Traditionally, the H2S partial pressure (PH2S) of the gas/hydrocarbon phase has been used as the primary sour severity metric for material qualification and selection under ANSI/AMPP (NACE) MR0175/ISO 15156 guidelines. While the PH2S is appropriate for characterizing low total pressure systems, the strict, or ideal, Henry’s Law approach leads to over estimation of the dissolved H2S concentration (CH2S) for high-pressure, high-temperature (HPHT) wells by up to approximately 20 times at 70°F (21°C). Alternatively, the Ensemble Henry’s Law equation corrects for the non-ideal phase behavior of H2S at HPHT conditions and avoids over-estimation of CH2S. Given the industry’s reliance on using thermodynamic models to evaluate sour HPHT systems, an investigation was initiated to determine the accuracy of these model calculations. An empirical program was undertaken to verify CH2S predictions for the H2S-N2-H2O system. Multiple 2.7 L C-276 lined autoclaves were charged with a fixed inventory of H2S in N2 at multiple total pressure steps, with increasing N2 pressure, between 30 psig and 20,000 psig (3 bar and 1,380 bar) at 70±5°F (21±3°C). Per total pressure step, H2S levels in both the headspace gas and liquid phases were measured using common H2S sampling techniques (H2S-specific colorimetric tubes and iodometric titration, respectively), following ANSI/NACE TM0177-2016 guidelines. The results were used to calculate total pressure corrected (apparent) H2S solubility coefficients (AkH2S). Very good agreement was observed between empirically and computationally derived AkH2S values.

A major challenge facing users when designing mildly sour high-pressure, high-temperature (HPHT) wells is selecting materials that have both the required mechanical strength and resistance to potential environmentally assisted cracking (EAC) threats, particularly sulfide stress cracking (SSC). Key to optimizing material selection for sour service conditions is to accurately characterize the environmental severity of HPHT wellbores based on the compositional analyses of the brine and hydrocarbon gas streams.

During the 1950s and 1960s, initial investigation of carbon and low alloy steels exposed to H2S revealed that susceptibility to SSC was influenced by the dissolved H2S concentration in the aqueous phase (CH2S) for certain steels hardened to >22 HRC at atmospheric pressure.1-2  However, the ability to measure and/or predict CH2S at full wellbore pressure was in its infancy in 1975. There were also practical issues related to field sampling techniques when attempting to capture representative water samples in the field and reliably measuring the CH2S. Therefore, an alternative sour severity metric to CH2S was sought. Both low-pressure SSC test results1-5  and field observations6-8  revealed an apparent trend of increasing SSC susceptibility with increasing H2S partial pressure (PH2S). This motivated the architects of the original NACE MR01759  standard in 1975 to define environmental severity based on PH2S, which can be easily assessed from limited environmental field data.

While PH2S is an appropriate surrogate for CH2S for low total pressure systems, recently PH2S has been demonstrated to over predict the corresponding CH2S by at least an order of magnitude at 10,000 psia (690 bar) and 70°F (21°C).10-11  (For a thorough description of the practical limitations to using PH2S, and arguments in favor of using fH2S and CH2S as alternative modern sour severity metrics, for high-pressure oilfield applications refer to Sherar, et al.,11  and the references cited therein.) Despite its many shortcomings, PH2S remains the primary sour severity metric in ANSI/NACE MR0175/ISO 15156-201512  (herein, referred to as the Standard12 ). However, recognizing the complications with using PH2S, the recent publication of ISO 15156-1:2020 now permits users the option to define sour severity by alternative metrics: fugacity (fH2S),13-15  activity (aH2S),16  and concentration (CH2S).11,17-19  These modern sour severity metrics may expand the application ranges of commercial materials in sour systems while maintaining reasonable, but not excessive, margins of safety.

Unlike PH2S, however, the modern sour severity metrics are usually calculated from advanced thermodynamic models, formally referred to as ionic-equation of state (EOS) frameworks. These frameworks are often semi-empirical in nature and are calibrated against experimentally derived thermochemical databases.20-22  While sour ionic-EOS frameworks are gaining acceptance,11,14-15,23  there are two potential concerns: First, there are only a handful experimental H2S solubility databases available, with the majority of measurements made at total pressures <5,000 psi (<345 bar) and at PH2S >> 10 psia.21,24-31  Therefore, using these databases to predict mildly sour phase behavior at 10,000 psig to 20,000 psig requires extrapolation by several orders of magnitude. Second, there are few empirical studies available to independently verify the accuracy of sour predictions at total pressures >5,000 psig.10,21,27 

In an attempt to evaluate the reliability of ionic-EOS frameworks for predicting sour severity of high-pressure systems, this paper discusses an empirical approach to quantify the relationship between CH2S and PH2S with total pressure. For this project, the authors evaluated the H2S-H2O-N2 “laboratory” system (a common surrogate of the typical H2S-H2O-CH4 “oilfield” system) from 30 psig to 20,000 psig at 70±5°F. All H2S solubility tests were performed at 70°F (21°C), because the Standard12  recommends qualifying materials for sour service at room temperature, where a material’s susceptibility to SSC is expected to be highest. A 2.7-L C-276 (UNS N10276(1)) lined autoclave rated for sour service up to 20,000 psig, with a fixed charge of H2S, was then pressurized with nitrogen at incremental total pressure steps from 30 psig to 20,000 psig. Multiple determinations of the gas and liquid phase H2S concentrations were made at each total pressure step using techniques optimized by the authors. The measured CH2S/PH2S set per total pressure step was then used to calculate a total-pressure corrected (apparent) solubility coefficient (AkH2S), an empirically derived parameter that could be used to benchmark ionic-EOS frameworks.

