MATHEMATICAL MODELING OF THE MOVEMENT OF MOISTURE
IN REFRACTORY CONCRETE AND GUNNING BODIES DURING DRYING
A. V. Zabolotskii,
L. M. Aksel’rod,
R. A. Donich,
E. I. Pospelova,
and D. A. Marchenko
Translated from Novye Ogneupory, No. 12, pp. 6 – 12, December, 2016.
Original article submitted May 11, 2016.
A mathematical model of the movement of moisture in refractory water-sealed materials of different densities
where there is an external temperature field present is constructed. The Fourier thermal conductivity equa
tions, Fick’s diffusion equation, and the method of finite elements are used to solve the problem. The diffusion
coefficients of water in the test materials are determined by means of laboratory tests from the loss of mass in
the course of drying of the samples. Features typical of the movement of moisture in refractory concrete for
the case of deposition on cold and hot surfaces are determined as a result of a subsequent computational exper
iment, using as examples the casting bottom of a casting ladle and guniting of an intermediate ladle.
Keywords: concrete, diffusion, method of finite elements
The use of unmolded materials, such as gunning bodies
and refractory concrete, which require preliminary mixing
with water, is a widespread technique in metallurgy. Such
materials are often used in the working layer of the lining of
apparatus that comes into direct contact with smelt. Obvi
ously, before it is used water must be removed from the ma
terial, i.e., the material must be dried. Drying is generally
conducted at 400 – 600°C, and the drying regime is a com
promise process that takes into account the recommendations
of the manufacturer of the refractories and the requirements
of the user to reduce the time needed to prepare the apparatus
for use. In existing practical applications we cannot be cer
tain whether complete or even sufficient removal of water
has occurred, since explosive rupture of the lining is rarely
observed in primary smelting and since signs indicating lib
eration of water from lining in primary smelts, for example,
elevated content of hydrogen in the finished products, are
quite often present.
Thus, there arises a need for the development of a
method of determining the minimal time and optimal heat
treatment regime preceding the use of unmolded refractory
materials in order to achieve sufficient removal of moisture.
The method must take into account, besides the properties of
the concrete or of the gunning body (for example, the rate of
diffusion of water in the material), features typical of the lo-
cation of the material in the lining as well as the method of
heating. Generally, a method of unidirectional heating is em-
ployed, where evaporation of water is possible only through
the heated surface.
A drop in the pressure of water vapor in the cavities of
the body, which arises due to the difference in the equilib
rium pressure at different temperatures, is the motive force of
diffusion of water in a nonuniformly heated solid. On the ini
tial stage of drying the water vapor is released from a thin
outer layer into the atmosphere and, to an equal extent, ex
truded into deeper layers of the lining. Over the course of
time, the outer layer is completely dried out and moisture
from deeper layers penetrate ever more deeply under the ef
fect of the temperature drop, partially diffusing to the surface
and evaporating. Thus, at the stage when the process of pre
liminary heating has frequently been completed, the working
surface appears to be dry, whereas in laboratory tests it also
contains an insignificantly quantity of moisture. At the same
time, deep layers may possess significant moisture. As metal
is poured into the ladle, the working layer of the lining rap
idly heats up, and a significant drop in the pressure of the wa
ter vapor arises in the deep (moist) layers of the lining which,
on the one hand, induces accelerated diffusion to the working
Refractories and Industrial Ceramics Vol. 57, No. 6, March, 2017
1083-4877/17/05706-0578 © 2017 Springer Science+Business Media New York
OOO Gruppa “Magnezit”, St. Petersburg, Russia.
OOO Gruppa “Magnezit”, Moscow, Russia.
OOO Gruppa “Magnezit”, Satka (Chelyabinsk District), Russia.