Download And scale tendency equation is

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Understanding, Predicting and Preventing
Oilfield Scale
This may be the only time you get to review this
part of oilfield chemistry, so we will go deeper
than the numbers
*
The thermodynamic basis and the models currently in use
(sorry, but you can no longer hide from thermo!)
 Names used for S
 Oilfield names
o
o
Scale Tendency (ST), Scale Ratio (SR)
Scale Index (SI) is log10 value of S
 Scientific names

o Saturation Ratio (SR, ), Supersaturation (S)
S is the thermodynamic driving force for solids to
precipitate or dissolve
 Supersaturated (S>1 or SI>0): precipitates spontaneously
 Subsaturated (S<1 or SI<0): dissolves spontaneously
 Saturated (S=1 or SI=0): neither dissolves nor precipitates
*
Definition: Scale tendency is the ratio of ion activity
product (IAP) to the solubility product constant (Ksp)
𝐶
𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛
𝑆𝑐𝑎𝑙𝑒 𝑇𝑒𝑛𝑑𝑒𝑛𝑐𝑦 = 𝑆 ∝
=
𝐶0 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑎𝑡 𝑒𝑞𝑢𝑖𝑙𝑖𝑏𝑟𝑖𝑢𝑚
Used in
lab and
field
Used in
thermodynamic
software
𝐶
𝑰𝑨𝑷
𝐼𝑜𝑛 𝐴𝑐𝑡𝑖𝑣𝑖𝑡𝑦 𝑃𝑟𝑜𝑑𝑢𝑐𝑡
∝𝑆=
=
𝐶0
𝑲𝒔𝒑 𝑆𝑜𝑙𝑢𝑏𝑖𝑙𝑖𝑡𝑦 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
need to define
these terms further
*
*
1) Precipitation reaction
𝑁𝑎𝐶𝑙 𝑠, ℎ𝑎𝑙𝑖𝑡𝑒 = 𝑁𝑎+ 𝑎𝑞 + 𝐶𝑙 − (𝑎𝑞)