As far as the authors are aware, this paper is the first publication of H2S solubility data up to 20,000 psig (1,380 bar ≡ 138 MPa). In addition to verification of ionic-EOS frameworks for high-pressure mildly sour oilfield systems, this paper also demonstrates the precision and accuracy of the H2S sampling and analysis techniques adopted from the ANSI/NACE TM0177-201632  and ANSI/NACE TM0284-201633  standards for this project.

In 1975, the architects of the original NACE MR0175 standard9  recognized that SSC was the result of the combination of: (1) a susceptible metallurgy, (2) the applied stress (tensile load), and (3) the CH2S in an acidic aqueous solution.1,8,34-35  At the time, however, both the complex thermodynamic models required to calculate CH2S under actual high-pressure wellbore conditions and personal computers powerful enough to run the complex mathematical algorithms were decades into the future. Therefore, the architects simplified the dissolved H2S problem by assuming that ideal gas law behavior applied. It was further assumed that CH2S was linearly proportional to the PH2S with total pressure (see Figure 1[a]).9,36  In addition, H2S solubility (IkH2S, the ratio of CH2S/PH2S) was assumed to be independent of the total pressure (see Figure 1[b]), temperature and of interactions with other molecules in the gas phase. Collectively, these concepts formalized the “PH2S Paradigm,” a term coined by the authors.

FIGURE 1.

(a) and (b) Historical H2S solubility assumptions based on the PH2S Paradigm.

FIGURE 1.

(a) and (b) Historical H2S solubility assumptions based on the PH2S Paradigm.

Historical PH2S Paradigm—Strict Henry’s Law Approach

The PH2S is defined as the mole fraction of H2S in the gas phase (yH2S) multiplied by the total pressure (PT):
formula
The use of PH2S as the sour severity metric assumes that PH2S is proportional to CH2S via the Strict (Ideal) Henry’s Law constant (IkH2S):
formula
where IkH2S = 230 mg/L/psia (0.1 mol/L/atm) for freshwater at 75°F (24°C) and 14.7 psia (101.3 kPa).11,37-40  Historically when qualifying carbon and low alloy steels for sour service at room temperature, stressed specimens were typically immersed in solutions containing up to 5 wt% NaCl and purged with either pure H2S at 1 atm or H2S in mixed gases to obtain PH2S less than 1 atm.34-35  At the time, the effects of ionic strength were not considered in the analysis of the resulting data. Under the above test conditions, an apparent H2S solubility coefficient of ∼200 mg/L/psia is obtained. Based on the atmospheric laboratory results, it was assumed that ideal gas behavior governed over the entire total pressure range for oil and gas systems, implying that the CH2S-PH2S relationship increases linearly with increasing PH2S with a constant slope of IkH2S (Figure 1[a]). Thus, IkH2S is independent of increasing PT (Figure 1[b]). These assumptions were considered reasonable in 1975, because PH2S is a relatively accurate approximation for CH2S at room temperature and low total pressures for dilute solutions.

The primary objective of researchers in the 1950s to 1970s was not to replicate the “real” sour phase behavior of an actual wellbore during sour qualification tests of candidate materials,41  but rather to select relatively severe laboratory environments for evaluating metallurgical factors.34-35,42-43  In addition, the operating pressures of the original SSC well failures were <5,000 psig (345 bar)8  and the vast majority of in-service failures were associated with wells producing >3.5 mol% (>35,000 mol ppm) H2S.44  Without going into detail, compensating for the effect of total pressure on H2S solubility for systems clearly identified as sour would have only had a marginal benefit in terms of optimizing material selection, at the time.

Forty-five years later, however, the increased reliance on high-strength materials, which typically have an enhanced sensitivity to H2S compared to their lower yield strength analogs, and increased accessibility of commercial ionic-EOS frameworks have facilitated a paradigm shift from defining sour severity on the basis of PH2S to that of either fH2S,13-15  aH2S,16  and/or CH2S11,17-19  metrics that better reflect actual sour severity of HPHT systems.

Modern Sour Severity Metrics—Ensemble Henry’s Law Approach

Regardless of the preferred sour severity metric, core to all of the modern metrics is the “Ensemble Henry’s Law equation.”45-47  The Ensemble Henry’s Law is an extension of the Strict Henry’s Law Equation (2), and incorporates three important thermodynamic correction factors to account for the change in H2S solubility with total pressure.38,48  To emphasize the aqueous (left-hand side of equation) and hydrocarbon (right-hand side of equation) based thermodynamic parameters, the equation may be written as:
formula
where γH2S is the activity coefficient (ionic strength correction), φH2S represents the fugacity coefficient (gas phase correction), and exp[ξ] refers to the Poynting (total pressure correction) factor on gas solubility in the aqueous phase.14-15,23  (A glossary of thermodynamic parameters is included at the end of this paper in the Nomenclature section.) For a thorough discussion on the derivation and parameterization of Equation (3), please refer to Sherar, et al.,11  and the references cited therein.

