Flow Impairment by Deposited
Sulfur - A Review of 50 Years of Research
Bruce E. Roberts
Rock Isle Consulting Services Ltd., Calgary, Alberta, Canada
Received March 30, 2017; Accepted May 11, 2017
Abstract:
Sulfur deposition in the reservoir formation and its impact on well
productivity and ultimate recovery has been investigated for close to 50
years. Experimental measurements and numerical modeling studies have
focused on the phase behavior of the sulfur-sour gas mixture system and
the flow of sulfur and natural gas through the formation. The key results
from these investigations are reviewed in this paper. The implementation
of the insights gained over these 50 years of research into the field
development planning and operation of sour gas fields is described.
Keywords:
Sulfur deposition, sour gas, hydrogen sulfide, formation damage
1
Introduction
Elemental sulfur is often present in significant quantities in sour gas at reservoir pressure and temperature conditions. The equilibrium sulfur content of
reservoir fluids decreases with pressure and temperature. Deposition of sulfur
will occur in the reservoir, well tubulars, or surface equipment when the equilibrium solubility of sulfur becomes less than the sulfur content of the fluid.
Although sulfur deposition in the well and surface equipment is a significant operational problem, it is deposition in the formation that most significantly impacts well productivity and ultimate recovery. Estimation of the
performance of wells producing reservoir fluid containing elemental sulfur
requires an understanding of the phase behavior of sulfur in sour gas mixtures
coupled with aspects of the flow of sulfur and gas through the formation. In
this review, the development of our current understanding of the deposition
Corresponding author(s): be.roberts1@gmail.com
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process within the formation and its impact on gas well productivity over the
last 50 years of study is outlined. An objective of this review is to demonstrate
how advances in this understanding may be implemented into the field development planning and subsequent management of sour gas containing elemental sulfur.
2
Field Experience
The early insights into the nature of sulfur deposition and the resulting operational issues may be attributed to the studies by J.B. Hyne and co-workers at
Alberta Sulfur Research Ltd. Hyne [1] surveyed more than 100 sour gas wells
world-wide and determined that a combination of high bottomhole pressure
and well temperature with low wellhead pressure provided a favorable set of
conditions for deposition in the well. However, the study focused on deposition in the well and surface equipment, with relatively little attention given to
the deposition within the formation.
Deposition of solid sulfur in the formation has significantly impacted well
performance during production of Shell Canada’s dry, sour gas from deep,
fractured, carbonate reservoirs located in southwest Alberta, Canada. The H2S
concentration of the reservoir fluid ranges from 15 to 30%, with initial pressure
from 30 to 40 MPa, and temperature from 80 to 100 ˚C. In a case described by
Roberts [2], well production dropped rapidly from an initial rate of 320 103
to 100 103 m3/d in 42 days. The well skin, as determined by a pressure
buildup test, increased from slightly negative before production to about +17
following this flow period. Hands et al. [3] noted that well life of the order of
only 2–3 years has been experienced for these gas pools. In a specific case, a
horizontal well had become quickly plugged with sulfur and required sidetracking just beyond 50 m from the original well. Field experience also showed
that solvent treatments can remove deposition within natural fractures, but
once the fracture has been allowed to bridge with sulfur, solvent treatments
become ineffective.
Deposition of sulfur is generally absent when the composition of the reservoir fluid is high in heavier hydrocarbons (Hyne [1]). Sulfur which precipitates
from the gas phase will dissolve into any hydrocarbon liquids which have
dropped out due to retrograde condensation.
The most detailed account of sulfur deposition within the formation is provided by Chernik and Williams [4] and Williams and Milligan [5] in their
description of production testing of Shell Canada’s ultra-sour (90% H2S) Bearberry gas reservoir. The reservoir fluid was determined to contain approximately 65 g/m3 (standard conditions) at a reservoir pressure of 37 MPa and
118 ˚C. At these conditions, sulfur would deposit in the formation as a liquid
phase. The project consisted of production from two wells. Production through
one well was via a large (88 m) perforated interval and was used to obtain
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data on the productivity of a commercial Bearberry well. For the second well,
only one meter of pay was perforated to generate a large pressure differential
at the well to accelerate sulfur deposition. However, impairment of gas flow by
the near-well bore accumulation of liquid elemental sulfur was not observed. It
should be noted that the Bearberry formation is highly permeable – the drawdown at the large perforated interval well was less than 1 MPa at 180 x 103
m3/d. The results for Bearberry may not be completely applicable to much
tighter formations.
3
Phase Behavior of Sulfur/Sour-Gas Systems
The following describe the main aspects of the phase behavior of sulfur-sour
gas mixtures that govern the sulfur deposition process within the reservoir.
