Salt precipitation in porous media and multi-valued
solutions
G. G. Tsypkin
Institute for Problems in Mechanics RAS, Moscow, Russia
• Petroleum engineering – gas hydrate, paraffin etc. formation
• Soil sciences – salt precipitation, ice formation etc.
• Chemical engineering – filters
• Geothermal reservoir engineering – salt precipitation,
crystallization of components due to chemical reactions etc.
Salt precipitation in soils
with destruction of porous media
SPE 68953
The Precipitation of Salt in Gas Producing Wells
W. Kleinitz, SPE, M. Koehler and G. Dietzsch, SPE, Preussag Energie
GmbH, Germany. 2001.
Scanning electron micrograph of precipitate formation in the sample of rock
Sketch of the problem:
salt precipitation in geothermal reservoirs
Basic equations
Vapor domain:


(1  S pr ) v  div( v v v )  0,
t
k ( S pr )

vv  
gradP,
v
Water domain:
P   v RT



k
 w  div( w v w )  0, v w   gradP,
t
w
 w   w0 1   w ( P  P0 ),


 c  v w  grad c  0
t



(  e) m  div( w hw v w  v hv v v )  div(m gradT )
t
 – porosity,  – density, k – permeability, µ – viscosity, w – compressibility, h –
specific enthalpy, e – the specific internal energy,  – thermal conductivity, T –
temperature, P – pressure, v – filter velocity, Spr – solid salt saturation, c – salt
concentration
Boundary conditions through the interface
Discontinuities of water and salt saturation functions
  (Vn  un )   0

Mass balance for H2O and salt:
P
Momentum balance:
T   0
Thermodynamic equilibrium:
Energy balance:
0
h(Vn  un )  (gradT ) 

n 
0
Initial and boundary conditions
x  0:
P  Pwell
t  0:
P  P0 ,
T  T0 ,
c  c0 ,
X (t  0)  0
Similarity solution
P  P( ), T  T ( ), c  c( ),
x
X (t )   t ,  
t
Variation of the mass of salt in the vapour domain as a
function of reservoir pressure
Tsypkin G., Woods A. J. Fluid Mech. 2005
msalt   S pr salt
500
m
salt
400
-3
[kg m ]
300
P
200
=4 bar
well
P
=6 bar
well
100
P
=8 bar
well
0
0
20
40
60
P [bar]
0
80
100
Analytic (1) and numerical results (2)
Tsypkin G., Calore C. Proc. 32nd Workshop on Geothermal Reservoir
Engineering, Stanford, 2007
= 0.1, T= 513.15 K, k = 0.5 10-17,
Pwell = 2 10
6
1
S
pr
0.8
2
0.6
1
0.4
1
1.2
1.4
1.6
1.8
2
-7
2.2
P 10 Pa
0
Salt diffusion influence in low-permeability reservoirs
Tsypkin G. Fluid Dynamics. 2009.

 salt
 v* 
 w  P*  exp( 2 D / 1 )  v* P* 1 K ( S pr )  Pw2 
1  
1  2   0,
F ( )  1  S pr
 (1  S pr )  

w
w 
1 D  P0  erfc( D / 1 )  w P0 D 4  P* 

w 
 w  P*  exp( 2 D / 1 ) c*  c0 exp((  Ac ) 2 ) 
kP
k
1  
S pr 
c* 1 

,  w  0 , 1 
 salt   1 D  P0  erfc( D / 1 )  c* erfc(  Ac ) 
 w
 w  w
-17
T = 450 K, k = 10
-18
(1) 10
(2), = 0.1,
6
Ac 
5
c = 0.1, P = 6 10 , P = 4 10
0
0
w
w
( P0  P* )
 P*
2
F()
   /2 D
1
2
0
T = const
1
-1
-2
0
0.4
0.8
1.2

Conclusions
 There are two self-similar solution branches for
precipitation problem
 These two branches coincide for critical values of the
parameters, and above these values, the self-similar
solution ceases to exist
 For a higher initial pressure and larger well pressure
rock becomes fully sealed with salt
 Salt diffusion may lead to a sleeping regime formation
in low-permeability rock