Figure 2 (reproduced from Nelson and Reddy10 ) compares the predicted values for CH2S obtained using the Ensemble Henry’s Law Equation (solid blue curve) and the ideal gas law predictions of the PH2S Paradigm (black line) with experimental data (red squares) up to 10,000 psia. The following observations can be made:

  • The agreement between the experimental data and CH2S predicted by the Ensemble Henry’s Law Equation are excellent,

  • Whereas, the experimental value of CH2S at PT = 10,000 psig was ∼10% of the value predicted by the ideal gas law.

  • These observations were later confirmed by Kumar, et al., in 201327  at CH2S values relevant for mildly sour wells.

FIGURE 2.

Goodness-of-fit comparison of the PH2S and CH2S paradigms to experimental data.10 

FIGURE 2.

Goodness-of-fit comparison of the PH2S and CH2S paradigms to experimental data.10 

Figure 2 also exhibits a flatline or “saturation plateau” in the CH2S, between 1,800 psia and 10,000 psia for the methane-rich system, which has been observed by others.20,23,25-26,49  Literature suggests that the observed dissolved H2S “plateau” is the result of two competing factors: (1) the increasing fH2S with increasing pressure and (2) the effect of increasing total pressure on the liquid as expressed in the Ensemble Henry’s Law (i.e., the Poynting effect, increasing the activity coefficient of H2S in the water phase). Within this “saturation plateau” region, the CH2S is nearly independent of PT,14  strongly suggesting that CH2S is a stable parameter that could be used as a reliable, scalable sour severity metric from atmospheric pressure to at least 10,000 psia.10 

The Ensemble Henry’s Law is often coded into ionic-EOS frameworks, which are usually validated against published H2S solubility data. Unlike the CO2-H2O-salt system,22  there are only a handful of H2S-H2O-salt system databases available,21,24-31  and the majority of the public datasets contain experimental data only up to 5,000 psig.20  For a review of the representative data sources reporting H2S solubility in water reaching above ambient conditions, please refer to Akinkiev, et al.20  (Excluding this paper, at the time of publication, the authors are not aware of any published experimental solubility H2S-N2-H2O-salt data performed above 10,000 psia.)(2)

Consequently, the reference H2S data have been obtained at much higher PH2S and much lower PT than the HPHT domain of interest,4,17-19,23  as shown in Figure 3. As a result, there are significant extrapolations from current reference data when modeling mildly sour HPHT conditions, potentially resulting in calculation errors. Independent validation of calculated H2S solubility data under mildly sour conditions to 20,000 psig is therefore needed to extend confidence in the predictions of the current ionic-EOS frameworks to the HPHT domain.

FIGURE 3.

Schematic comparison between the available H2S-H2O-salt public database domain versus the HPHT sour service domain of interest.11  Arrows indicate the direction and magnitude of extrapolation.

FIGURE 3.

Schematic comparison between the available H2S-H2O-salt public database domain versus the HPHT sour service domain of interest.11  Arrows indicate the direction and magnitude of extrapolation.

An effective method to evaluate the accuracy of sour predictions involves comparing the computationally and empirically derived H2S solubility coefficients (kH2S). Empirically, H2S solubility can be derived by grouping the thermodynamic parameters together from Equation (3) into Equation (4):
formula
This is simplified to Equation (5):
formula
where AkH2S represents the Real (apparent) H2S Henry’s Law Solubility Coefficient. AkH2S has the units of mg/L/psia,(3) when PH2S is in psia, and CH2S has the dimension of mg/L.38,48,51  The AkH2S is temperature, total pressure, hydrocarbon composition, and ionic strength dependent due to non-ideal solubility effects.52  At normal pressure and temperature (NPT), IkH2S equals AkH2S. As temperature and/or total pressure increase, AkH2S decreases.

The following sections of this article describe an internal study to experimentially benchmark calculated AkH2S values in 10,000 mg/L Cl from 30 psig to 20,000 psig at 70±5°F.

The objectives of this empirical H2S solubility study were:

  1. To investigate the effect of total pressure on H2S solubility in the H2S-H2O-N2 system at total pressures between 30 psig and 20,000 psig (2 bar and 1,380 bar) at 70±5°F (21±3°C).

  2. To verify the analytical reproducibility when measuring the concentration of H2S of both the liquid (CH2S) and headspace gas (yH2S) phases by iodometric titration and H2S-specifc colorimetric tubes, respectively, in accordance ANSI/NACE TM0177-2016 procedures32  modified to positively exclude air, thus preventing loss of H2S.

  3. To empirically derive AkH2S (i.e., the ratio of measured CH2S/[yH2S × PT] values) between 30 psig and 20,000 psig at 70±5°F.

  4. Compare the experimental results to the predictions of a commercial sour ionic-EOS framework22-23  widely used in the sour service industry.

Table 1 shows the environmental test parameters evaluated during this project. Because the purpose of this project was focused on quantifying AkH2S up to 20,000 psig (1,380 bar), and not evaluating a material’s susceptibility to a specific sour environment, typical ANSI/NACE TM0177-201632  test specimens were not included in the test design. For this study, ultrahigh purity (UHP) N2 was used as a surrogate for methane to boost the internal pressure. UHP N2 is the preferred booster gas in the laboratory, because, unlike methane, it is nonflammable and does not form clathrates/hydrates at low temperatures and high total pressures, which could interfere with H2S sampling methods.

