing (AGF) under oil tank by Simmakers Ltd in Frost 3D software.Oil Tank

During the construction of buildings and structures in the Far North, permafrost thawing in the immediate vicinity results in ground settlement and deformation of foundations. This issue is particularly topical for pipelines and tanks containing petroleum products with elevated temperatures. The most effective method for providing foundation stability is by establishing control over the ground thermal regime through the operation of seasonal or year-round cooling units. It is impossible to formulate an accurate plan for the collocation of cooling devices or assess ground freezing potential without computer simulation.


To predict the ground thermal regime for passive refrigeration under an oil tank, it is necessary to use specialized software — Frost 3D.


In order to create a computer model according to the geometric magnitudes of the tank and system of cooling units, a 90х90х33 m computational domain is created. The geological and lithological structure of the soils in the considered domain – sand, peat, loam and sandy loam – is reconstructed on the basis of geotechnical boreholes by means of interpolation.


Soil basement under oil tank, section of geological horizons according to wells and system of cooling units

2D contour map of the tank bottom (left) and section view of the tank and cooling units (right), both constructed according to the data from the geotechnical boreholes


The surfaces on which boundary conditions are subsequently specified are determined on the reconstructed 3D geometry of the simulation area.


3D simulation area with cooling devices and reconstructed soil morphology under oil tank

Reconstructed 3D model for simulation with cooling units and soil basement under oil tank


The 3D simulation model is discretized into an irregular hexahedral computational mesh.


3D simulation area after discretization

Discretized 3D simulation area


For different soil layers such as sand, peat, loam and sandy loam, the following thermophysical properties are specified: volumetric heat capacity of soil in thawed and frozen states, thermal conductivity of soil in thawed and frozen states, moisture content of soil, freezing point, and an empirical parameter in the equation that approximates the quantity of ice content for given temperatures.


Heat transfer with the air is specified on the upper boundary of the computational domain by means of the heat transfer coefficient and changes in air temperature over time. To consider the influence of snow cover on the heat transfer between soil and air, the change of snow cover thickness over time is specified.

Boundary conditions for computation of convection in soils

Specifying boundary conditions for convective heat transfer

Physical and thermal properties of ground

Specifying thermophysical properties of ground

Dependence of air temperature on time

Export of air temperature dependence on time


Seasonal dependence of snow cover thickness

Specifying snow cover thickness on time dependence


Tank bottom temperature and heat transfer coefficient are specified for the soil basement of oil tank.


A constant temperature equal to -1.7oC is specified on the lower boundary of the computational domain, and on the side boundary – heat flow is equal to zero.


Heat flow on the evaporating section of the system of cooling devices is automatically calculated on the basis of form factors of the cooling system.


The initial temperature distribution is specified in the form of dependence over depth.


Distribution of temperatures in ground for freezing simulation

Specifying initial temperature distribution


After all the input data is entered, the simulation for the required period of time is conducted. The resulting predictions for the ground thermal regime are shown below as color distribution of sections of the simulation area at different moments in time.


Temperature distribution from flat loop thermosyphon

Simulation results of ground thermal regime after 90 days – longitudinal section of

simulation area along the plane of cooling device installation


Visualization of ground thermal stabilization under oil tank

Simulation result of ground temperature distribution after 1 year


Forecast of temperature regime during construction on frozen ground in the Far North

Result of thermal regime simulation in the form of temperature isolines

along the longitudinal section of the simulation area


On conclusion of the simulation process, design engineers obtain full information regarding the dynamics of a 3D temperature field in the ground during specified time intervals.