PSI - Issue 32

A.A. Baryakh et al. / Procedia Structural Integrity 32 (2021) 17–25 Baryakh A.A/ Structural Integrity Procedia 00 (2021) 000 – 000

19 3

The implementation of the numerical calculation for salt rock dissolution was carried out using the Chemical Reaction option using the Dual-domain mass transfer submenu. This made it possible to simulate the mass transfer between the flow and stagnant pores in a medium with double porosity, taking the kinetics of the mass transfer into account:



 m im 

im dt n dC     im

C C

,

(1)

where im n is the part of the total porosity determined for the stagnant pores; C im and C m is the current concentration of the substance in the stagnant and flowing zones, respectively (g/dm 3 ); and  is the constant of the mass transfer rate between the flowing and the stagnant pores, (day – 1 ). When balance is achieved, then:

im

m

dt n dC im 

dt n dC m

,

  

where n m is the part of the total porosity determined by the flowing pores equation (1) and is transformed into the following relationship:



 im m 

m dt n dC     m

C C

(2)

which fully corresponds to the equation of the dissolution kinetics:

m dt dC   



 n m 

K S C C

(3)

K is the dissolution-rate constant of sylvine (0.20 m/day); S is the specific surface of dissolution, equal to the ratio of the area of dissolution to the dissolving volume of the brine, (m – 1 ); C n is the saturation concentration of the brine in relation to KCl (107.18 g/dm 3 ) and is subject to the following conditions: C im is set equal to C n ; n im is set infinitely large, which provides C im = C n = const ; and  is calculated from the relation  = K  S  n m . The parameter of the longitudinal hydrodispersion in all the layers was set equal to  long = 10 m, which approximately corresponds to the distance between the mines. The parameter of the horizontal, transverse hydrodispersion was set at   horiz = 0 m, since in the absence of the connecting channels between the subparallel mines, a dissipation of the dissolved substance in the direction transverse to the main flow is almost absent. The numerical calculation of damage (degradation) to the inter-chamber pillars, due to the dissolution, was carried out based on the calculated value of the current (at each k time step) salt concentration in each computational block, with coordinates i and j . is the resulting value obtained when solving the combined problem of the solute transfer and dissolution. The modelling of such a migration process at each time step in the Mt3DMS program is implemented in two stages: 1) the problem solution of the actual transfer of the substance within the entire model. 2) modelling the actual dissolution (the mass transfer between the stagnant and flowing pores), in accordance with equation (3). In numerical calculations, equation (3) is transformed into the following form:   k k n m i j k m i j k i j i j t C C C K S C C          ( , ) ( , ) ( , ) ( , ) (4) where Δ t k is the calculated time step value, day; and k ǡ is the concentration of the substance calculated on a model for this time step at the first stage before the dissolution, (g/dm 3 ). k i j C , k i j C ,