Table 1.

H2S-N2-H2O System Investigated

H2S-N2-H2O System Investigated
H2S-N2-H2O System Investigated

Test Procedure Overview

As a brief introduction, this project required the use of a very high pressure (VHP) 2.7 L C-276 internally lined autoclave rated to 20,000 psig. Acid gas charging was simulated using a commercially-available ionic-EOS framework22-23  prior to physical testing. CH2S/PH2S sets were sampled directly from the autoclave at multiple total pressure steps. To ensure adequate liquid and gas headspace, the sample volumes were maintained at each sampling pressure and the autoclave was half-filled (1.3 L) with test solution.

A fixed inventory of 0.02 mol H2S was added to the deaerated and evacuated autoclave as a certified mixed gas (10% H2S, balance N2) at the beginning of each run. The autoclave was pressurized to the first target using UHP nitrogen, and pneumatically actuated autoclave shakers were used to speed equilibration of the gas and aqueous phases. A minimum 24 h equilibration was maintained between sampling periods to ensure the autoclave reached thermodynamic equilibrium. A 24 h hold was considered sufficient time to reach equilibrium, based on previous in-house experience. However a formal kinetic study was not pursued at the time of testing.

For this project, a maximum of 2 total pressure steps per autoclave run were conducted and 13 individual total pressure steps were performed in total. For safety reasons, the autoclave was placed within an individual booth that had an exhaust line connected directly to an industrial H2S scrubber. The booth provided physical separation between the technician and the autoclave containing H2S.

The following sections describe the experimental procedure that the authors developed in detail.

Autoclave Gas Inventory Modeling

In accordance with the current best practice for charging autoclaves with acid gases, the equilibrium autoclave conditions at the target total pressure were simulated using a commercial ionic-EOS framework22-23  (specifically OLI MSE-SRK v. 9.6.2 with a second liquid phase toggled) before physical testing. To predict the charging requirements per autoclave, the following parameters were fixed: the molar quantities of water, NaCl, and acetic acid were combined to yield a total aqueous volume of 1.3 L (representing half the internal volume of the autoclave), a fixed inventory of 0.02 mol (0.68 g) H2S, temperature, and the internal autoclave volume. The total pressure and N2 input were iteratively adjusted to maintain a constant internal autoclave volume of 2.7 L. The output calculated parameters were CH2S, yH2S, PH2S, and AkH2S (CH2S/PH2S) per total pressure step.

Physical Acid Gas Autoclave Loading at 70°F with Fixed H2S Inventory

Figure 4 shows a schematic of the procedure used to load acid gases into a VHP autoclave. This procedure was followed for each autoclave run. The autoclave was sealed and leak-tested with UHP-N2 up to 20,000 psig prior to solubility testing. After a successful leak test, the autoclave was triple flushed with UHP-N2 by pressurizing to ∼50 psig with nitrogen, then a vacuum was pulled using a mechanical vacuum pump. After successfully deaerating the autoclave, the following activities were performed:

  1. The deaerated test solution (prepared with analytical reagent chemicals) was then transferred into the autoclave under a nitrogen blanket and purged in situ with UHP nitrogen for at least 1 h as a safeguard against any chance of oxygen contamination.

  2. The required H2S charge was later quantitatively transferred into the autoclave as certified mixed gas containing 10 mol% H2S in nitrogen. In this case, a total of 0.02 mol (0.68 g) H2S was loaded into a 300 mL gas transfer cylinder (GTC) per each autoclave run. 0.02 mol H2S was inferred by raising the internal pressure of the GTC to 225±1 psig. The internal pressure was monitored via a 600 psig rated pressure transducer.

  3. After charging the GTC with 0.02 mol H2S, the GTC was directly connected to valve V4 off the dip tube line of the autoclave, to ensure that the H2S gas bubbled through the liquid solution. To ensure the entire H2S charge was displaced into the autoclave, a UHP-N2 bottle was directly tethered to the GTC containing H2S. Next, a vacuum was pulled on all piping and valves to remove air from the lines. After releasing the H2S from the GTC into the autoclave, up to a few hundred pounds of N2 pressure was pushed through the GTC to ensure full displacement. Afterward, the GTC was disconnected and replaced with a pneumatically operated pump that was connected directly to the autoclave. The pump was then used to boost the internal pressure to the desired target with UHP-N2.

FIGURE 4.

Acid gas autoclave loading at 70°F with a fixed H2S inventory. Refer to text for details.

FIGURE 4.

Acid gas autoclave loading at 70°F with a fixed H2S inventory. Refer to text for details.

After gas charging, pneumatic shakers were used to agitate the autoclaves to rapidly equilibrate the immiscible H2S/N2 headspace gas with the test solution. Following a 24 h or longer duration, H2S samples of the autoclave headspace and brine were taken per total pressure step. (Recall that two total pressure steps were evaluated per autoclave run involving a single H2S charge of 0.02 mol.)

