The application of pitting resistance equivalent number (PREN) equations for stainless steels has become ubiquitous across many industries, none more so than the petroleum industry. These useful equations are often used to develop new alloys based on generating the highest possible PREN, however, they are frequently applied incorrectly to environments that are not consistent with the original basis of their development. This focused review presents some of the origins of the PREN equations and their limitations especially for use in oil and gas applications.

GENESIS OF THE PITTING RESISTANCE EQUIVALENT NUMBER EQUATION FOR STAINLESS STEELS

The original introduction of the most common form of the pitting resistance equivalent number (PREN) equation has been attributed to Lorenz and Medawar.1  These authors studied a variety of austenitic stainless steels in boiling nitric acid, boiling magnesium chloride, and artificial seawater to better define the effect of alloy composition on pitting and stress corrosion cracking resistance. They found that the breakdown potential in seawater was a function of 1% Cr and 3% Mo and by combining the results from other researchers arrived at the basic PREN = %Cr + 3.3% Mo equation. Subsequent work by others2-3  demonstrated the benefit of nitrogen additions resulting in variations for the effect of N resulting in the most common expression stated by ISO 214574  as:
formula
and further refinement to include tungsten:
formula

However, there is considerable work that questions the numerical multiplier for N as cited by Jargelius5  ranging from 9 to 36. Moreover, the original equations do not account for interaction of elements which can further complicate the validity of some of the factors especially when Mn is present.5  The extent to which W is beneficial is also open to question and may be limited to a small range for stainless steels, especially for super duplex stainless steels, but for nickel-based alloys may have a multiplier as high as one rather than the typical 0.5.6  Furthermore, it has been suggested that W in Equation (2) does not improve pitting resistance unless Mo is also present.7 

It is of paramount importance to recognize that the original work,1  and subsequent work by many researchers confirming and extending the PREN, is explicitly only applicable to seawater or saline waters that implicitly include the presence of dissolved oxygen or other oxidizers. This latter factor is often not recognized in an effort to provide simple methods to compare alloys. The presence of an aerated environment, or as shown by Lorenz and Medawar also strong oxidizing environments, are necessary to the applicability of these equations. This important requirement is often not appreciated by many researchers resulting in the misapplication of PREN to environments for which they are not applicable.

Furthermore, the original early work on PREN and the critical pitting temperature (CPT) was performed on austenitic stainless steels that are basically single-phase microstructures with a relatively uniform microstructure. In addition, the elements in Equations (1) and (2) are required to be in solid solution. The application of CPT and PREN to dual-phase alloys such as duplex stainless steels and alloys containing multiphases, such as precipitation hardening stainless steels and nickel-based alloys, calls into question the validity of such measurements and predictions when the specific processing paths and resulting microstructures are not described or considered.

APPLICABILITY OF PITTING RESISTANCE EQUIVALENT NUMBER-AERATED SALINE WATER

Further to the point above, standard methods for determining the resistance of stainless steels to pitting are the ASTM G48 test that applies 6% FeCl3 at various temperatures and the ASTM G150 for defining the CPT of alloys. Whereas these two standards are the most common methods to generate a CPT, other electrochemical methods have been used. All of these environments are by their nature oxidizing which is a fundamental requirement for the application of any PREN equations and in the case of the G48 Methods A and C includes an extremely low pH ranging from 0.4 to 1.6.8-9 

Many efforts have been made to correlate CPT values of alloys with PREN which is reasonable as both are strongly dependent on alloy composition but again are prefaced on the assumption of an oxidizing environment and more specifically seawater. Figure 1 shows one such correlation.10 

FIGURE 1.

Critical pitting temperature vs. PREN for some stainless steels in naturally aerated seawater.

FIGURE 1.

Critical pitting temperature vs. PREN for some stainless steels in naturally aerated seawater.

As already stated, another important factor contributing to the early work establishing the original PREN equations was the fact that fully austenitic stainless steels were used for the evaluations. As Charles has shown11-12  for duplex stainless steels, especially the lean duplexes, there is a detrimental effect of Mn such that the relationship between CPT and PREN is best addressed with the following equation:
formula

Furthermore, for a single-phase austenitic stainless steels containing high Mn contents and low Ni (approximately 18% Mn, 2% Ni) others13  have found Equation (3) to be more representative of the pitting potential than the standard Equation (1) above. These authors included a 0.5 multiplier to Mn in Equation (3).