3.1
Sulfur Solubility in H2S and Sour Gas - Experimental Data
Kennedy and Wieland [6] provided the first data set on the solubility of sulfur
in sour gas mixtures at pressures to 40 MPa and temperatures to 394 K. However, their results have been found not to be consistent with studies that followed. Solubility measurements in pure H2S have been reported by Roof [7],
Swift [8], Brunner and Woll [9], Gu et al. [10] and Migdisov et al. [11]. Brunner
and Woll [9] also measured sulfur solubility in four gas mixtures, with H2S
concentrations ranging from 1 to 20%. Brunner et al. [12] followed up this
study with additional measurements in seven gas mixtures that included a specific examination of the impact of ethane and butane components on sulfur solubility. Gu et al. [10] measured the solubility of two sour gas mixtures of high
H2S concentration (44 and 95%). To facilitate the evaluation of equation of state
binary interaction parameters, Gu et al. [10] also determined the solubility of
sulfur in pure CO2 and CH4. Sun and Chen [13] determined sulfur solubility in
seven sour gas mixtures, with a focus on the low temperature range from 30 to
90 ˚C. A summary of the experimental studies reported to date is shown in
Table 1.
3.2
Sulfur Solubility Trends
Analysis of the experimental sulfur solubility data reveals several key trends
that are relevant to an analysis of the sulfur deposition process:
1. At a constant temperature, sulfur solubility in H2S and sour gas
mixtures decreases with declining pressure. As noted previously, such a
decrease in solubility in a saturated reservoir fluid will result in
deposition of sulfur in the formation.
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Table 1
Experimental studies on the solubility of sulfur in fluid systems.
Authors
Fluid system
H2S concentration (mol% )
Pressure
(MPa)
Temperature
(K)
Roof [7]
H2S
100
to 30
316–383
Swift [8]
H2S
100
35 - 140
394–450
Brunner and
Woll [9]
H2S and
4 sour gas
mixtures
1–20
10–60
373–433
Brunner et al.
[12]
7 sour gas
mixtures
9–84
7–155
398–485
Gu et al. [10]
H2S,
CO2,
CH4 and 2 sour
gas mixtures
44–95
12–50
363–383
Migdisov
et al. [11]
H2S
100
0.5–20
323–563
Sun and
Chen [13]
7 sour gas
mixtures
5–27
20–45
303–363
2. At a constant pressure, sulfur solubility in sour gas mixtures decreases
with a decrease in temperature. However, the effect of temperature on
the solubility of sulfur in pure H2S is more complicated. At pressures
less than approximately 20 MPa, solubility increases with decreasing
temperatures. At higher pressures, the trend is reversed. These trends
may be explained by the effect of temperature on two competing factors
that influence solubility. A decrease in temperature increases the gas
phase density that favors higher solubility, but decreases the vapor
pressure of elemental sulfur. At lower pressures, the effect on fluid
density with changes in temperature dominates, whereas at higher
pressures for more highly compressed mixtures, the vapor pressure
effect is more significant.
3. At all pressure and temperature conditions, sulfur solubility increases
with H2S concentration.
4. At a given pressure and temperature, replacement of methane with CO2
or heavier alkanes increases the sulfur solubility in the sour gas mixture.
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3.3
Sulfur Solubility in the Gas Phase: Chemical vs. Physical
Solubility
The solubility of sulfur in sour gas at reservoir conditions is orders of magnitude greater than would be expected assuming ideal gas behavior. Chemical
reaction and physical solubility mechanisms have been proposed to explain
this high solubility.
Hyne [14, 15] proposed that a chemical reaction between sulfur and H2S
occurs in the gas phase to form hydrogen polysulfides (H2Sx):
H2 S þ Sx ¼ H2 Sx
(1)
High H2S partial pressure and temperatures favor polysulfide formation.
Hyne concluded that a reduction in pressure and temperature would alter the
chemical reaction equilibrium leading to a reduction in solubility and deposition of sulfur.
A second mechanism to explain the high solubility of sulfur in sour gas is a
physical solvation process in which strong interactions between H2S and elemental sulfur result in highly nonideal gas behavior. High solubilities have
also been reported for other solid/compressed gas systems, and form the basis
of many industrial supercritical fluid separation processes (Brenecke and
Eckert [16]).
As noted by Roberts [2], the nature of sulfur solubility is important in the
evaluation of the deposition process. Sulfur held physically in a sulfur-saturated gas phase will deposit immediately upon a reduction of pressure or temperature. However, if sulfur exists as a polysulfide species, the kinetics of the
chemical reactions will govern the deposition process.
Reported studies have provided evidence that the polysulfide reaction
mechanism is relatively unimportant at temperatures generally encountered in
the natural gas industry. Hydrogen polysulfides were not detected in liquid
H2S saturated with elemental sulfur to 100 ˚C (Smith et al. [17]). A study by
Migdisov et al. [11] on the stability of polysulfides in gaseous H2S concluded
that sulfur solubility is dominated by physical solubility at 125 to 170 ˚C, and
polysulfide formation at 200 to 290 ˚C. The polysulfide formation mechanisms
also cannot account for the reduction of sulfur solubility in H2S with increasing
temperature as noted previously.