Sampling Gas and Brine From Autoclave Without Losing H2S

As mentioned earlier, the advantage of using Equation (5) is that AkH2S can be empirically derived and used as an independent check to benchmark thermodynamic calculations. At each total pressure step, the following parameters were measured in the lab:

  1. PT (psia)—The internal gauge pressure of the autoclave, plus atmospheric pressure, was recorded at the time of sampling. Recall: PH2S = yH2S × PT. The total pressure was monitored using a pressure transducer rated to 20,000 psig.

  2. yH2S (mol ppm)—Headspace gas samples were analyzed using a variety of H2S-specific colorimetric tubes with different concentration ranges.

  3. CH2S (mg/L)—Indirectly measured using a modified version of the iodometric titration procedure described in ANSI/NACE TM0177-2016,32  Appendix C.

At each total pressure step, headspace gas samples were pulled first prior to sampling the brine phase. (For closed systems with a high water cut, removing a few hundred milliliters of test solution dramatically reduces the internal autoclave pressure.) Figure 5 demonstrates how the H2S solubility measurements were performed:

  1. The autoclave headspace H2S concentration (yH2S) was measured in triplicate using sulfur-specific gas chromatography analysis. A finite volume of the headspace gas was captured in a 0.5 L Tedlar bag off the vacuum line. The gas sampling bag was then immediately connected to a syringe containing an H2S-specific colorimetric tube. A known volume of gas was drawn through the colorimetric tube to detect H2S. The H2S-specific tubes are filled with lead acetate, which changes color from white to brown in the presence of H2S:
    formula
    According to the manufacturer, yH2S measurements are accurate within ±5%. As the total pressure varied by two orders of magnitude, a variety of colorimetric tubes with different yH2S ranges were used.
  2. For accurate quantification of CH2S, the test solution was collected directly off the dip-tube line of the autoclave and entered a graduated cylinder that contained a premeasured volume of 0.1 N iodine solution. Continuous UHP-N2 purging of iodine solution was performed while sampling the test liquid to minimize air contamination. The liquid was bled off slowly to minimize two-phase “slug” flow. By regulating the flow of the discharged brine, nearly all dissolved H2S reacted with the iodine solution prior to gas break out. The CH2S was later determined via iodometric titration method (to be discussed later). This process was performed in triplicate.

  3. The ratio of each measured CH2S/PH2S set represented the empirically derived AkH2S per total pressure step.

FIGURE 5.

Sampling brine for titration analysis directly from an autoclave while avoiding air contamination. This maintained in situ properties as practically possible.

FIGURE 5.

Sampling brine for titration analysis directly from an autoclave while avoiding air contamination. This maintained in situ properties as practically possible.

To quantify the CH2S recovered during triplicate brine sampling, both ANSI/NACE TM0177-201632  and ANSI/NACE TM0284-201633  standards recommend the iodometric titration method. Figure 6 pictorially shows the progressive colorimetric changes observed during iodometric titration, and the following paragraph describes the corresponding chemical reactions:

  • After collection of 50 mL test solution directly from the autoclave, the dissolved H2S reacts with 25 mL of acidified 0.1 N iodine. H2S reduces iodine (I2 + I ⇌ I3) to iodide:
    formula
  • The recovered samples, originally collected in a graduated cylinder, were individually transferred to an Erlenmeyer flask prior to titration. The amount of dissolved H2S collected was inferred indirectly by quantifying the excess iodine in solution. Any excess iodine was slowly titrated with 0.1 N sodium thiosulfate via a burette:
    formula
  • Near the end point: as the solution lightens in color, starch indicator was added turning the solution a deep purple color. The indicator forms a starch–I3 complex, which helps to identify the end point.

  • End point: the solution color changes from deep purple to colorless. The total volume of thiosulfate used during titration was read off the burette and recorded.

FIGURE 6.

(a) through (d) Endpoint for the determination of CH2S by iodometric titration. Refer to text for details.

FIGURE 6.

(a) through (d) Endpoint for the determination of CH2S by iodometric titration. Refer to text for details.

After titration, the following equation32-33  was used to calculate the CH2S of the test solution:
formula
where A is the normality of standard iodine solution (equivalents/L) times the volume used (L), B the normality of standard sodium thiosulfate solution (equivalents/L) times the volume used (L), and C represents the volume of test solution sampled (L). The conversion factor of 17,040 is derived from 34 g/mol H2S × 1,000 mg/g / 2 equivalents per mol H2S.

It is important to note that this procedure requires estimation of the CH2S in advance of physical sampling. For meaningful results, the total moles of iodine must be in excess of the moles of dissolved H2S collected. Last, in recognition that the iodometric titration procedure relies heavily on (subtle) colorimetric changes, to improve sampling reproducibility, the same technician performed all analyses throughout this project.

The results of the recent empirical H2S solubility study conducted at 70±5°F are shown in Figure 7 and are also reported in Table 2, where the term “C of V” refers to the coefficient of variation. Figure 7 is comprised of four subplots, where each subplot shows the chemical behavior of individual sour parameters between 30 psig and 20,000 psig: (a) yH2S, (b) PH2S, (c) CH2S, and (d) AkH2S. A common feature in all subplots are the blue and orange data dots which refer to experimental measurements and model22-23  predictions, respectively.

Table 2.

Summary of H2S Solubility Data Obtained from Autoclave Testing and Model22-23  Predictions at 70°F (21°C)

Summary of H2S Solubility Data Obtained from Autoclave Testing and Model22-23 Predictions at 70°F (21°C)
Summary of H2S Solubility Data Obtained from Autoclave Testing and Model22-23 Predictions at 70°F (21°C)
FIGURE 7.

