Casandra

Modelling

A guide to the use of

corrosion prediction

models for risk assessment

in oil and gas production

and transportation

facilities

A J McMahon, D M E Paisley

Sunbury Report No. ESR.96.ER.066

dated November 1997

Introduction 1 "Cassandra 98" Corrosion Prediction Spreadsheet

by A J McMahon

Introduction 5

Quick Start 6

Limitations of Corrosion Prediction Models 8 Detailed Description of the Spreadsheet 11 Comparing Output from the "Cassandra 98" Model with Field Data 27 Appendix 1: Henry's Law Constans for CO2 Dissolved in Brine 29 The Use of Corrosion Prediction Models During Design

by D E Paisley

Introduction 31

Important Factors not Covered by the Corrosion Model 35

Effect of Corrosion Inhibitors 42

Predicting the Effectiveness of Corrosion Inhibitors - 48 'The Inhibitor Availability Model'

Recommended Values for use in the Inhibitor Availability Model 51 Comparisons of the Inhibitor Availability Model with BP's Previous Model 62 Corrosion Rates of Low Alloy Steels 64

Preferential Weld Corrosion 65

Effects of Pitting 66

Choosing an Optimum Corrosion Allowance 67 Applying Models to Different Flow Regimes 69 Applying Models to Transportation Equipment 72 Applying Models to Process Equipment 86 Flow Velocities in Process Pipework 89 Economic Tools to Use During Materials Selection 92

References 95

use during the design of pipelines and facilities. It is divided into two sections.

The first section introduces a new prediction spreadsheet called Cassandra 98* which is BP's implementation of the CO₂prediction models published by de Waard et al. It builds on these models to include BP's experience of such systems. The pocket inside the front cover of this report contains a floppy disc which contains the necessary programs and spreadsheets to run it together with a set of installation instructions.

The second section discusses how the prediction model may be used for design purposes and it introduces several improvements from previous guidelines. These include the use of the probabilistic approach to corrosion prediction and the use of corrosion inhibitor availabilities instead of efficiencies. It also discusses the use of "corrosion risk categories" as a way of quantifying the corrosion risk at the design stage. The floppy disc also contains a spreadsheet for calculating the risk category.

To illustrate the points made examples have been obtained from many BP assets worldwide. Where financial data are shown it is from 1997.

Since this subject is continually changing it is anticipated that these guidelines will be updated in future years and so any comments or suggestions regarding either the content or appearance of them would be very welcome.

*In Greek mythology Cassandra was the daughter of Priam and Hecuba. She was endowed with the gift of prophecy but fated never to be believed. She is generally regarded as the prophet of disaster...especially when disregarded.

The authors would like to thank the following BP staff for their contributions to these guidelines.

Jim Corbally Laurence Cowie Mike Fielder Don Harrop Bill Hedges Will McDonald Tracy Smith Simon Webster Richard Woollam

carbon steel equipment in a production environment. Compared with the incidences of fatigue, erosion, stress corrosion cracking or over-pressurisation, the incidences of CO₂ related damage are far more common. Unfortunately, the engineering solutions to eradicating the CO₂ corrosion risk require high capital investments in corrosion resistant materials. As Figure 1 shows, providing a corrosion allowance of 8 mm to carbon steel flowlines costs a significant sum at circa US$1 million per 5 km but even this is insignificant in terms of the costs of the various corrosion resistant flowline options.

Similar relative costs are incurred when specifying corrosion resistant materials downhole or in facilities. This is rarely justified. For this reason, CO₂ corrosion of carbon steel will always be a problem that BPX has to deal with. Managing CO₂corrosion therefore becomes a priority and it can become expensive. The replacement of the original Forties MOL and the severe damage to the Beatrice MOL are two examples of high costs that BPX have incurred in recent years due to unpredicted corrosion rates. Successful management of CO₂corrosion starts off with the identification of risks and continues with the provision of suitable controls and the review of the success of the controls via monitoring - as illustrated in Figure 1: Fully

Installed Costs for Various Flowline Materials Options in Colombia (1997) 0 5 10 15 20 25 30 35 6 8 10 12 14 16 18 20 22 24 26 28 30

Nominal Flowline Diameter - Inches Cost per 5 Km ( $m i l l) Carbon steel 8mm ca Duplex SS 13%Cr Bi-metal 13Cr liner Carbon steel, no ca

This document sets out BP’s approach to the quantification of CO₂ corrosion risk through the use of predictive models. In doing so, it also discusses the reliance that can be placed on corrosion inhibition as the only viable control measure for carbon steel and the importance of suitable corrosion monitoring. To put the importance of this into context, corrosion costs BPX 8.3% of its capex budget and increases lifting costs by 14%, an average of over 8 cents per barrel. Figure 3 shows that the costs are distributed across the entire range of facilities.