3.4
Freezing Point of Elemental Sulfur
Formation flow impairment by sulfur deposition may be manageable when
sulfur deposits as a liquid phase as shown by the field results for the Bearberry
project. The freezing point of elemental sulfur at atmospheric pressure is
115–119 ˚C. A study by Woll [18] provided data on depression of the freezing
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point due to dissolution of H2S into the liquid phase. The magnitude of the
depression increases with increasing H2S concentration. The minimum freezing
temperature is observed at 94 ˚C for pure H2S at approximately 7.5 MPa. Further increases in pressure increases the freezing temperature.
4
Modeling of Sulfur Solubility
Two main approaches to the modeling of sulfur solubility in H2S and sour gas
mixtures have been reported in the literature – equation of state modeling, and
the use of analytical expressions, incorporating empirical constants. In addition
to these two approaches, the application of an artificial neural network to the
prediction of sulfur solubility has been described. Details on these methods are
outlined below.
4.1 Thermodynamic Modeling with an Equation of State
At equilibrium, the fugacity of sulfur is equal in all phases:
fss ¼ fsl ¼ fsv
(2)
For the solid phase, assuming a constant molar volume of sulfur, vs, the
fugacity of sulfur may be given by the following expression, where Pss is the
vapor pressure of sulfur, and the exponential term is the Poynting correction
factor:
fss ¼ Pss exp vs P � Pss =RT
(3)
An equation of state may be used to determine the fugacity of sulfur in the
liquid or vapor phases. Studies reported to date have all used the Peng-Robinson equation of state for the fugacity calculation with different approaches
being used to determine the equation parameters and in the incorporation of
chemical reactions.
An application of the Peng-Robinson equation of state to calculate sulfur solubility in a fluid phase was first reported by Tomcej et al. [19]. The model was
applied to a range of possible cases in which sulfur (in solid or liquid phase)
distributes between a single-phase vapor, single-phase liquid, or two-phase
liquid. The experimental sulfur melting data of Woll [18] was used to determine if the sulfur fugacity calculation was to apply equation (3) for the solid
sulfur case, or the equation of state for the liquid phase equilibrium. This
approach resulted in a slight discontinuity in the solubility curves at the sulfur
melting temperature. Solid sulfur vapor pressure and sulfur critical temperature used to calculate the EOS parameters were adjusted to provide the best
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match to the available experimental data. A reasonable fit to the experimental
data of Roof [7], Brunner and Woll [9] and Brunner et al. [12] was obtained.
The Peng-Robinson equation of state was also used by Karan et al. [20] but
with a different approach to the calculation of the equation parameters. For the
liquid and vapor phases, the a and b parameters of the equation of state were
adjusted to provide the best match to the vapor pressure and liquid density.
The solid sulfur fugacity was calculated by an empirical function of temperature and pressure with the parameters adjusted to fit experimental solubility
data. In addition, binary interaction parameters were determined from available experimental data. The match obtained between predicted and experimental solubility for the data of Roof [7], Brunner and Woll [9], and Brunner et al.
[12] was similar to that reported by Tomcej et al. [19], as based on a visual
comparison of the paper figures.
A much more complicated model was developed by Heidemann et al. [21],
by the incorporation of chemical reactions. Sulfur was modeled as a mixture of
eight species, S1 to S8, with each available to react with H2S:
H2 S þ
n�1
S8 ¼ H2 Sn ; n ¼ 2; . . . ::9
8
(4)
A method to estimate the equation of state parameters for all the species
was described. The calculation of the equation of state parameters for pure S8,
and estimation of the binary interaction parameters followed the approach of
Karan et al. [20] Despite the added complexity of the model, the match
between predicted and the experimental data was similar to the model of
Karan et al. [20].
Gu et al. [10] used the Peng-Robinson equation of state to determine sulfur
solubility at temperatures less than the melting point. A correction function
incorporating two temperature-dependent interaction parameters were introduced to modify the mixing rule for the b parameter of the Peng-Robinson
equation of state. These new interaction parameters, plus the usual interaction
parameter to calculate the a parameter were determined by fitting to the available experimental data. The average absolute deviation between experimental
and predicted solubility for two sour gas mixtures of 44 and 95% H2S was
approximately 7%. Sun and Chen [13] used a similar approach, but considered
the interaction parameters to be temperature independent. An average absolute
deviation between experimental and predicted solubility of 6.5% was determined for seven gas mixtures of H2S content of approximately 5 to 27%.
The Peng-Robinson equation of state model by Cézac et al. [22] was developed specifically to investigate sulfur deposition in natural gas transmission
networks. An approach similar to Heidemann et al. [21] was used with the
incorporation of reactions between the eight sulfur species and H2S to form
polysulfanes. The pressure and temperature conditions studied were outside
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the range of available experimental data, so no conclusions could be drawn
regarding the accuracy of the prediction.