2) Equilibrium equation (solid phase exists)
𝐾𝑠𝑝
𝑎𝑁𝑎+ ∗ 𝑎𝐶𝑙− 𝑦𝑁𝑎+ ∗ 𝑚𝑁𝑎+ ∗ 𝛾𝐶𝑙− ∗ 𝑚𝐶𝑙− 𝐼𝐴𝑃
𝑁𝑎𝐶𝑙, ℎ𝑎𝑙𝑖𝑡𝑒 =
=
=
𝑁𝑎𝐶𝑙 (𝑠)
𝑁𝑎𝐶𝑙 (𝑠)
1
=1.0 by definition
3) Rearrange. If system is at equilibrium then
𝑦𝑁𝑎+ ∗ 𝑚𝑁𝑎+ ∗ 𝛾𝐶𝑙− ∗ 𝑚𝐶𝑙−
=1
𝐾𝑠𝑝 𝑁𝑎𝐶𝑙, ℎ𝑎𝑙𝑖𝑡𝑒
If the system is not known to be at equilibrium, then
𝑦𝑁𝑎+ ∗ 𝑚𝑁𝑎+ ∗ 𝛾𝐶𝑙− ∗ 𝑚𝐶𝑙−
=𝑆
𝐾𝑠𝑝 𝑁𝑎𝐶𝑙, ℎ𝑎𝑙𝑖𝑡𝑒
*
This is the equation that gets solved for all scales
𝛾𝑁𝑎+1 ∗ 𝑚𝑁𝑎+1 ∗ 𝛾𝐶𝑙−1 ∗ 𝑚𝐶𝑙−1
𝑆=
𝐾𝑠𝑝,𝑁𝑎𝐶𝑙,(𝑇,𝑃)
𝒎𝑵𝒂+𝟏 & 𝒎𝑪𝒍−𝟏 are measured in the lab
𝜸𝑵𝒂+𝟏 & 𝜸𝑪𝒍−𝟏 are calculated using scale prediction software
𝑲𝒔𝒑,𝑵𝒂𝑪𝒍,(𝑻,𝑷) is calculated using scale prediction software
*
For CaCO3, the chemical reaction is:
𝐶𝑎𝐶𝑂3 = 𝐶𝑎+2 + 𝐶𝑂3 −2
And scale tendency equation is:
𝑎𝐶𝑎+2 ∗ 𝑎𝐶𝑂3−2
𝛾𝐶𝑎+2 ∗ 𝑚𝐶𝑎+2 ∗ 𝛾𝐶𝑂3−2 ∗ 𝑚𝐶𝑂3−2
𝐶
𝑆 =
=
𝐶0 𝐾𝑠𝑝,𝐶𝑎𝐶𝑂3 (𝑐𝑎𝑙𝑐𝑖𝑡𝑒),(𝑇,𝑃)
𝐾𝑠𝑝,𝐶𝑎𝐶𝑂3 (𝑐𝑎𝑙𝑐𝑖𝑡𝑒),(𝑇,𝑃)
*
𝐾𝑠𝑝,𝐶𝑎𝐶𝑂3 (𝑐𝑎𝑙𝑐𝑖𝑡𝑒),(𝑇,𝑃) = 2.44𝑥10−9 (25𝐶, 1𝑎𝑡𝑚)
For BaSO4, the chemical reaction is:
𝐵𝑎𝑆𝑂4 = 𝐵𝑎+2 + 𝑆𝑂4 −2
And scale tendency equation is:
𝑆=
𝑎𝐵𝑎+2 ∗ 𝑎𝑆𝑂4−2
𝐾𝑠𝑝,𝐵𝑎𝑆𝑂4 (𝑏𝑎𝑟𝑖𝑡𝑒),(𝑇,𝑃)
=
𝛾𝐵𝑎+2 ∗ 𝑚𝐵𝑎+2 ∗ 𝛾𝑆𝑂4−2 ∗ 𝑚𝑆𝑂4−2
𝐾𝑠𝑝,𝐵𝑎𝑆𝑂4 (𝑏𝑎𝑟𝑖𝑡𝑒),(𝑇,𝑃)
*
𝐾𝑠𝑝,𝐵𝑎𝑆𝑂4 (𝑏𝑎𝑟𝑖𝑡𝑒),(𝑇,𝑃) = 1.06𝑥10−10 (25𝐶, 1𝑎𝑡𝑚)
𝐶𝑎𝑆𝑂4 . 2𝐻2 𝑂(𝑔𝑦𝑝𝑠𝑢𝑚) = 𝐶𝑎+2 + 𝑆𝑂4 −2 + 2𝐻2 𝑂
And scale tendency equation is:
𝑆=
𝑎𝐶𝑎+2 ∗ 𝑎𝑆𝑂4−2 ∗ 𝑎𝐻2 𝑂 2
𝐾𝑠𝑝,𝐶𝑎𝑆𝑂4.2𝐻2𝑂 (𝑔𝑦𝑝𝑠𝑢𝑚),(𝑇,𝑃)
=
𝛾𝐶𝑎+2 ∗ 𝑚𝐶𝑎+2 ∗ 𝛾𝑆𝑂4−2 ∗ 𝑚𝑆𝑂4−2 ∗ 𝑎𝐻2𝑂 2
𝐾𝑠𝑝,𝐶𝑎𝑆𝑂4.2𝐻2𝑂 (𝑔𝑦𝑝𝑠𝑢𝑚),(𝑇,𝑃)
𝒂𝑯𝟐𝑶 is activity of the water molecule