Apply Controls

Monitor

_{Effectiveness}

Quantify

Risk

Loop that is Required for Successful Management of CO2 Corrosion

The quantification of corrosion risk is required at several stages during an assets life. The most obvious period is during the project phase when the original materials of construction are being selected. This process must be repeated during the life of the asset if failures or expansions require the procurement of additional facilities. Quantifying the corrosion risk is also important in tailoring inspection strategies. Risk based inspection is now widely adopted and, as CO₂corrosion represents one of the most important factors governing the probability of failure for much equipment, a reasoned approach should be taken. It is important that this approach is theoretically sound but also reflects past experience.

This version of the BP CO₂prediction model is the first to be published since 1993/4 when the guidelines on multiphase and wet gas transport respectively were issued. The new guidelines incorporate changes by the authors to the semi-empirical model used in the original guideline as well as comprehensive guidance on how to use the spreadsheet included with this version. The new model also includes the ability to predict the affects of changing flow velocities on uninhibited corrosion rates.

Downhole 13% Subsea 59% Chemicals 4% Topsides 23% Personnel 1% Figure 3: The Distribution of Costs of Corrosion Across Ten BPX North Sea Assets, 1990 to 1994.

The new guidelines also consider the probabilistic approach to predicting CO₂ corrosion. Probabilistic approach to design in general is becoming more widespread and offers several advantages over the traditional deterministic approach. The probabilistic approach is neither endorsed nor disallowed but is discussed as, in some cases, it may be more appropriate than a deterministic approach.

The approach to designing for the use of corrosion inhibitors has been changed significantly. The previous approach described the affects of an inhibitor through the use of an efficiency factor, such as 90%. This does not reflect BPX’s recent field data generated under severe conditions which showed inhibitors can be more effective than predicted. "Inhibitor efficiencies" have therefore been replaced with "inhibitor availabilities" that more closely reflect field experience. There is a general move in the industry towards this methodology and it offers several advantages.

However, it has become clear that for inhibitors to work effectively the corrosion management system must be highly organised. Recommendations are therefore included on methods to ensure that the inhibitor availabilities assumed at the design stage occur during the operational stage.

"Cassandra 98” is BP's new implementation of the 1991, 1993 and 1995 CO₂ corrosion prediction models published by De Waard et al. The pocket inside the front cover of this report contains a floppy disc with the programme together with a set of installation instructions.

The 1991 and 1993 De Waard models are already widely used within BP and elsewhere in a variety of customised forms. This report describes the new Cassandra 98 spreadsheet for Microsoft Excel. It is based primarily on the 1993 De Waard model, incorporates some equations from the 1991 model, and uses the 1995 model to assess velocity effects. The spreadsheet is intended to capture all the best features of the 1991, 1993 and 1995 models [1,2,3]. Certain extra features from outside the De Waard papers, based on standard physical chemistry, have also been included. The sourc e , background and limitations of all the assumptions and equations in the spreadsheet are fully documented in these guidance notes.

The Cassandra 98 spreadsheet is written in a simple and accessible format within Microsoft Excel (version 7.0). It avoids the use of macros or special techniques so that the logic and the calculations are as transparent as possible. This approach also ensures that the spreadsheet is immediately compatible with new versions of Excel.

The Excel add-in module "CRYSTAL BALL" (from Decisioneering Ltd, 1380 Lawrence Street, Suite 520, Denver, Colorado 80204, USA. Tel: +1 303 292 2291. Cost ~£100) enables probability distributions to be set for each input cell and it then uses Monte-Carlo simulation to combine these into a probability distribution for the resulting corrosion rate. You must buy "CRYSTAL BALL" separately for your Excel environment. It can't be bundled with this spreadsheet. The detailed use of CRYSTAL BALL is well covered in the manufacturer's handbook and therefore is not repeated in these guidelines.

Care is required when comparing the output of any existing in-house version of the De Waard models against this new Cassandra 98 spreadsheet. It is very easy for errors and untested assumptions to be entered into a spreadsheet which might then perhaps be passed on from user to user and often compounded with other assumptions. Cassandra 98 has been written from

This section gives enough information to allow experienced modellers to make a start. The subsequent section gives a more detailed description of all the input and output parameters. The spreadsheets themselves also carry frequent "cell notes". These are marked by a red dot in the top right hand corner of those cells. Just double click on the cell to read the contents. To carry out a basic calculation enter the following input values into the cells with a white background:

Only the inputs in the preceding Table are needed for a straightforward numeric calculation. Some further information is required in order to carry out a probabilistic calculation using CRYSTAL BALL. The spreadsheet can easily be customised by individual users to permit more extensive handling of probabilities:

QUICK START

Input Parameters

Probabilistsic Inputs

P total gas pressure bar F7

%CO₂ CO₂in gas mole % (NB = v/v%) F8

%H2S H2S in gas mole % (NB = v/v%) M8

water composition ion ppm values ppm (NB = mg/ltr) A15-L15

brine pH enter known value, F17

or enter "d", "o", or "x" to accept one of the calculated values shown in F18-F20 (see Page 17)

T System temperature oC F24

T_s Scaling temperature, enter oC F25

the calculated scaling temperature, given in cell F26, or another known or preferred value

d hydraulic diameter m M24

U velocity m/s M25

Parameter Comments Units Cell

Table 1: Input

parameters for a numeric calculation

P F7 use a uniform distribution; set F7 as the maximum; set G7 as the minimum

%CO₂ F8 use a normal distribution; adjust

standard deviation as necessary

brine pH F17 must enter a known or a calculated value; use a normal distribution; adjust standard deviation as necessary

T F24 use a uniform distribution; set F24 as

the maximum; set G24 as the minimum

d M24 use a uniform distribution; set M24 as

the maximum; set N24 as the minimum

U M25 use a uniform distribution; set M25 as

the maximum; set N25 as the minimum

Output Parameters

1993 basic Vcor E32 the uncorrected corrosion rate for static conditions

1993 correction factors G32-K32 correction factors for pH, fugacity, scaling, and glycol

1993 corrosion rate G34 the corrosion rate for static conditions corrected for pH

1995 corrosion rate G39 the corrosion rate for dynamic conditions calculated from the components Vr and Vm in G37

Parameter Cell Comment

Parameter Cell Comments

The resulting output parameters are described in Table 3. See p23 for a more detailed description of how to interpret and use these values. Briefly, the 1993 rate should be regarded as the minimum. Velocity effects may increase this minimum rate as shown by the 1995 rate. Hence, the 1993 and 1995 rates will normally give the lower and upper bounds on the expected corrosion rate. The 1995 model is not accurate at low velocities and so it should be ignored whenever it falls below the 1993 value.

Table 2: Additional

Input Parameters for a Probabilistic

Calculation

Table 3: Output

The use of simple equations and the precision of the spreadsheet environment can lead one to think that the De Waard corrosion models are equally precise. However, this is not the case. The models are only valid over a certain range of conditions, and even within this range a certain amount of data has been ignored if it doesn't fit the main trends. Each model appears to be constructed by obtaining a large number of corrosion rates over a range of conditions and then finding an equation which draws a line passing close to the majority of this cloud of points. The equations appear to be freely adjusted in order to give the best fit to the data. The primary concern is to obtain a good fit to the data, rather than obtaining mechanistically rigorous equations. These are empirical engineering models rather than scientific theories.

Neither the 1991 or 1993 De Waard papers give many precise details about the range of validity of the models. The 1995 paper does give a more thorough set of figures (see below) but still omits important features such as the type of brine used in the tests, and the elapsed time when the corrosion rates were measured. De Waard's very early work used a 0.1% NaCl solution [4] and this may well have been used in all the subsequent studies because his main focus has always been low salinity water in gas lines. Table 4 shows the approximate ranges of validity for the different parameters in the Cassandra 98 spreadsheet.

LIMITATIONS OF CORROSION PREDICTION MODELS

Table 4: Range of

Validity of De Waar d Models

P <200 bar not defined

fCO₂ <10 bar 0.3-6.5 bar

Oddo & Tomson pH -- -- <200oC, <1000 bar

XLpH -- -- <120oC

T <140oC 20-80oC

U 0 m/s 1.5 -13 m/s

Parameter Range of 1991 Range of 1995 Comments

& 1993 Model

The spreadsheet gives freedom to enter any value for most parameters. When the input value is outside the approximate range of the 1991 and 1993 De Waard models then the text will turn RED in the cell as a warning. The predicted corrosion rate may still be useful but the user must accept the additional risk of going beyond the known limits of the correlations.

To develop the 1995 model [3] corrosion rates were obtained on the IFE flow loop (Kjeller, Norway) using a radiochemical technique to measure corrosion rates. Tests were carried out over 2-3 days but there is no information about the corrosion rate profile over this time or when the final data point was taken. Data were obtained for the following conditions.

- St-52 DIN 17100 steel (Cr 0.08%, C 0.18%) which is similar to ASTM A537 Gr1

- 0.1, 3.1, 8.5, 13 m/s flow velocity - 20 - 90oC

- 0.3 - 20 bara CO₂

Certain inconsistencies in the data set were eliminated prior to developing the model. These included:

- 0.1 m/s excluded

- 13 m/s excluded when corrosion rate less than at 8.5 m/s - 90oC excluded

- CO₂>6.5 bar excluded

Eventually 221 data points were used in the main correlation (Figure 2 ref 3). The main equations are specific to St-52 steel because, "The equations obtained for St-52 showed a complete lack of correlation for the other steels". The 15 other steels were normalised steels and quench-and-tempered (Q&T) low alloy steels. These were examined over the following conditions to produce some modified equations which take account of steel composition. - 3.1, 8.5, 13 m/s flow velocity - 60o_C - ca 2 bar CO₂ - pH 4,5,6 Limits of the 1995 Model

For normalised steels a "Cr correction" and a "C correction" can be calculated separately and together. For Q&T steels the "C correction" has no effect and only the "Cr correction" is relevant. The Cassandra 98 spreadsheet does not include the steel composition equations due to the poor correlations obtained when fitted to the model.