Change in (a) yH2S, (b) PH2S, (c) CH2S, and (d) AkH2S vs. total pressure at 70°F with a fixed inventory of 0.02 mol H2S per total pressure step. Experimental data and model22-23  predictions colored in blue and orange data dots, respectively.

FIGURE 7.

Change in (a) yH2S, (b) PH2S, (c) CH2S, and (d) AkH2S vs. total pressure at 70°F with a fixed inventory of 0.02 mol H2S per total pressure step. Experimental data and model22-23  predictions colored in blue and orange data dots, respectively.

Figure 7(a) confirms that, for a fixed molar quantity of H2S in a closed system, as the total pressure increased yH2S decreased logarithmically. The high r2 value indicates that the colorimetric tubes provide sufficient precision to quantify the change in yH2S over a total pressure range spanning two orders of magnitude. Reproducibility of individual sample measurements was within the ±5% tolerance as specified by the manufacturer. In Figure 7(b), as expected, both experimental and computed PH2S (yH2S × PT) values increased linearly with total pressure. In summary, within the yH2S and PH2S ranges investigated, there was excellent agreement between empirical measurements and model predictions.

Unlike the similar trend observed for yH2S and PH2S, Figure 7(c) shows a significant divergence in measured versus calculated CH2S values. Whereas measured values indicate CH2S decreases linearly, thermodynamically derived values suggest that CH2S decreases logarithmically. (It is acknowledged that the concentration dataset is relatively small, and the effect of time/agitation was not fully explored and may have contributed to the discrepancy.) On the one hand, the discrepancy in CH2S behavior observed, particularly at both high and low total pressures, is likely a consequence of the ionic-EOS framework extrapolating the literature solubility data obtained from highly sour systems to predict a mildly sour (i.e., “undersaturated”) system. On the other hand, reaching thermodynamic equilibration may take much longer than 24 h hold adopted in this study. Anecdotal evidence by gas chromatography suggests that thermodynamic equilibration may actually take up to 5 d to 15 d near room temperature and total pressures up to 5,000 psig (345 bar), regardless of whether pneumatic shakers or mechanical sparging methods are used.53  As such it is important to recognize: (1) possibly the equilibration time is shorter for the higher total pressure systems and (2) that fixed inventory vs. continuous purging may be a factor that leads to underestimations. A thorough discussion on the kinetics of H2S partitioning, however, is beyond the scope of this paper, although the authors recognize its importance when executing high-pressure autoclave tests, and continue to investigate this issue internally. Nevertheless, in terms of using CH2S as a sour severity metric for material qualification purposes, model predictions appear to slightly overestimate the actual CH2S present, at least for the system investigated. This would imply that the thermodynamic calculations are moderately conservative.

While quantifying the differences between empirical and theoretical CH2S is an important activity, it is not the most significant finding. Remarkably, the modifications made to improve liquid sample collection directly off an autoclave and the enhancements to the iodometric titration procedure were successful. The coefficient of variation (C of V, i.e., the ratio of the standard deviation divided by the mean of a triplicate sample set represented as a percentage) varied between 1.6% and 7.3% within the total pressure range investigated, providing confidence in the measured concentration results. Therefore, in spite of the practical challenges to measuring CH2S nearly in situ, the authors have demonstrated a reliable methodology, which could be adopted by other institutions. Furthermore, the concentration results reinforce that CH2S could be used as a reliable sour severity metric if liquid sampling and analysis is performed correctly.

In contrast to the observations made by Nelson and Reddy,10  where CH2S reached a “saturation plateau” at PT > 1,800 psia (as shown in Figure 2), in this study CH2S continually decreased with increasing total pressure (Figure 7[c]). In the previous study, the authors10  investigated a system with a fixed yH2S = 15 mol% resulting in CH2S ranging from 15 g/L to 20 g/L within the “saturation plateau” region.10  In this study, the focus was to extend the previous research10  to the mildly sour system using a fixed charge of H2S of 0.02 mol per autoclave run. As a result, both yH2S and CH2S decreased with increasing mole fraction of nitrogen per total pressure step. Consequently, the partitioning of H2S, on a total molar basis, shifted from the aqueous phase to the nitrogen-rich phase. While the two studies are not directly comparable (because Nelson and Reddy10  used a constant yH2S source, whereas we investigated a system with constant total molar inventory of H2S per autoclave), the results of the two studies are not contradictory. The two papers, although using different test methodologies, arrive at the same conclusion: that H2S solubility logarithmically decreases with total pressure.