In summary, an equation of state is generally able to provide an estimate of
sulfur solubility in sour gas of sufficient accuracy for screening calculations.
Development of more complex models incorporating chemical reactions does
not improve the predictive capability.
4.2 Analytical Models
A simple correlation developed by Chrastil [23] for predicting the solubility of
solids in fluids at high pressure was first applied by Roberts [2] to the sulfursour gas system:
cr ¼ �k exp
a
T
þB
(5)
where cr (g/m3), is the concentration of the solid component at reservoir
temperature and pressure, � is the fluid density (kg/m3), and T is the fluid
temperature (K). The parameters, k, a, and B are empirical constants determined by matching experimental solubility measurements.
As this equation has been used extensively in subsequent studies on the sulfur deposition process, it is useful to note the key aspects of its application and
parameter determination. Roberts [2] used solubility data for two sour gas mixtures comprised of 20% H2S and 6% H2S reported by Brunner and Woll [9] to
estimate the correlation parameters. These mixtures were selected as the H2S
concentration bounded the H2S concentration of the reservoir fluid under
study (16% H2S). The parameter, k, was estimated by plotting ln cr versus ln �
at a constant temperature (100, 120, 140 and 160 ˚C) for both gas mixtures. Values for k for the four temperatures studied varied from 3.7 to 4.1. The parameters a and B were determined by plotting ln cr versus 1/T at a constant density
equal to the value for the reservoir fluid at reservoir pressure (36.6 MPa) and
temperature (81 ˚C). The linear trend observed in the plot was determined to
coincide with the sulfur content of the reservoir fluid as measured in a bottomhole sample. This analysis of the Brunner and Woll [9] data for the two mixtures thus yielded the following expression for the sulfur solubility of the
fluid:
�4666
� 4:5711
cr ¼ �4 exp
T
(6)
The solubility as predicted by eq. (6) is expressed for fluid at reservoir temperature and pressure. Recent papers by Hu et al. [24] and Guo and Wang [25]
have incorrectly assumed solubility prediction by eq. (6) is expressed for fluid
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at standard temperature and pressure conditions. It is also important to stress
that this equation was developed based on data for a narrow range of H2S concentrations (6 to 20%) and should not be applied outside of this range. A
recent study by Wang et al. [26] proposed an improved method to estimate the
parameters for the Chrastil equation.
A modified approach to the application of the Chrastil equation was provided by Carroll [27] by expressing the solubility in equation (5) in terms of
mass of solute per unit volume of solvent at standard conditions. Carroll [27]
evaluated the equation parameters by fitting experimental data by least squares
regression for pure H2S grouped in three categories: solid sulfur in high density fluid, liquid sulfur in high density fluid, and liquid sulfur in low density
fluid. The model predictions were generally with +/-20% of the experimental
values. Model parameters were determined for 20 sour gas mixtures studied
by Brunner and Woll [9], Brunner et al. [12], Gu et al. [10], and Sun and Chen
[13]. For each mixture, parameters for the solubility of solid sulfur and liquid
sulfur were determined. The average absolute error for each gas mixture
ranged from approximately 4 to 35%, with average for all mixtures equal to
15%. In general, the correlation was significantly more accurate in the highpressure region.
The application of similar Chrastil-type equations to the prediction of sulfur
solubility in sour gas has recently been investigated by Eslamimanesh et al.
[28]. The correlations of Adachi and Lu [29], del Valle and Aquilera [30] and
Méndez-Santiago and Teja [31] were considered in this review, in which the
optimal parameters were determined by fitting the available experimental data
for each fluid composition. The 23 data sets investigated spanned the range of
temperature, pressure, and fluid compositions encountered in the natural gas
industry. A summary of the correlations and the absolute average deviation
(AAD) between predicted and experimental results is shown in Table 2. The
Table 2
Comparison of Chrastil-Type equations [28].
Reference
Chrastil [23]
Adachi and Lu [29]
del Valle and
Aguilera [30]
Méndez-Santiago and
Teja [31]
Correlation
c ¼ �k exp Ta þ b
Chrastil equation,
with
k ¼ e1 þ e2 � þ e3 �2
c ¼ �k exp a þ Tb þ Td2
y2 ¼ P1 exp Ta þ b�
T þd
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Number of adjustable
parameters
AAD
%
3
21
5
12
4
19
3
20
Bruce E. Roberts: Flow Impairment by Deposited Sulfur - A Review of 50 Years of Research
Adachi and Lu equation in which the k parameter is determined as a function
of density was determined to provide the best fit to the experimental data, as
may be expected given the incorporation of more adjustable parameters in the
correlation. Improvements in the match for the solubility of sulfur in pure H2S
were obtained by eliminating thermodynamically inconsistent data as identified by Eslamimanesh et al. [32].