Klapper and Rebak14  also explained the limitations of the ASTM G48 tests for defining the CPT of nickel-based alloys due to the thermal instability of FeCl3 at temperatures above 85°C. Therefore, electrochemical methods are required to accurately define a CPT value for highly alloyed Ni-Cr-Mo alloys, yet as noted below this is not always considered.

Finally, as concluded by Cleland15  the PREN is just a statement of the obvious. The greater the alloying of stainless steels, the higher the PREN and therefore the CPT. This same basic fact also holds true for nickel-based alloys and for this reason care should be taken not to place too much emphasis on small differences in PREN values between similar alloys.

INAPPROPRIATE USES OF PITTING RESISTANCE EQUIVALENT NUMBER AND CORRECTIONS FOR ANOXIC ENVIRONMENTS

There are numerous examples of incorrectly applying the standard PREN equations to nonaerated environments in the literature. Some of the prominent examples of inappropriate use of PREN for anoxic environments are from the upstream oil and gas industry where the producing environment is completely devoid of oxygen and other oxidizers. Two examples are codified in ISO 15156 Part 316  and ISO 21457.4  The former lists the PREN for stainless steels which is misleading and technically invalid because primary oil and gas production does not include oxygen. Still more confusing, ISO 15156 states in a separate paragraph that PREN does not really apply except in the presence of dissolved chlorides and oxygen which, while true, contradicts the use of this equation in the remainder of the document. Thus, by implication both industry standards present Equation (1) as relevant to deaerated oil and gas applications.

Hibner, et al.,17  demonstrated the unreliability of the PREN by testing Alloy 28 and Alloy 825 in an environment containing H2S and CO2. The PREN value for Alloy 28 is higher than for Alloy 825 but pitting tests showed Alloy 825 to be superior to Alloy 28 for pitting resistance. This behavior was attributed to the higher nickel content of 825, however, Ni is not included in any PREN equations. These authors referenced a modified PREN for oil and gas environments but does not include Ni:
formula
and in another publication presented an alternate version as:17 
formula

The origin of these equations is from a proprietary software program for which no independent verification can be, or has been, made and to data for which no other research work has confirmed their validity. Moreover, work by Herbsleb3  on austenitic stainless steels, in solutions with only H2S bubbled into them, showed that the positive influence of Mo on pitting resistance was completely lost compared to results by others in seawater. This then would contradict Equations (4) and (5).

The complication of more than one phase, especially when second phases such as in duplex stainless steels are present, can have a dramatic effect on the pitting resistance depending on the phase balance. Moreover, the presence of carbides, which are nominally absent in austenitic stainless steels, can substantially impact the PREN and CPT.

Another example of questionable use is for martensitic stainless steels that are widely used in oil and gas developments. The PREN values indicate they would be untenable under expected well conditions. However, several efforts have been made to define their use by testing in H2S and CO2 environments. Hashizume and others19  derived the following equation for a pitting index (PI) for a variety of martensitic stainless steels containing 13% to 15%Cr and 0 to 1% Mo.
formula

The detrimental effect of carbon is notable as is the beneficial effect of Ni, neither of which are present in the standard PREN equations. Likewise, others have demonstrated the high CPT values for similar martensitic stainless steels obtained in deaerated sour solutions using electrochemical noise measurements.20  They reported CPT values as high as 144°C.

In other research, Kane and Abayarathna21  evaluated the CPT of 22Cr duplex stainless steel and several nickel-based alloys, including Alloys 825 and 2550, under simulated sour gas (H2S) producing conditions. At pH ≥ 4.0 and moderate chlorides (10,000 ppm) the CPT of 22Cr (PREN, 34) was 115°C while Alloy 825 (PREN, 31) at the same conditions was >200°C as was Alloy 2550 (PREN, 45) (tested at pH < 4). It is evident, when compared to the very low CPT and PREN values for these alloys in seawater, that the use of PREN for these oil and gas applications is completely unreliable.