Overall, as total pressure rises from 30 psig to 20,000 psig there was a 7.5-fold and 11.5-fold decrease in empirically and computationally derived AKH2S, respectively. As the data clearly demonstrates in Figure 7(d), AkH2S is not constant as assumed in the PH2S Paradigm, but rather it decreases logarithmically with total pressure. Clearly, the denominator (PH2S) is the dominant vector driving AkH2S down with total pressure. The agreement in PH2S masks the relatively minor differences in empirically versus computationally derived CH2S. This result is consistent with the original observations by Nelson and Reddy10  and provide verification of the thermodynamic calculations described previously.11,17 

The implication of our research is, for systems containing at least 175 mg/L H2S, thermodynamic predictions are generally consistent with physical reality. Therefore, ionic-EOS frameworks can be used to help users assess the mildly sour severity of high-pressure low-temperature (HPLT) environments. Such an analysis, in turn, could help optimize the design of laboratory SSC tests if the goal is to expand material selection options by adjusting the CH2S in the test solution to the same concentration predicted for a high-pressure well.10-11,17-18  However, users should remain cautious when applying thermodynamic predictions (be it fH2S, aH2S, and/or CH2S) without independent verification, particularly for systems involving <100 mg/L H2S. Recent in-house investigations reveal that the PH2S-CH2S relationship at very low concentrations is nonlinear at constant temperature and total pressure. While not a concern for medium and severely sour systems, small changes in H2S solubility may lead to undershooting of target parameters, leading to under conservatism and poor metallurgical decisions.

Lastly, the authors recognize that while it may be feasible to directly measure CH2S in a controlled laboratory environment, it is generally impractical at a wellsite. As such, to assess sour severity of a particular well, CH2S will likely remain computationally derived from at least one of the following parameters: yH2S, PH2S, fH2S, and/or aH2S.15  This further emphasizes the need to extensively validate ionic-EOS frameworks within the mildly sour HPHT domain.

Consequence of Substituting N2 for CH4 During High-Pressure Laboratory Tests

For this project, the H2S-N2-H2O system was used as a surrogate of the H2S-CH4-H2O system typically associated with the oilfield. While it was historically assumed that H2S would share the same phase behavior in either inert gas, the H2S phase behavior predicted for N2-rich and CH4-rich environments are not identical at PT > 1,000 psig (>70 bar). A direct N2-hydrocarbon substitution has a significant impact on H2S solubility, particularly at elevated pressures.

Figure 8 shows the individual AkH2S (i.e., ratio of CH2S/PH2S) corresponding to two different H2S sources: H2S in a N2-rich gas versus H2S in a CH4-rich gas. Both gas compositions are in equilibrium with liquid water phase. Apparently, the calculated AkH2S are different depending upon the source gas, which results in different observed CH2S at elevated total pressures. At 14.7 psia, H2S solubility for both environments are nearly identical. While both sour solubility coefficients decrease logarithmically with total pressure, the solubility at the high-pressure asymptote are different. At 1,000 psig, a direct 1:1 substitution of N2 for CH4 is predicted to increase CH2S by 40% at equal PH2S as indicated by the purple dashed line. Between 5,000 psig and 20,000 psig, substituting N2 for CH4 in laboratory tests more than doubles CH2S. This effect is related to fugacity11,14-15,54  and implies that H2S solubility is dependent upon the primary gas composition. Because AkH2S(N2)AkH2S(CH4), when holding yH2S constant, material qualification tests ought to be considered conservative. Recent in-house H2S-CO2-N2-H2O and H2S-CO2-CH4-H2O experiments performed at 4,800 psig and 70°F (332 bar and 21°C) by the authors confirm the difference in H2S solubilities per source gas (unpublished data).

FIGURE 8.

Model22-23  calculations performed at a water gas ratio of 10 bbl/MMscf (1 m3/18×103 sm3), 75°F (24°C), and 60 ppm H2S + 10 mol% CO2 + balance CH4.

FIGURE 8.

Model22-23  calculations performed at a water gas ratio of 10 bbl/MMscf (1 m3/18×103 sm3), 75°F (24°C), and 60 ppm H2S + 10 mol% CO2 + balance CH4.

Applying the Learning Outcomes from This Study to Improve the Understanding of the Environmental Severity of Mildly Sour High-Pressure Low-Temperature Systems

While “user-friendly” ionic-EOS frameworks are now widely available, allowing for greater understanding of the high-pressure systems, there is still much work to be done. Improvements to the Standard12  from a chemical perspective have been slow, in part due to competing interests between chemical thermodynamists, metallurgists, and corrosion experts. In addition, thermodynamic terminology commonly used to describe chemical phase equilibria (such as fugacity, activity, critical point, and super critical phase) requires in-depth knowledge that may not be readily available to most users. Hence, complicated phase equilibria parameterization was historically simplified to merely evaluating material performance on the basis of PH2S.

In an effort to help facilitate further improvements to the Standard,12  Figure 9 is a visualization of the change in H2S phase behavior with applied (total) pressure for a biphasic oilfield system. In this example, a water gas ratio of 10 bbl/MMscf (1 m3/18×103 sm3) was selected and yH2S is fixed in a methane-rich phase under isothermal conditions. The roman numerals listed within Figure 9 refer to specific chemical transformations that occur (i) below, (ii) at, and (iii) above the bubble point (saturation) pressure. The key observations are as follows (and also highlighted in Table 3):

  • PT < P(sat): Increasing the applied (total) pressure compresses the methane-rich phase and increases its density. Simultaneously, as the PH2S increases a proportional amount of H2S dissolves into the aqueous phase. Algebraically, IkH2S remains constant versus total pressure for an ideal gas, but AkH2S linearly decreases versus total pressure for a real gas due to changes in the fugacity coefficient (φH2S).13,15 

  • PT = P(sat): For an ideal gas, nearing the bubble point (saturation) pressure of the methane-rich phase is inconsequential as IkH2S remains constant. For a real gas, however, the bubble point is important. As the methane-rich phase shifts from a low-density gas to a high-density “super-critical liquid,” CH2S happens to reach a “saturation” plateau. This region also corresponds to an inflection point when AkH2S is plotted against total pressure.