4.3 Artificial Neural Network
An artificial neural network (ANN) is a compositional model loosely based on
the structure of the brain. It does not require a mathematical description of the
physical process. Mohammadi and Richon [33] developed an ANN algorithm
for estimating sulfur content in H2S. The algorithm was extended to sour gas
mixtures by Mehrpooya et al. [34]. A subset of available experimental data was
used to train the ANN model prior to a validation step in which deviations
between the experimental and predicted values were determined. Inputs to the
model were temperature, pressure, gas gravity (acid-gas free basis) and mole
fraction of H2S. Mehrpooya et al. [34] reported a 17% average absolute deviation between experimental and predicted data.
5. Formation Damage by Sulfur Deposition – Experimental Studies
Several studies have attempted to experimentally assess the degree to which
solid sulfur deposition will impact fluid flow in the formation. Guo et al. [35]
flowed sulfur-saturated gas containing 19% H2S through carbonate core samples and measured the distribution of sulfur deposited within the core using a
Scanning Electron Microscope. A buildup of deposited sulfur near the core exit
was attributed to a significant reduction in pressure in this region of the core.
A core flow experiment by Guo et al. [36] in which the pressure of a sulfursaturated gas containing 7% H2S was reduced from 19 to 10 MPa resulted in a
16% reduction in core permeability. In a follow-up study, Guo et al. [37] conducted a series of coreflow experiments and illustrated that the impact of sulfur deposition on formation permeability increased significantly with
increasing H2S content of the reservoir fluid. Hu et al. [38] conducted depletion
experiments by reducing saturated sour gas containing 7% H2S from 40 to
8 MPa and observed approximately a 13% reduction in core permeability.
Higher reduction in permeability was reported by Xuefeng et al. [39] for similar
reservoir fluid composition – a decline of pressure from 45 to 8 MPa resulted
in a 45% loss in permeability.
Abou-Kassem [40] conducted a series of tests involving the flow of nitrogen
saturated with sulfur through limestone cores at relatively low pressure (3 to
6 MPa) and approximately 90 ˚C. A 15% reduction in permeability was
observed which was attributed to adsorption of elemental sulfur onto the rock
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surface. Mahmoud [41] conducted a flow experiment by injecting liquid sulfur
at 150 ˚C into an outcrop limestone core saturated initially with fresh water. A
pressure drop across the core was greater than would be expected based only
on the difference in viscosity between fresh water and elemental sulfur, which
Mahmoud [4] attributed to the adsorption of sulfur onto the rock surface.
However, Mahmoud assumed that sulfur displaced all the water after 1 porevolume was injected. A second explanation for the higher than expected pressure drop is the presence of a residual water phase.
The above noted studies all investigated the impact of deposited sulfur in
the solid phase. The impact of liquid sulfur deposition was investigated by
Coskuner [42] by conducting a unique set of experiments using glass micromodels. The studies attempted to qualitatively explain the field results for the
Bearberry Demonstration Project previously noted. Flow of reservoir fluid containing 90% H2S, liquid sulfur, and water was visualized under reservoir conditions of 31 MPa and 120 ˚C. It was observed that the gas wets the sulfur/
water interface and flows relatively easily through the pore network. It was
concluded the deposition of liquid sulfur in the formation would not significantly impair the flow of gas as observed in field for the Bearberry project.
In summary, the experimental studies, even for the deposition of solid sulfur
have shown only modest decreases in formation permeability which would
unlikely lead to serious production problems. However, the coreflow tests are
unable to replicate the transport of elemental sulfur from the bulk of the reservoir to the near-wellbore region where deposition occurs.
6
Formation Damage Modeling
A number of numerical models which incorporate phase behavior and fluid
flow elements have been derived to assess the impact of sulfur deposition on
reservoir inflow performance. These models range from relatively simple analytical equations to more complex expressions incorporating velocity effects
and flow through natural fractures.
6.1
Initial Models
The first attempt to model the impact of sulfur deposition on fluid flow was
reported by Kuo and Closmann [43], with a follow-up paper by Kuo [44]. Continuity equations based on the isothermal, one-dimensional form of Darcy’s
law for the fluid phase and sulfur components were derived and solved
numerically. The deposited sulfur phase was assumed to be immobile. The
fluid density and viscosity and sulfur solubility were considered to be functions of pressure. An expression based on the data reported by Archie [45] was
derived for fluid permeability as a function of porosity, which is reduced due
to the deposition of sulfur. The example reservoir chosen for study represented
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an extreme case for sulfur deposition – reservoir pressure set at approximately
100 MPa and reservoir temperature at 200 ˚C. Solubility data of Roof [7] for
pure H2S was extrapolated to these reservoir conditions. The reservoir fluid
was determined to be undersaturated, with a saturation pressure of 38 MPa.
Modeling results demonstrated that sulfur deposition may completely plug the
formation near the wellbore. Flow rate reduction, decreased well spacing, or
an increase in effective wellbore radius were determined to reduce the impact
of sulfur deposition.