Errors in matching equations to data points are defined in the 1995 paper by "coefficients of determination". This is a complicated statistical function ranging from 0 (poor correlation) to 1 (perfect correlation). It is not the same as the "correlation co-efficient" in regression analysis which scales from -1 to 1. The "co-efficients of determination" in the paper are 0.91 for the main St-52 equations (after excluding the data that doesn't fit), 0.83 for the normalised steels, and 0.80 for the Q&T steels. For the main St-52 correlation this corresponds to a standard deviation of 25% on the predicted corrosion rate. This is the error given in this spreadsheet. Because of this error the predicted corrosion rates are only shown to one decimal place. A "CRYSTAL BALL" probabilistic analysis gives a more realistic impression of the error on each prediction.

The De Waard models were all developed using water-only systems in the laboratory. The 1993 model is intended for nearly static, aqueous conditions and so for all but the lowest velocities (see page 77) it can be regarded as the minimum corrosion rate of a water wet region in a gas/water, water/oil, or a water/oil/gas system. Due to the different hydrodynamics in these field cases some assumptions are required in order to apply the 1995 model effectively. These assumptions will only affect the diameter and velocity values used as inputs in the model. The other inputs will be unaffected. Table 5 gives some suggested assumptions. However, users are free to develop their own approaches to meet the demands of their own particular circumstances. Some of the issues involved in extrapolating the models to the field are discussed in more detail on pages 27-28.

Errors on Corrosion Rates

Units are specified for each parameter listed in this section. The same units are assumed in all the equations given below and throughout the Cassandra 98 spreadsheet. The spreadsheet has a "units conversion box" at cell P5. The UNITS spreadsheet allows conversions between a wider range of units. The SALTS spreadsheet enables conversion between an ionic analysis of brine and the salts re q u i red to pre p a re a synthetic analogue. The FUGACITY spreadsheet is a data-base used to calculate fugacity corrections at high total pressures.

P...total gas pressure (bara, i.e. bar absolute) INPUT cells F7 and G7 For a multiphase system this is simply the prevailing local P in the gas. For aliquid only system it is the P in the last gas phase which was in equilibrium with the liquid, e.g. the separator gas in the case of a crude oil export line. For a downhole liquid pressurised above the bubble point then use the

DETAILED DESCRIPTION OF THE SPREADSHEET

Total Pressure

Water only use pipe diameter and water velocity

Liquid/Gas use hydraulic diameter (see p 21)

use true liquid velocity rather than nominal velocity (see p 22)

Water/Oil use pipe diameter and total liquid velocity

(n.b. this ignores the possibility of water drop out or stratification which could lead to the water phase moving more slowly than the oil phase)

Water/Oil/Gas use a specialist multiphase program to calculate the wall shear stress or the "C factor" for the pipe system, then choose diameter and velocity inputs which reproduce this hydrodynamic value.

Field Situation Recommended Approach

Table 5: Applying the

1995 De Waard Model to Field Situation

Figure 4: Schematic Diagram of an Oil Production System (downhole, separator, export)

%CO₂...CO₂ in gas (mole%, which is same as v/v%) INPUT cell F8 For a multiphase system this is simply the prevailing local %CO₂in the gas. For a liquid only system it is the %CO₂ in the last gas phase which was in equilibrium with the liquid, e.g. the separator gas in the case of a crude oil export line. For a downhole liquid use the %CO₂ in the gas formed at the bubble point. If this gas analysis is not available then use the CO₂dissolved in the brine, the Henry's constant, and the bubble point pressure to back-calculate the "effective %CO₂" which would be required in the bubble point gas in order to sustain the known level of dissolved CO₂ (see box at cell P19). Indeed, this procedure can be followed for any region where the CO₂ dissolved in the brine is known, but the gas analysis is unknown.

There may be occasions when it is helpful to apply parts of the Cassandra model to a water which is in equilibrium with ambient air (e.g. for pH predictions). The appropriate atmospheric inputs are P = 1 bara and %CO2=0.035 mole%. Remember that under these conditions the corrosion prediction from the model will only relate to the dissolved CO2 component and not the dissolved O2.

For a probabilistic calculation using "CRYSTAL BALL", set up a normal %CO₂

pCO₂...partial pressure of CO₂(bara) OUTPUT cell F9

fCO₂...fugacity of CO₂(bar) OUTPUT cell F10

The non-ideality of gases means that at high total pressures the partial pressure is not an accurate description of the activity of a gas component.