Another example is for Type 316 stainless steel with PREN nominally of 25 and a CPT given variously as 20°C to 31°C22-24  depending on test methods and the surface conditions of the specimen. All three of these cited references used solutions of 1 M NaCl open to the atmosphere and in the last case the authors also measured CPT in 2 M NaCl as well. If in fact the PREN were universally applicable to all environments as suggested, then Type 316 would not be suitable in deaerated oil and gas environments above 20°C. However, Figure 2 shows the application limit of Type 316 stainless steel can be as high as 200°C in the absence of chlorides and still above 100°C in the presence of high chlorides and low-CO2 partial pressure (which is the main driver for pH).25  Therefore, the inappropriate use of PREN for all environments, most especially deaerated ones, can be unnecessarily punitive for the selection of cost effective alloys.

FIGURE 2.

Corrosion resistance of Type 316/316L stainless steel in CO2/NaCl environments in the absence of oxygen and H2S (with permission of the Nickel Institute). The area inside the curve boundaries defines the acceptable general corrosion rate of ≤0.05 mm/y (2 mils/y) and no sulfide stress cracking or stress corrosion cracking.

FIGURE 2.

Corrosion resistance of Type 316/316L stainless steel in CO2/NaCl environments in the absence of oxygen and H2S (with permission of the Nickel Institute). The area inside the curve boundaries defines the acceptable general corrosion rate of ≤0.05 mm/y (2 mils/y) and no sulfide stress cracking or stress corrosion cracking.

DISCUSSION

The widespread use of PREN equations applied to environments that are not aerated brine or contain oxidizers is not only inappropriate but ultimately overly conservative. Furthermore, PREN equations implicitly require the elements considered important for pitting resistance to be in solid solution and not tied up as carbides, nitrides, and other precipitates and phases. For this reason current PREN equations are quite limited in application when properly applied. While the use of simple alloy compositional equations to compare the pitting resistance of comparable alloys would be useful for a multitude of environments, much more intensive investigations must be performed specific to for specific environments in order to justify such simple equations. Moreover, for multiphase alloys, especially nickel-based alloys, a more complete solution lies in the application of software modeling programs, such as New PHACOMP (PHAse COMPutation),26  CALPHAD (CALculation of PHAse Diagrams),27  and JMatPro (Java-based Materials Properties)28  to describe the specific microstructure after various thermal treatments. In fact, some of these modeling programs must be used together to allow complete description of the phases and microstructures that can be generated through various processing steps. For example, New PHACOMP can predict the formation of TCP (topologically close-packed) constituents such as Laves, sigma, and mu but not the equilibrium phases for which CALPHAD is better suited. Coupling the microstructural/phase distribution with electrochemical testing will provide more complete and accurate CPT data and possibly development of useful PREN equations. Recent efforts have been made to develop new alloys with optimized properties by combining CALPHAD with PREN and electrochemical methods.29 

Complementary to the use of phase and microstructure modeling is work that quantifies not only the dual phases in duplex stainless steels but includes the formation of deleterious third phases such as sigma and chi as a function of thermal treatments.30  These authors demonstrated that not only changes in the ferrite to austenite ratio produced significantly different PREN values and CPT but also formation of sigma and Cr2N precipitates further decreased the CPT, demonstrating there is no single value for CPT of duplex stainless steels and thus PREN is meaningless unless it can be tied to a specific microstructure and phase balance.

The proper development of appropriate PREN formulae for alloys of differing families for various environments requires the coupling of alloy modeling programs with electrochemical methods to accurately define CPT within strict boundaries as a function of the environment and alloy processing history. Only then can PREN equations be suggested for specific uses.

CONCLUSIONS

  • Application of the standard equations for PREN is strictly only applicable to single-phase austenitic stainless steels in aerated or oxidizing environments. Use of these equations beyond these narrow boundaries is not fundamentally sound. For multiphase alloys such as duplex stainless steels and nickel-based precipitation hardening alloys, any PREN formulae must be described and bounded by their processing history, phase balances, and microstructure.

Trade name.

ACKNOWLEDGMENTS

The author greatly appreciates the assistance of Prof. Dr. Thomas Ladwein, FNACE in obtaining the very difficult to find original paper by Lorenz and Medawar. While this paper is often cited by those working in the field of stainless steel pitting behavior, it is a reminder how important it is to review the actual original work.

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