6.2 Analytical Approaches
An alternate approach was taken by Roberts [2] by deriving an analytical equation to describe the rate of sulfur buildup in the formation. Instead of applying
the transient flow equations of Kuo [44], one-dimensional, semi-steady state
radial flow was assumed. The rate of sulfur-saturation buildup, dSs =dt; was
derived as shown in eq. (7):
q2
� �
dc
dp Bu
dSs
¼ 2
4p ka kr h2 fð1 � Swi Þr2
dt
(7)
An approximate expression for the sulfur saturation (as a fraction of the
hydrocarbon pore volume) as a function of time may be derived by integrating
eq. (7) assuming constant values for B, m, and dc/dp and an expression for kr.
The relationship for relative permeability, kr, was taken from the study by Kuo
[44]:
lnkr ¼ ASs
(8)
Equation (7) may be integrated to yield:
2
Ss ¼
A q2 Bm
� �
dc
dp
t
3
ln 44p2 ka h2 fð1�Swi Þr2 þ 15
A
(9)
Based on equation (7) and (8), Roberts [2] identified four key factors which
govern the rate of buildup of deposited sulfur and the magnitude of flow
impairment:
1. Transport of elemental sulfur to the region in which sulfur is deposited
is required. Dropout of sulfur in the bulk of the reservoir due to
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pressure depletion would have little impact on formation porosity or
gas permeability.
2. Pressure drop near the well results in reduced solubility of sulfur of the
sulfur-saturated sour gas. The greater the pressure gradient, due to high
flow rates or low permeability, the greater the deposition rate.
3. The volume of pore space in which sulfur deposits influences the rate of
sulfur buildup. The buildup rate will be less in formations of high
porosity and pay thickness or in cases in which deposition is spread out
within a large volume, such as flow to a horizontal well or to hydraulic
fractures.
4. Flow impairment is controlled by the relative permeability of the gas
phase in the presence of the deposited phase.
Follow-up studies have subsequently used the analytical model derived by
Roberts to further quantify the impact of sulfur deposition. Mei et al. [46] used
eq. (7) to determine gas deliverability in terms of the AOF potential. Impairment of gas flow due to sulfur deposition as reflected in the AOF was shown
to be more severe during the early time of production. Mahmoud and
Al-Majeb [47] used eq. (9) and the relative permeability expression given by
eq. (8) to investigate the deposition process and reached similar conclusions as
outlined in the Roberts [2] study. Adesina et al. [48] incorporated a slightly different expression for the impact of deposition of elemental sulfur on gas flow
into eq. (7) which resulted in a higher rate of sulfur buildup near the wellbore
than predicted by Roberts [2].
The model of Roberts [2] has been extended to include the additional pressure drop due to non-Darcy flow by Hu et al. [49–51]. Guo et al. [52] included
both the impact of non-Darcy flow and compaction in their model and allowed
for variation of gas properties and dc/dp with pressure. They compared the rate
of sulfur buildup with the Roberts [2] model to show that including these elements into the model resulted in a significantly higher rate of sulfur buildup.
Hu et al. [53] investigated the impact of sulfur deposition on horizontal well
productivity by incorporation of the expression for gas relative permeability
given by eq. (8) into common equations for horizontal well productivity. It
should be noted that although these equations illustrate that sulfur buildup
near horizontal wells will reduce productivity, the time to reach a given sulfur
saturation may be orders of magnitude greater than for vertical wells, given
the lower pressure gradient near the well and the larger pore volume over the
length of the horizontal wells.
Mahmoud [41] derived an expression for near-wellbore sulfur saturation
that accounts for adsorption of sulfur onto the carbonate formation surface. At
the temperature conditions of this study (150 ˚C), elemental sulfur exists as a
liquid phase. An expression for the added increase in sulfur saturation due to
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adsorption was added to the Roberts [2] derived expression given by eq. (9).
However, eq. (9) is specifically derived for the deposition of solid sulfur and
assumes no mobility of the phase. Predictions by the Mahmoud [41] expression
results in complete plugging of the formation (Ss equal to one). However, this
result for the deposition of sulfur in the liquid phase would not be expected,
as the liquid sulfur saturation would begin to flow once the critical saturation
has been obtained. Field evidence given by the Bearberry project shows relatively little impairment by liquid sulfur deposition.
6.3 Incorporation of Non-Equilibrium Effects
The main limitation of the Roberts [2] model and other variations cited above
is that the location of sulfur precipitation and deposition are assumed to be the
same. However, it is likely that precipitated sulfur particles would be carried
with the gas stream for a distance before deposition. Civan [54] developed an
analytical model applicable to any precipitate to account for the delay in the
deposition which resulted in less deposit relative to the equilibrium case. A
numerical model to account for non-equilibrium effects specifically for sulfur
deposition was derived by Du et al. [55]. An expression for the velocity of carried sulfur was introduced into the partial differential equation describing the
flow of components through the formation. An equation was derived for the
critical velocity of the gas stream, below which any suspended particles would
deposit in the formation. However, the equation is a function of highly uncertain parameters, such as particle mass, pore diameter, and friction coefficients.