The fugacity is the true activity of the gas component. The 1991 and 1993

models use pCO₂in the main corrosion prediction equations and then at the end apply a fugacity correction factor (F_fug) to account for fugacity effects. In Cassandra 98 the equations from the 1991 and 1993 models use fCO₂ directly, therefore there is no need to use a fugacity correction factor (F_fug). The equations from the 1995 model in Cassandra 98 also use fCO2 directly -instead of pCO₂. Hence, in Cassandra 98, it is fCO₂ which is used as the primary parameter for all the equations which consider CO₂as an input. Fugacity data from the work of R H Newton [5] are tabulated in the FUGACITY.XLS spreadsheet in the workbook. The Cassandra 98 spreadsheet uses the input values of temperature and total pressure to look-up the correct value of the fugacity co-efficient (γ) in the FUGACITY spreadsheet,

fCO₂= pCO₂γ

The R H Newton data are generally applicable to many pure gases. The data show fugacity co-efficients as a function of "reduced temperature" and "reduced pressure",

where T_r is reduced temperature (dimensionless) T is the prevailing local temperature (o_C)

T_c is the critical temperature for the gas (from tables) (o_C) pCO2 fCO2 T_r = T T_c pCO₂=P.%CO2 100

where P_ris reduced pressure (dimensionless) P is the total pressure (bar)

P_c is the critical pressure for the gas (bar)

Oilfields produce gas mixtures rather than pure gases. Hence, a difficulty arises in deciding whether it is the Tc and Pc for methane or for CO₂ that one should use. In the Cassandra 98 spreadsheet, empirical values of Tc and Pc are assumed which allow the Newton model to agree with the CO₂/methane mixed gas fugacity data in Figure 5 of the 1993 De Waard paper to ± 10%. In other words the De Waard data are used to calibrate the Newton model.

The De Waard calibration data are valid up to 140oC and 250 bar. The Newton data extends beyond these levels up to 300o_{C and 400 bar. The} general trends in the data will be accurate under these extreme conditions, however, the absolute values are unchecked. For accurate work it will be necessary to calculate or obtain the correct value of fugacity from elsewhere and then manipulate %CO₂ in cell F8 by trial and error in order to obtain the correct fugacity in cell F10.

%H 2S...H2S in gas (mole%, which is same as v/v%) INPUT cell M8

H2S is not included in any of the De Waard models. It is only used in the Cassandra 98 spreadsheet in the calculation of solution pH by XLpH (see below). It can be ignored completely simply by entering zero.

P_r= P P_c

CO₂ 31 73

methane -82 45.8

empirical values used to correlate with De Waard data -37 56.7

%H2S Tc Pc (o_{C) (bar)} Table 6: Reduced Temperature and Reduced Pressure Values for CO2 and Methane

It is by lowering the solution pH that H2S can potentially increase the corrosion rate, often in synergy with CO_{2. In practise, H2S tends to promote} FeS surface films which reduce the observed general corrosion rate but which increase the likelihood of localised corrosion whenever the film fails. The CO₂ general corrosion rate is often assumed as the worst-case localised corrosion rate for the regions with no FeS film.

An alternative approximate approach for handling the presence of H2S is to assume that every 1 mole% H2S has the same corrosivity as 0.01 mole% CO2. This rule of thumb assumes that 1 ppm dissolved CO₂and 200 ppm dissolved H2S give roughly equal corrosion rates [6], and that H2S is roughly twice as soluble in water as CO₂ for a given partial pressure [7].

pH2S...partial pressure of H2S (bar) OUTPUT cell M9 pH2S = P . %H2S

water chemistry ..ion concentrations (ppm, same as mg/ltr) INPUT cells A15-L15 The water chemistry is used to calculate the solution pH (see below). Enter ppm values for Na+, K+, Ca2+, Mg2+, Ba2+, Sr2+, Cl-, HCO3-, SO42-_{, Fe2+,} acetate. (NB enter the sum of all organic acids as acetate). Enter the %v/v value for glycol in cell L15. Use the SALTS spreadsheet to check that the total positive and negative charges of the ions are roughly balanced. Any significant misbalance (e.g. >10%) may invalidate the pH calculation. Note that ion charges are handled in general chemistry by using the term "equivalents": 1 mole of positive charges is equal to one equivalent; in other words 0.7 mole of Ca2+ ions is equal to 1.4 equivalents of positive charge. Some further aspects of the acetate entry are discussed on p.19.