*
𝐾𝑠𝑝,𝐶𝑎𝑆𝑂4 .2𝐻2𝑂 (𝑔𝑦𝑝𝑠𝑢𝑚),(𝑇,𝑃) = 3.20𝑥10−5 (25𝐶, 1𝑎𝑡𝑚)
𝐶𝑎𝐹2 , 𝑠 𝐹𝑙𝑢𝑜𝑟𝑖𝑡𝑒 = 𝐶𝑎+2 + 2 ∗ 𝐹 −1
The scale tendency equation is
Where…
𝑎𝐶𝑎+2 1 ∗ 𝑎𝐹−1 2
𝑆=
𝐾𝑠𝑝 (𝐶𝑎𝐹2 𝐹𝑙𝑢𝑜𝑟𝑖𝑡𝑒 )
𝑎𝐶𝑎+2 = the activity of the Ca+2 ion in water
𝑎𝐹−1 2 = activity of dissolved F-1, squared because there are two F- in the reaction
𝐾𝑠𝑝 (𝐶𝑎𝐹2 𝐹𝑙𝑢𝑜𝑟𝑖𝑡𝑒 ) = T & P dependent solubility constant for fluorite
Therefore…
𝛾𝐶𝑎+2 1 ∗ 𝑚𝐶𝑎+2 1 ∗ 𝛾𝐹−1 2 ∗ 𝑚𝐹−1 2
𝑆, 𝑓𝑙𝑢𝑜𝑟𝑖𝑡𝑒 =
𝐾𝑠𝑝 (𝐶𝑎𝐹2 𝐹𝑙𝑢𝑜𝑟𝑖𝑡𝑒 )
*
We will discuss the details of each variable and the significance of this equation
in these slides
𝐼𝐴𝑃
=
𝑎𝑐𝑎𝑡𝑖𝑜𝑛 𝛼 ∗ 𝑎𝑎𝑛𝑖𝑜𝑛 𝛽
= 𝑚𝑐𝑎𝑡𝑖𝑜𝑛 𝛼 ∗ 𝛾𝑐𝑎𝑡𝑖𝑜𝑛 𝛼 ∗ 𝑚𝑎𝑛𝑖𝑜𝑛 𝛽 𝛾𝑎𝑛𝑖𝑜𝑛 𝛽
for calcite, CaCO3, IAP looks like this:
𝐼𝐴𝑃𝐶𝑎∗𝐶𝑂3 = 𝑚𝐶𝑎+2 ∗ 𝛾𝐶𝑎+2 ∗ 𝑚𝐶𝑂3 −2 ∗ 𝛾𝐶𝑂3 −2
where
𝑚𝐶𝑎+2 𝑎𝑛𝑑 𝑚𝐶𝑂3−2 𝑎𝑟𝑒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑎𝑛𝑑 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑
𝛾𝐶𝑎+2 𝑎𝑛𝑑 𝛾𝐶𝑂3−2 𝑎𝑟𝑒 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑
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The general equation for Ksp
𝑲𝒔𝒑 =
∆𝑮𝒓𝒆𝒂𝒄𝒕𝒊𝒐𝒏 𝒂𝒕 𝒆𝒒𝒖𝒊𝒍𝒊𝒃𝒓𝒊𝒖𝒎
𝑹𝑻
𝒆−
when calcite is the solid
∆𝑮
𝑲𝒔𝒑,𝒄𝒂𝒍𝒄𝒊𝒕𝒆 = 𝒆−
𝑪𝒂+𝟐 +𝑪𝑶𝟑 −𝟐 =𝑪𝒂𝑪𝑶𝟑 (𝑪𝒂𝒍𝒄𝒊𝒕𝒆)
𝑹𝑻
𝒂𝒕 𝒆𝒒𝒖𝒊𝒍𝒊𝒃𝒓𝒊𝒖𝒎
Defining S in a simulation tool
𝑆=
𝑚𝑐𝑎𝑡𝑖𝑜𝑛 𝛼 ∗ 𝛾𝑐𝑎𝑡𝑖𝑜𝑛 𝛼 ∗ 𝑚𝑎𝑛𝑖𝑜𝑛 𝛽 𝛾𝑎𝑛𝑖𝑜𝑛 𝛽
𝒆
∆𝑮𝑻,𝑷
− 𝒓𝒆𝒂𝒄𝒕𝒊𝒐𝒏
𝑹𝑻
for calcite
𝑆=
𝑚𝐶𝑎+2 ∗ 𝛾𝐶𝑎+2 ∗ 𝑚𝐶𝑂3 −2 ∗ 𝛾𝐶𝑂3 −2
𝒆−
*
∆𝑮𝑻,𝑷+𝟐
𝑪𝒂
+𝑪𝑶𝟑 −𝟐 =𝑪𝒂𝒍𝒄𝒊𝒕𝒆
𝑹𝑻