Du et al. [55] did not explain how these values may be determined, or provide
the values used in their example analysis. The model predictions were compared with the results of Roberts [2] for the simulation of the impact of sulfur
deposition on the performance of a sour gas well. Incorporating the effect of
carried sulfur in the gas stream was shown to slightly increase the productive
life of the well. The model of Du et al. [55] predicted complete plugging after
320 days, whereas Roberts [2] predicted a productive life of 270 days.
6.4 Modeling Deposition in Naturally Fractured Reservoirs
The deposition of elemental sulfur in naturally fractured reservoirs will be significantly different than for reservoirs in which fluid flow is mainly through
the rock matrix. Often gas productivity is governed by number and conductivity of open natural fractures that intersect the wellbore. A model for deposition
of solid elemental sulfur in natural fractures was first described by Hands et al.
[3] to aid in the design of sulfur solvent treatments for Shell Canada’s wells in
their dry sour gas fields. An equation for the pressure profile within a natural
fracture was derived as a function of gas flow rate and fracture properties. The
temperature profile was incorporated into the model to account for JouleDOI:10.7569/JNGE.2017.692504
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Thomson cooling which would impact sulfur solubility. The model requires
specification of a critical velocity, below which precipitated sulfur is allowed to
deposit. To be useful as a tool to manage sulfur solvent treatments, a calibration process was implemented, in which reservoir and performance data for
one representative well within a field was used to estimate fracture properties
and critical velocity. The calibrated model was subsequently used to determine
the schedule for solvent treatments, and to estimate productive life and ultimate recovery for each well of interest.
The field calibrated modeling results of Hands et al. [3] identified three specific zones of sulfur deposition within the natural fracture: (1) a zone nearest
the well in which sulfur deposition has been reduced due to dynamic effects
(gas velocity exceeds the critical value), (2) a zone of deposition which can be
removed by solvent treatments, and (3) a zone of permanent plugging which
cannot be reached by conventional solvent injection. The model indicated that
this deep deposition may occur 15 to 30 m into the formation, a distance much
greater than would be expected for deposition in a non-fractured reservoir.
Reducing the gas flow rate was shown to bring the deposition closer to the
wellbore, thus making solvent treatment more effective. The model and field
evidence also confirmed that high flow rates are to be avoided to prevent
“uncontrollable” deposition – for a given set of reservoir and wellbore properties, an optimum production rate may be calculated which maximizes the economic value of the well.
More recently, models for sulfur deposition in natural fractures have been
reported by Hu et al. [56] and He and Guo [57]. However, unlike the model of
Hands et al. [3] these models do not take into account transport of sulfur particles within the gas phase, nor incorporation of a temperature profile along
the fracture.
6.5
Use of Conventional Reservoir Simulators
The above-described numerical models for predicting the impact of sulfur deposition on inflow performance into gas wells have all used homogeneous properties. For example, the models have assumed one value for formation
porosity, pay thickness, permeability, etc. To model deposition within an actual
reservoir requires a more detailed and realistic reservoir description. Such
modeling will generally require the use of conventional reservoir simulators.
Roberts [2] used a black-oil simulator in which the deposited sulfur is represented by the “oil” phase. The phase behavior is specified in terms of a condensate (sulfur)/gas ratio. For the deposition of solid sulfur, the relative
permeability of the “oil” is set to 0 for all saturations. Although not reported in
the paper, flow of liquid sulfur may be also modeled, by using properties for
liquid sulfur for the “oil” phase, and specifying a relative permeability curve
for sulfur. Mahmoud et al. [41] stated that this application of a reservoir
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simulator would not give an accurate prediction of the sulfur damage in gas
reservoirs as hydrocarbon condensate properties were being used. However, in
the Roberts [2] study, hydrocarbon condensate properties were not used, but
instead well-established literature values for liquid sulfur.
It should be noted that conventional simulation models may not be able to
model non-equilibrium deposition. Results from such simulation models
should be considered a “worst-case” since sulfur that is carried in the gas
phase may not deposit in the reservoir but be carried through to the well.
Neglecting non-equilibrium effects may be offset by adjustment of reservoir
parameters by calibration with field or analogue performance data.
The key benefit of a reservoir simulation model over the analytical models
is that the effect of formation heterogeneities near the wellbore may be investigated. A two-layer system consisting of a 22 m thick, 0.2 mD layer in communication with a 8 m 2.0 mD layer was modeled. Sulfur plugging was found to
occur rapidly in the small-volume, high permeability streak because most of
the flow is through this layer. This layer is subsequently plugged off, and flow
to the well must take place through the low permeability layer resulting in a
rapid reduction in gas flow rate. Further simulations of a highly layered system demonstrated that formation impairment by deposited sulfur becomes
more severe as the degree of heterogeneity increases. Field performance of the
Waterton gas well noted earlier in this paper was simulated. A match between
simulated and actual performance and the following pressure buildup was
obtained by adjusting the effective wellbore radius of a layered system, to
reflect differing degrees of stimulation for each of the model layers.