T D S...total dissolved solids in water phase (ppm, same as mg/ltr) OUTPUT cell M17 pH2S

LIQUID PARAMETERS

Water Chemistry

Total Dissolved Solids

This is the sum of all the individual dissolved ions concentrations. TDS and [HCO3-] are used in the Oddo & Tomson pH calculation. TDS is also used to estimate the "salting-out" of CO₂ as salinity increases. This will tend to reduce the concentration of dissolved CO₂and thereby reduce the corrosion rate [8]. The box at X19 shows how to apply the salting-out correction. The procedure uses "Henry's Law" to calculate the solubility of a gas in a liquid.

pCO₂ = K_H X_CO2

where K_His Henry's constant (bar/mole fraction) X_CO2 is mole fraction of CO₂ dissolved in brine.

The Henry's constant from the De Waard paper is only valid for a low salinity brine (ca 0.1% NaCl). Therefore, by calculating the true Henry's constant for a specific brine it is possible to apply a salinity correction to the De Waard corrosion rate.

The salt-correction procedure first calculates the Henry's constant used by the De Waard model (equation 28 from the 1993 paper- which is used in the derivation of equation 13 in the 1993 paper),

where K_H is Henry's constant (mole/ltr bar)

Note that this K_H equation from the De Waard paper has different units (mole/ltr bar) from those given earlier (bar/mole fraction). Much of the confusion over Henry's constants arises from the wide and sometimes awkward range of units which can be used to express the parameter. For consistency in this report the De Waard equation for an aqueous solution can be rewritten in order to maintain K_H in units of (bar/mole fraction)..

where K_His Henry's constant (bar/mole fraction) log₁₀K_H=1088.76 T+273−5.113 log₁₀K_H= − 1088.76 T+273−5.113       18 1000

The true Henry's constant is a function of both salinity and temperature (Appendix 1) so that,

Therefore, the salt-correction factor, F_salt, is,

The best way to use F_salt is to apply it to fCO₂ to give an "effective CO₂ fugacity". This "effective fCO₂" will give the correct dissolved CO₂ concentration when used with the other equations in the Cassandra 98 model. The salt correction effect only becomes significant for TDS > 10% w/v.

pH...brine pH control parameter INPUT cell F17

Enter the known pH value, or else enter a letter to accept one of the calculated pH values given in cells F18, F19, or F20

❍ "d" or "D" will accept the De Waard distilled water pH ❍ "o" or "O" will accept the Oddo & Tomson brine pH ❍ "x" or "X" will accept the BP XLpH calculated value. The accepted value is displayed in cell F21 for confirmation.

K_Htrue(for 0−125°C)=(1.77 T+47.1) TDS 10000+(45.2 T+559) K_Htrue(for 125−200°C)=250 TDS 10000+6500 F_salt= KH De Waard K_Htrue Brine pH

When doing a probabilistic calculation using CRYSTAL BALL then a numeric value of pH (either known or calculated) must be entered. Use a normal distribution for the probability adjusting the standard deviation so as to cover appropriate minima and maxima.

pH(CO₂)...pH of distilled water containing CO₂ OUTPUT cell F18

Equation (8) from the 1995 paper...

pH(CO₂) = 3.82 + 0.000384 T - 0.5 log₁₀(fCO₂)

fCO₂ is used here rather than the pCO₂ quoted in the original paper. The equation is valid over 10-80oC. It gives the pH for pure water containing dissolved CO₂ at the prevailing temperature and fCO₂.

pH(act, Oddo) ..Oddo & Tomson calculated pH in brine OUTPUT cell F19

An empirical equation from reference 9...

+0.000000458 (T * 9/5 * 32)2 - 0.0000307 (P * 14.5)...

fCO₂ is used here rather than the pCO₂ quoted in the original paper. The equation is valid up to 200oC and 1200 bar, but is inaccurate for low values of [HCO3-]. The Cassandra 98 spreadsheet is set to give an error for pH(act, Oddo) if [HCO3-] < 50 ppm. pH(CO₂) pH(act) −0.477 TDS 58500       1 / 2 +0.193 TDS 58500       pH=log₁₀ HCO₃−

[

]

pH(act, XLpH) ...XLpH calculated pH in brine OUTPUT cell F20

XLpH is an Excel add-in function for calculating both pure water and brine pHs with no restrictions on salinities or component concentrations. It was developed by XTP, Sunbury using well documented code published by the US Geological Survey (the "PHREEQ" model). The original version of XLpH [10] has since been updated to include pH2S as an input parameter. XLpH has been validated against other pH models such as in CORMED and also against literature and recent laboratory values.

XLpH uses the individual ion concentrations in cells A15-L15. The positive and negative charges must be approximately balanced (see "water chemistry", p15, above). XLpH will automatically compensate for any small misbalances by adding Na+ or Cl- ions.