• The equilibrium constant, Ksp is unitless
𝐾𝑠𝑝 =
∆𝐺𝑓
−
𝑒 𝑅𝑇
=
𝑒𝑛𝑒𝑟𝑔𝑦 𝑢𝑛𝑖𝑡𝑠
−
𝑒 𝑒𝑛𝑒𝑟𝑔𝑦 𝑢𝑛𝑖𝑡𝑠
• IAP is also unitless…
𝐼𝐴𝑃 = 𝑚𝑐𝑎𝑡 +𝑦 𝛼 ∗ 𝛾𝑐𝑎𝑡 +𝑦 𝛼 ∗ 𝑚𝑎𝑛−𝑧 𝛽 𝛾𝑎𝑛−𝑧 𝛽
• S is therefore unitless…
𝐼𝐴𝑃 𝑢𝑛𝑖𝑡𝑙𝑒𝑠𝑠
𝑆=
=
𝐾𝑠𝑝 𝑢𝑛𝑖𝑡𝑙𝑒𝑠𝑠
*
Scale
Scale Tendency Equation
Ksp
FeCO3, siderite
FeCO3 = Fe+2 + CO3-2
Ksp,siderite (25C,1atm)=3.9x10-11
FeS, mackinawite
FeS = Fe+2 + S-2
Ksp,mackinawite(25C,1atm)=4.5x10-17
FeS, pyrrhotite
FeS = Fe+2 + S-2
Ksp,pyrrhotite (25C,1atm)=7.6x10-19
Fe(OH)3, amorphous
Fe(OH)3 = Fe+3 + 3(OH)-
Ksp,Fe(OH)3,am (25C,1atm)=3.2x10-38
CaCO3, aragonite
CaCO3 = Ca+2 + CO3-2
Ksp,aragonite (25C,1atm)=5.8x10-9
Ca0.5Mg0.5CO3,dolomite
Ca0.5Mg0.5CO3 =0.5Ca+2 + 0.5Mg+2 + CO3-2
Ksp,dolomite (25C,1atm)=1.7x10-17
SiO2, amorphous
SiO2 = SiO2
Ksp,SiO2,am (25C,1atm)=1.9x10-3
*
Scale
Scale Tendency Equation
FeCO3, siderite
𝑆=
𝐾𝑠𝑝 (𝑠𝑖𝑑𝑒𝑟𝑖𝑡𝑒)
𝛾𝐹𝑒 +2 ∗ 𝑚𝐹𝑒 +2 ∗ 𝛾𝑆 −2 ∗ 𝑚𝑆 −2
𝑆=
𝐾𝑠𝑝 (𝑚𝑎𝑐𝑘𝑖𝑛𝑎𝑤𝑖𝑡𝑒)
𝛾𝐹𝑒 +2 ∗ 𝑚𝐹𝑒 +2 ∗ 𝛾𝑆 −2 ∗ 𝑚𝑆 −2
𝑆=
𝐾𝑠𝑝 (𝑝𝑦𝑟𝑟ℎ𝑜𝑡𝑖𝑡𝑒)
FeS, mackinawite
FeS, pyrrhotite
Fe(OH)3, amorphous
iron hydroxide, rust
𝛾𝐹𝑒 +3 ∗ 𝑚𝐹𝑒 +3 ∗ 𝛾𝑂𝐻 − 3 ∗ 𝑚𝑂𝐻− 3
𝑆=
𝐾𝑠𝑝 (𝑎𝑚 𝐹𝑒 𝑂𝐻 3)
𝛾𝐶𝑎+2 ∗ 𝑚𝐶𝑎+2 ∗ 𝛾𝐶𝑂3−2 ∗ 𝑚𝐶𝑂3−2
𝑆=
𝐾𝑠𝑝 (𝑎𝑟𝑎𝑔𝑜𝑛𝑖𝑡𝑒)
CaCO3, aragonite
Ca0.5Mg0.5CO3,
dolomite
SiO2, amorphous
silica
𝛾𝐹𝑒 +2 ∗ 𝑚𝐹𝑒 +2 ∗ 𝛾𝐶𝑂3−2 ∗ 𝑚𝐶𝑂3−2
𝑆=
𝛾𝐶𝑎+2 0.5 ∗ 𝑚𝐶𝑎+2 0.5 ∗ 𝛾𝑀𝑔+2 0.5 ∗ 𝑚𝑀𝑔+2 0.5 ∗ 𝛾𝐶𝑂3−2 ∗ 𝑚𝐶𝑂3 −2
𝐾𝑠𝑝 (𝑑𝑜𝑙𝑜𝑚𝑖𝑡𝑒)
𝛾𝑆𝑖𝑂2 ∗ 𝑚𝑆𝑖𝑂2
𝑆=
𝐾𝑠𝑝 (𝑎𝑚 𝑠𝑖𝑙𝑖𝑐𝑎)