B41oa oil and Gas Processing Section a flow Assurance Heriot-Watt University

A. The Stiff-Davis Method: Calcium Carbonate Formation 
The Stiff-Davis method is one of the easiest ways to calculate calcium 
carbonate scaling tendencies and takes into account the influence of high 
levels of dissolved solids on the solubility of calcium carbonate at a given 
temperature. 
Stiff-Davis created this method in 1952 to allow prediction of calcium 
carbonate scaling tendencies in brines. The use of this method results in a 
calcite Saturation Index and is valid from 0-100ºC (32-212ºF) and for ionic 
strengths from 0-4. The Stiff and Davis Scale Index (
DSI
&
S
) is defined by 
(
)
K
pAlk
pCa
pH
+
+
−
=
DSI
&
S
……………
.
…
.(2.2) 
The inputs that are needed are pH, alkalinity, calcium concentration, and ionic 
strength). The Stiff-Davis method is very simple, but it may not be accurate 
unless the pH is measured immediately at the sample site. In addition, it does 
not take into account the total pressure or the amount of dissolved or 
undissolved carbon dioxide gas. 

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TOPIC 2: Oilfield Scale 
 
 
 
10 
©H
ERIOT
-W
ATT
U
NIVERSITY B41OA December 2018 v3 
B. The Skillman-McDonald-Stiff Method: Gypsum & Barite 
The Skillman-McDonald-Stiff method is one of the most commonly used 
methods of predicting the solubility of gypsum scale in oilfield brines, and is 
valid between temperatures of 10-80ºC (50-176ºF) and ionic strengths from
0-6. Inputs needed are ionic strength, and sulphate and calcium ion 
concentrations. 
It does not take into account the pressure of the system, or any barium or 
strontium concentrations – these are most likely to precipitate out barite 
(BaSO
4
) or celestite (SrSO
4
), thereby reducing the available sulphate ion 
concentration. 
The solubility constant, 
SP
K
is calculated using the graph of 
SP
K
versus 
temperature and ionic strength. The Skillman-McDonald-Stiff method can also 
be used to predict the solubility of barite and celestite scale, so long as the 
SP
K
variation with temperature and ionic strength are known. 
The solubility of sulphate scales, including gypsum (CaSO
4
.2H2O), barite 
(BaSO
4
), and celestite (SrSO
4
) can be predicted using the following equation: 
(
)
⎥
⎦
⎤
⎢
⎣
⎡
−
+
=
x
K
x
S
SP
2
4
1000
2
………………………
.....(2.3) 
Where, 
S
is the solubility (meq/L) 
SP
K
is the solubility product 
x
is the excess ion concentration (mol/L) 
The actual concentration (
A
) of CaSO
4
in solution is equal to the lesser cation
(
)
+
2
Ca
or anion 
(
)
-
2
4
SO
concentration in meq/L. In order to determine if scale 
formation is likely, the actual concentration is compared with the solubility (
S
), 
with three possible scenarios: 
I. 
If 
A
S
=
: the water is saturated with CaSO
4
. 
II. 
If 
A
S
>
: the water is undersaturated and scale formation is 
unlikely. 
III. 
If 
A
S
<
: the water is supersaturated and scale formation is likely.