Enter the sum of all organic acids as acetate. Note that the pH of CO 2-containing-brine will differ depending on whether the acetate is added in the form of sodium acetate salt or acetic acid...

pH of 0.5 M NaCl / 300 ppm NaHCO3, 1 bar CO₂, 25o_{C plus...} no acetate 6.8 mM Na acetate 6.8 mM acetic acid

(i.e. 571 ppm) (i.e. 422 ppm)

5.53 5.41 4.17

XLpH assumes that the acetate value entered in cell K15 is acetic acid, because this is the worst case. If one wishes to assume Na acetate then zero should be entered for Ac and the molar equivalent of Na acetate should be added to the Na and Cl entries. Unfortunately a field water analysis will not directly reveal whether Na acetate or acetic acid should be used to simulate the water chemistry. This can only be established by making laboratory pH measurements under CO₂ saturation and comparing the results with the XLpH model.

Inclusion of the organic acid concentration will always improve the reliability of a prediction. However, when organic acid data is not available it is possible to make some rule-of-thumb approximations in order to aid progress. Organic acids are typically present in formation water at <30ppm. Therefore, for bicarbonate >150ppm, the presence of organic acids is likely to make little pH(act, XLpH)

accepted pH ...confirmation of selected pH OUTPUT cell F21

This is confirmation of the pH value which has been accepted for the corrosion prediction equations.

T...temperature (oC) INPUT cell F24

The prevailing local temperature. When doing a probabilistic calculation using CRYSTAL BALL then use a uniform distribution for the temperature : set F24 as the maximum and G24 as the minimum.

Ts...selected scaling T (o_{C) INPUT cell F25}

Enter a preferred value for the scaling temperature or enter "a" (or "A") to accept the calculated value shown in cell F26.

Researchers are still actively investigating the issue of what happens to corrosion rates at temperatures above the scaling temperature. Previous work has shown that sometimes the scale films are protective and can reduce the corrosion rate, whereas sometimes the films are non-protective so that the corrosion rate continues to increase. Choosing one or other of these options could on the one hand lead to significant under-design, and on the other hand to significant over-design. Therefore, until the matter is fully resolved BP prefers to choose a middle course for design purposes. BP assumes that the corrosion rate reaches a peak at the scaling temperature and remains on a plateau at the same value for higher temperatures. The Cassandra 98 spreadsheet follows this approach. In order to achieve this outcome both fCO₂ and pH are set to a plateau for T > T_s.

T Scaling T IFE, Norway data BP approach De Waard approach Corrosion Rate Accepted pH

Figure 5: The Possible

Effects of High

Temperature Scaling on the Corrosion Rate

T_s...De Waard calculated scaling T (o_{C) OUTPUT cell F26} Equation (13) from the 1995 paper,

This is obtained by setting log₁₀F_scale = 0 (i.e. F_scale = 1) in equation (13) in the 1995 paper. Note that the equation above is expressed in o_{C and uses} fCO₂rather than the oF and pCO₂used in the paper. The 1993 paper gives a similar equation to the 1995 paper but uses a factor of 0.67 in front of the log term instead of 0.44.

d...hydraulic diameter (m) INPUT cell M24

A diameter input value is only required for the velocity equations in the 1995 model. It is not needed for the 1993 model. The 1995 paper actually uses "hydraulic diameter" rather than a simple pipeline diameter. Let D_p be pipeline diameter, and let D_h be hydraulic diameter, then,

..for gas/liquid pipelines, D_h< D_p D_h= 4 A / S

..where A is the cross-sectional area of the liquid in the pipe S is the cross-sectional perimeter length of the liquid region (i.e. liquid/pipe + liquid/gas interfaces, see Figure 6) ..therefore for a pipeline full of liquid, D_h= D_p

De Waard Calculated Scaling Temperature T_s = 2400 6.7 −0.44log₁₀fCO₂       −273 Diameter

There is a box at cell P39 for calculating hydraulic diameters in gas/liquid lines. The ratio of the liquid and gas cross-sectional areas, or the ratio of the liquid depth to the pipe radius, is required as an input parameter. Calculation of this parameter is outside the scope of the Cassandra 98 spreadsheet.

When doing a probabilistic calculation using CRYSTAL BALL then use a uniform distribution for the hydraulic diameter : set M24 as the maximum and N24 as the minimum.

U...flow velocity (m/s) INPUT cell M25

A flow velocity input value is only required for the velocity equations in the 1995 model. It is not needed for the 1993 model. There is a box at cell P5 which enables calculation of flow velocity from pipe diameter and flow in liquid only lines. The calculation is more complicated for the liquid phase in gas/liquid lines, therefore, the box at cell P39 should be used.

When doing a probabilistic calculation using CRYSTAL BALL then use a uniform distribution for the flow velocity : set M25 as the maximum and N25 as the minimum.

cross-sectional perimeter length of the liquid region

Flow Velocity

Figure 6: Explanation

of Parameter "S" in a Gas/Liquid System

V_cor...basic corrosion rate (mm/yr.) OUTPUT cell E32 Equation (13) from the 1993 paper,

The basic corrosion rate is adjusted by multiplying with the pH and occasionally the glycol correction factors (F_pH and F_glyc respectively). The application of each of these is discussed below.