  • PT > P(sat): Above the bubble point pressure, the methane-rich phase is often thermodynamically described as a “second” (nonpolar) liquid phase but remains separate from the denser (polar) aqueous phase. Although perhaps not technically considered a “gas,” because yH2S remains constant in the “super-critical” methane-rich phase, a “pseudo-PH2S” can still be calculated. Because CH2S remains constant and the (pseudo)-PH2S continues to increase linearly, AkH2S logarithmically decreases with increasing total pressure.

Table 3.

A Description of the H2S Phase Behavior of an Ideal Gas Versus a Real Gas Below, at, and Above the Bubble Point Pressure

A Description of the H2S Phase Behavior of an Ideal Gas Versus a Real Gas Below, at, and Above the Bubble Point Pressure
A Description of the H2S Phase Behavior of an Ideal Gas Versus a Real Gas Below, at, and Above the Bubble Point Pressure
FIGURE 9.

(a) Pictorial and (b) mathematical representations of the change in H2S phase behavior with applied (total) pressure for a biphasic (methane and aqueous) system with yH2S held constant. Refer to Table 3 and the main text for details.

FIGURE 9.

(a) Pictorial and (b) mathematical representations of the change in H2S phase behavior with applied (total) pressure for a biphasic (methane and aqueous) system with yH2S held constant. Refer to Table 3 and the main text for details.

While most of the observed chemical changes in H2S phase behavior are related to the pressure-sensitive methane-rich phase, the propensity for cracking, however, is dependent upon the CH2S in the pressure-insensitive aqueous phase. Because CH2S remains nearly constant above the bubble point pressure, it is possible that the risk of a material to fail by SSC may not change with increasing total pressure at 70°F within this domain.

  • AkH2S from H2S-N2 mixed gas has been rigorously quantified from 30 psig to 20,000 psig at 70°F.

  • Experimental H2S solubility data and model predictions are in very good agreement between 30 psig and 20,000 psig total pressure for CH2S > 175 mg/L.

  • In-house modifications to common laboratory techniques to quantify H2S concentrations in both the gas and liquid phases provide adequate accuracy and precision. The experimental charging and H2S verification procedures presented could be adopted by other institutions.

  • The results by Nelson and Reddy,10  and also shown in this article, arrive at the same conclusion: That H2S solubility logrimically decreases with total pressure.

  • Based on thermodynamic modeling, a direct 1:1 substitution of N2 for CH4, as a booster gas when designing high-pressure laboratory tests, more than doubles CH2S between 5,000 psig and 20,000 psig.

(1)

UNS numbers are listed in Metals & Alloys in the Unified Numbering System, published by the Society of Automotive Engineers (SAE International) and cosponsored by ASTM International.

(2)

In the articles cited, optical spectroscopy using small, high-pressure cells with optical windows was the classic technique used to measure H2S solubility.29  Alternative analytical methods used to quantify H2S solubility include calorimetry25-26  and iodometric titration.50  Regardless of analytical technique, the objective of the cited H2S solubility studies were to quantify the change in H2S solubility with temperature. (While important, the effect of temperature on H2S solubility is beyond the scope of this article.) The effect of total pressure on H2S solubility, while recognized by the reseachers,25-26  was of secondary importance.

(3)

Following the United States customary (USC) units convention.

Trade name.

The authors wish to thank Honeywell Connected Enterprise (Houston, Texas) for its support of time and underwriting this study, and for its approval to disseminate these results.

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,
Wilms
M.E.
,
Chambers
B.D.
, “
Conservatism in Sour Testing with Hydrogen Sulfide Partial Pressure Exposures: Towards a More Consistent Approach
,”
CORROSION 2015, paper no. 6050
(
Houston, TX
:
NACE
,
2015
).

NOMENCLATURE

     
  • ai

    Activity of i in the aqueous phase, mol/L

  •  
  • ci

    Dissolved i concentration in the aqueous phase, mg/L

  •  
  • fi

    Fugacity of i in the gas phase, psia

  •  
  • i

    Component

  •  
  • ki

    Henry’s constant of i solubility, mg/(L·psia)

  •  
  • ni

    Number of i moles in gas phase, mol

  •  
  • Pi

    Partial pressure of i, psia

  •  
  • PT

    Total pressure, psig

  •  
  • R

    Ideal gas constant, 8.3144 J/(mol·K)

  •  
  • T

    System temperature, K or °F

  •  
  • V

    Volume of the gas phase, L

  •  
  • xi

    Mole fraction i in the aqueous phase, mol%

  •  
  • yi

    Mole fraction of i in gas/liquid hydrocarbon phase, mol% (mol ppm)

  •  
  • γi

    Activity coefficient of i in the aqueous phase: corrects for the nonideal behavior of i in the aqueous phase

  •  
  • ξi

    The Poynting correction factor—is often expressed as an exponential term related the partial molar volume of i. It adjusts for the effect of total system pressure on the solubility of i in the aqueous phase

  •  
  • i

    Fugacity coefficient of i in the gas phase—a correction for non-ideal behavior of H2S in the hydrocarbon phase