
Scale in the Oil Field
Introduction to Scale in the Oil Field
In the oil production industry, the most common scales are calcium carbonate
(calcite), calcium sulfate, usually in the form of gypsum, and barium and/or strontium
sulfates (barite and celesite, respectively.) Both barite and celesite have very
low solubilities; thus, when either barium or strontium is present together with
sulfate in water, scale formation is very likely. At atmospheric pressure, barite
is about 20 times less soluble than calcite, which is in turn almost 500 times less
soluble in water than gypsum (Patton, 1986). However, barium and strontium are not
usually major species in natural waters, so calcium carbonate and calcium sulfate
scales are much more common.
There are many methods of predicting scale in the oil field industry. Simple
prediction methods include the Stiff and Davis method to predict the formation of
Calcium carbonate scale, and the Skillman McDonald Stiff Method to predict the formation
of gypsum and barite. (Celesite formation can also be predicted using this method
but is not included in our scale prediction tools.) The Oddo and Tomson method is
a more complex but accurate method of predicting formation of all the common oil
field scales.
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Definitions
Solubility calculations are used to predict the formation of various types of
scales. All minerals are soluble in water to a limited extent. Many minerals are
salts and will dissociate into ions, for example,
NaCl ? Na^{+} + Cl^{}
.
Multiplying the concentrations of the ions together (Cl^{} x Na^{+})
will give the ion product (IP). If the solution is saturated with respect
to that mineral and in equilibrium, the ion product will equal the solubility product
constant, K_{sp}
.
The solubility product constant for any salt will vary with pressure, temperature,
ionic strength, and possibly pH. All salts increase in solubility as the pressure
is increased, because when a salt is dissolved in water, there is a decrease in
volume. As the ionic strength is increased, solubility increases up to a point when
the water simply cannot hold any more salt, and then decreases. The effect of temperature
on solubility differs with different salts.
The Saturation Index (SI) is the logarithmic ratio of the ion product and
the solubility product, SI = log (IP / K_{sp}). In other words, the
SI is the log of the actual amount of mineral forming ions over the solubility of
that mineral. Thus, a saturated solution (in equilibrium) will have a SI of
0, an undersaturated solution will have a negative SI, and a supersaturated solution
will have a positive SI. In addition, the saturation index has a logarithmic scale.
For example, a solution with a SI of 3 is ten times more oversaturated than a solution
with a SI of 2.
It is important to remember that a positive SI does not necessarily mean that scale
will form, since the kinetics of scale formation may be too slow; rather, it is
an indicator that formation is possible.
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Methods of Predicting Scale
Stiff Davis Method  Calcium Carbonate
The StiffDavis method is one of the easiest ways to calculate calcium carbonate
scaling tendencies; the use of this method results in a calcite Saturation Index,
and is valid between temperatures from 0  100ºC (32  212ºF) and ionic strengths
from 0  4. Inputs needed are pH, alkalinity, calcium concentration, and ionic strength.
Stiff and Davis created this method in 1952 to be able to predict calcium carbonate
scaling tendencies in brines (Stiff and Davis, 1952). Experimental data was collected
for different ionic strengths at 0, 30, and 50ºC to find the K constant. These curves
were extrapolated to get curves for 0 to 100ºC in steps of 10 degrees (Stiff and
Davis, 1952). The Stiff page calculates the SI for calcium carbonate for temperatures
ranging from 0 to 100ºC, using a polynomial fit for each K constant curve. Figure 1 and Tables 1 and 2 show the K constant
for CaCO_{3}
.
The Stiff Davis method is very simple, but it may not be accurate if the pH is
not measured immediately at the sample site. In addition, it does not take into
account the total pressure or amount of dissolved or undissolved carbon dioxide
gas.
Skillman McDonald Stiff Method  Gypsum and Barite
The Skillman McDonald Stiff method is a way of predicting the solubility of gypsum
scale (NOT the Saturation Index OR the total possible scale formed), and is valid
between temperatures of 10  80ºC (50  176ºF) and ionic strengths from 0  6. Inputs
needed are ionic strength, and sulfate and calcium ion concentrations. It
does not take pressure into account, or any barium or strontium concentrations,
which would most likely precipitate out barite (BaSO_{4}) or celesite (SrSO_{4}),
reducing the available sulfate ion concentration. The solubility constant, K_{sp},
is calculated using the graph of K_{sp} versus temperature and ionic strength
(Appendix 15, Patton, 1986). The Skillman McDonald Stiff method can also be
used to predict the solubility of barite and celesite scale, if the K_{sp}
variation with temperature and ionic strength are known. The solubility of
sulfate scales, including gypsum (CaSO_{4} x 2 H_{2}O), barite (BaSO_{4}),
and celesite (SrSO_{4}) can be predicted using
Equation 1
.
The actual concentration (A) of CaSO_{4} in solution is equal to the lesser
cation (Ca^{2+}) or anion (SO_{4}^{2}) 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:

(1) If S = A, the water is saturated with CaSO_{4};

(2) if S > A, the water is undersaturated, and scale formation is unlikely;
and

(3) if S < A, the water is supersaturated, and scale formation is likely.
The Skillman, McDonald, and Stiff method gives K_{sp} values for gypsum,
and is the most commonly used method of predicting the solubility of gypsum in oilfield
brines. Tables 3 and 4 and Figures
2, 3, and 4 show the K_{sp} for CaSO_{4}
, and Tables 5 and 6 and Figure 5
show K_{sp} for BaSO_{4}
.
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Stiff Page
The Stiff page uses both the Stiff Davis method for SI calculation for calcite,
and the Skillman McDonald Stiff method for solubility of gypsum and barite. It also
calculates the total possible scale amount for gypsum and barite using Equation 2
(total calcite scale is calculated using a modified version of this equation).
The Stiff page will give you graphs or tables of calcite SI, and gypsum and barite
scale solubility, or total possible scale vs. temperature. Each graph has different
temperature points because the original solubility data was collected at different
temperatures. When using this page, you must choose whether you want graphs of the
solubility or total possible scale. Regardless, the first graph will be the calcite
SI vs temperature. Stiff page options:

1. Solubility and Actual concentrations ?Choosing this option will give three graphs,
the first of Saturation Index for Calcite, and the second and third of Gypsum and
Barite solubilities, along with actual concentrations in meq/L if the two values
are close.
For example, for gypsum scale in any water sample, if the graph shows that the
actual concentration of possible gypsum is below the solubility of gypsum, then
no scale will occur. If it is above, then scale may occur.
The actual concentration of gypsum is the lesser of the amounts of Ca^{2+}
or SO_{4}^{2}
in meq/L, which is equivalent to the total possible gypsum in meq/L if all the water
was evaporated from the sample.

2. S Index ?The three graphs show the SI index for calcite, and S indexes for
gypsum and barite at various temperatures.
The S index is related to the first option (Solubility and Actual concentrations)
because the S index is defined as the Actual concentration (meq/L) ?Solubility (meq/L).
Thus if the S index is negative, then scale will not form; if positive, then scale
is possible.

3. Total possible scale in mg/L ?Choosing this will give four graphs, the first
of Saturation Index for calcite using the Stiff Davis method, and the rest are graphs
of total possible scale in mg/L for calcite, gypsum, and barite, using Equation 2
.

4. Total possible scale in PTB (A index) ?The A index is defined as the total
possible scale in pounds per thousand barrels (PTB). This is simply a conversion
of choice 3.
Choosing this will give four graphs, the first of Saturation Index for calcite using
the Stiff Davis method, and the rest, graphs of total possible scale in PTB for
calcite, gypsum, and barite, using Equation
2 .
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Oddo Tomson Method
The OddoTomson method is another way of predicting the formation of calcium
carbonate and various sulfate scales by calculating SI values. It is valid between
temperatures of 0  200ºC (32  392ºF), ionic strengths of 0  4.0, and pressures
of 1  1380 bar (0  20000 psig) (Patton, 1986).
Saturation indices are calculated for the different types of calcium sulfate minerals,
including gypsum (CaSO_{4} ?2 H_{2}O), hemihydrate (CaSO_{4}
?1/2 H_{2}O), and anhydrite (CaSO_{4}
). Gypsum is the most common scale former and occurs at relatively low temperatures.
Above about 100 ºC (212ºF), anhydrite is the stable phase; however, hemihydrate can
form in temperatures ranging from 90 to 120 ºC (Oddo and Tomson, 1991). The OddoTomson
method can also predict the formation of barium and strontium sulfate scales.
Inputs needed are chemical analysis (including calcium, barium, strontium, bicarbonate,
carbonate, and sulfate ions), temperature in ºF, pressure in psia (psig + 14.7),
and mole percentage of carbon dioxide in the gas phase or, if there is no gas phase,
the amount of dissolved carbon dioxide in the water. If the amount of carbon dioxide
is unknown but there is an accurate pH measurement, the method uses the pH to calculate
the saturation indices.
The Oddo Tomson method is more accurate than the Stiff Davis method because it
takes pressure as well as temperature and ionic strength into account. In addition,
the method does not require a pH measurement, but calculates the pH based on the
amount of carbon dioxide gas and bicarbonate in the water. This allows a greater
accuracy in calculating the actual Saturation Index of a water sample, since pH
measurements decline in accuracy very quickly after the sample is taken out of its
natural environment.
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Oddo Page
The Oddo page uses the OddoTomson method to predict Saturation Indices for calcite,
gypsum, barite and celesite, taking temperature, pressure, and ionic strength into
account.
This page can also calculate pH values, if one inputs the mole fraction of CO_{2}
in the gas phase or, if no gas phase is present, the concentration of dissolved
CO_{2}
in mol/L in the water sample. If the pH value is known to be accurate, the measured
pH can be used; however, using a measured pH is discouraged because the method was
developed partially as a way to calculate Saturation Indices (and pH) without a
measured pH value. This is because changes in temperature and pressure as the water
sample is taken from a formation often leads to degassing, which in turn leads to
inaccurate pH measurements, even if measured as soon as a water sample is taken.
The equilibrium concentration of CO_{2} depends on temperature, pressure,
and salinity. Gas concentration decreases with increasing temperature and salinity,
and increases with increasing pressure. Atmospheric mole fraction of CO_{2}
is approximately 0.00035, and pure water in contact with the atmosphere will have
about 0.52 mol/L dissolved CO_{2}
using a Henry’s Law constant of 0.034 M/atm.
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Mixing Page
Mixing waters will often result in some scale formation, whether mixing different
waters in a holding tank or injecting incompatible water into a formation. The mixing
page will allow you to mix waters with a known chemical analysis. You may specify
the ratio that the waters are mixed at, and the program will assume complete mixing,
resulting in the maximum amount of possible scale. (A mixing ratio of 1:1 will give
the maximum possible scale when the two waters have similar ionic strengths.) The
result will be the chemical composition of the mixed water, before any precipitation
occurs. This can then be plugged into the Oddo Page or Stiff page to give you an
idea of what scales will form, and in what amounts.