7
Reservoir Engineering Applications - Development of Sour Gas
Reservoirs
Development of a newly discovered sour gas reservoir will generally require
an assessment of well productivity and ultimate recovery, determination of
well type (vertical, horizontal, slant) and spacing, and specific requirements for
well stimulation such as hydraulic fracturing. A production forecast will be
needed for the design of surface processing facilities and gas marketing. The
potential for sulfur deposition in the formation will increase the level of uncertainty for many of these key reservoir performance parameters, and increase
the risk of uneconomic performance. Based on the investigations reviewed in
this study, the following factors will increase development risk:
1. high H2S content
2. high reservoir pressure
3. at or near saturated solubility conditions
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4. dry gas composition (absence of hydrocarbon condensate in the
formation)
5. low permeability, porosity, and pay thickness
6. high level of reservoir heterogeneity (layering at the well)
7. reservoir temperature below sulfur melting point.
Given the above risk assessment, additional data gathering will be required
over and above what is typically needed for gas reservoir development. The
additional data should include:
1. Bottomhole sampling and analysis to determine sulfur content at
reservoir conditions.
2. Determination of sulfur solubility as a function of pressure at reservoir
temperature.
3. If reservoir temperature is between approximately 100 and 120 ˚C,
measurement of sulfur melting point at reservoir pressure. The data of
Woll [18] may be used as a guide to determine if measurements are
required.
Given the above risk assessment and reservoir data, low-mid-high production forecasts for individual wells may be generated using simple single well
simulation models. A range of forecasts may be obtained by varying the most
uncertain parameter (e.g. level of sulfur saturation, or gas relative permeability). Production forecasts which include the impact with sulfur deposition
should be compared with any available analogue data. A range of forecasts for
the reservoir may be determined by considering a set of scenarios. For example, the scenarios may consider varying the number of wells which experience
extensive plugging and low ultimate recovery. Given both field observations
and the results of the modeling studies, scenarios should include constraining
the well rate to prolong well life and ultimate recovery.
The development plan should also include additional surveillance requirements. These may include the installation of permanent downhole gauges and
the scheduling of pressure buildup tests to monitor any changes in the well
skin. The single well simulation models may also be updated based on production and pressure data as a tool to guide future operation of the wells, scheduling of any solvent treatments, or the need for hydraulic fracturing.
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8
Conclusions
1. Sulphur deposition has been established as a near-wellbore process that
may lead to significant loss in well productivity, production life and
ultimate recovery.
2. Key reservoir properties that govern the deposition process are:
(a) Rate of sulfur precipitation per unit pressure drop
(b) Absolute permeability and gas relative permeability (control near-well
pressure gradient)
(c) Formation porosity and pay thickness (sets the total pore volume
available for deposition)
3. Field experience combined with laboratory investigations indicate that
the impact of the deposition of liquid elemental sulfur in the formation
may not be important for high permeability formations. The impact of
liquid deposition in tighter formations has yet to be established.
4. The following operational considerations have been identified from field
experience and modeling results:
(a) Constraining the production rate may lengthen the well life and yield
a higher ultimate recovery.
(b) Monitoring flow and downhole pressure data, combined with
periodic pressure transient testing should be implementeted into the
surveillance plan, as rapid plugging of the formation may occur once
deposition has initiated.
(c) Sulfur deposition will become less a factor later in the life of the
reservoir as the reservoir pressure declines due to gas depletion.
Acknowledgement
Discussions with John Carroll on aspects of sour gas development were very
helpful and appreciated. Thanks also to Erin Roberts for her help with the literature search.
Nomenclature
a
A
B
B
cr
fss
fsl
fsv
h
empirical constant in eq. (5)
empirical constant in eq. (8)
gas formation volume factor
empirical constant in eq. (5)
concentration of sulfur in gas phase at reservoir conditions, g/m3
fugacity of sulfur in the solid phase, Pa
fugacity of sulfur in the liquid phase, Pa
fugacity of sulfur in the vapor phase, Pa
pay thickness, m
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k empirical constant in eq. (5)
ka absolute permeability, m2
kr relative permeability
n stoichiometric coefficients in eq. (4)
P pressure, Pa
Pss vapor pressure of sulfur, Pa
q gas flow rate, m3/s
R gas constant, J K–1 mol–1
Ss sulfur saturation as a fraction of the hydrocarbon pore volume.
Swi initial water saturation
r radial distance from well, m
t time, s
T temperature, K
v specific molar volume of sulfur, m3/mol
f porosity
m gas viscosity, Pa.s
� gas density, kg/m3
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