For the basic corrosion rate and the correction factors, the values reached at the scaling temperature are set to remain the same at higher temperatures. This is to ensure that the corrosion rate reaches a peak at the scaling temperature and then remains on a plateau at the same value for higher temperatures (see T_s section above). Hence, the BP approach does take account of scaling at high temperatures but doesn't use the De Waard scaling factor, F_scale, directly.

F_pH...pH correction factor OUTPUT cell G32 Equations (9) and (10) from the 1991 paper,

log₁₀F_pH= 0.32 (pH_CO2- pH_act) for pH_CO2 > pH_act

where ...pH_act is the actual pH of the brine which wets the pipewall ...pH_CO2is the pH under the same conditions but in pure,

salt-free water

log₁₀ F_pH= - 0.13 (pH_act - pH_CO2)1.6 for pH_CO2 < pH_act

Outputs : 1993 De Waard Model

Vcor...Basic Corrosion Rate log₁₀V_cor =7.96− 1710 T −0.67 log10(fCO2) pH Correction Factor

These equations show that as pH_act rises, F_pH will get smaller and so the corrosion rate will fall.

These equations use pH_CO2 instead of the "pH_sat" used in the De Waard paper. pH_sat is the pH at which a brine first becomes saturated with either FeCO₃or Fe₃O₄ as a result of the steel corroding and building up dissolved Fe2+ in the solution. The problem with pH_sat is that it is difficult to define. Even the De Waard paper only gives some approximate expressions for one particular brine composition (10% NaCl). Furthermore, there is serious doubt over the whole concept of a fixed saturation pH due to the observation of massive supersaturation effects by IFE (Norway) and also within BP. Dissolved Fe2+ _{concentrations can often reach hundreds of ppm and can} exceed the theoretical saturation values by orders of magnitude. Hence, pH_sat is not a reliable concept.

Until the pH_sat issue is resolved BP prefer to use pH_CO2 as an alternative reference point. It has the advantage that it is well defined and is valid over a wide range of conditions. Therefore, a pure water system will give pH_act = pH_CO2 and so F_pH = 1 in the BP approach. Certain conditions can make pH_act < pH_CO2 (e.g. high salinity, zero bicarbonate) and so F_pH > 1. The presence of bicarbonate will tend to make pH_act > pH_CO2 and so F_pH < 1. One way of reconciling these divergent approaches is to say that the direct De Waard approach uses Fph to derive the initial corrosion rate in a brine before corrosion products build up and gradually reduce the corrosion rate until it reaches a steady state. This is the issue discussed in the 1993 De Waard paper. The BP approach on the other hand does not deal with initial corrosion rates at all. It deals only with steady state corrosion rates and uses Fph to express the effect of water composition on the steady state rate. This effect is not covered in the direct De Waard approach. In essence BP have taken an equation from the direct De Waard approach and then adapted it for another purpose. Hence, overall, the two approaches are different but consistent.

F_fug...fugacity correction factor OUTPUT cell J32 Equation (3) from the 1991 paper,

Fugacity Correction Factor log₁₀F_fug=0.67 0.0031− 1.4 T+273       P

F_fugis not required in the BP approach because fCO₂ is used in preference to pCO₂ throughout the calculation and so fugacity has already been accounted for.

F_scale...scaling correction factor OUTPUT cell K32

Equation (16) from the 1993 paper,

where ... T > T_s otherwise F_scale = 1

... T_scale is scaling temperature (defined above)

This factor is not used directly in the BP approach. It is included in the spreadsheet only for completeness.

F_glyc...glycol correction factor OUTPUT CELL H32 Equation (20) from the 1993 paper,

log₁₀ F_glyc = A (log₁₀W - 2)

where ... A is a constant = 1.6 to a first approximation ... W is water content (%) of water/glycol mixture

BP only use this factor for cases without corrosion inhibitor. When a corrosion inhibitor chemical is used or is planned then BP assume that any effect of glycol is included within the corrosion inhibitor efficiency (normally 90%, but see discussion on pages 42-48).

V'_cor...corrected corrosion rate (mm/yr.) OUTPUT cell G34

This is BP's preferred output from the 1993 DeWaard model. It is the base corrosion rate multiplied by the F_pHcorrection factor. Note that for the basic corrosion rate and the correction factor, the values reached at the scaling temperature are set to remain the same at higher temperatures. This is to log₁₀F_scale=2400 1 T+273− 1 T_scale+273       Glycol Correction Factor Corrected Corrosion Rate Scaling Correction Factor

The 1995 De Waard model is derived in a different fashion from the 1993 model, in particular it does not use the idea of correction factors applied to a base corrosion rate. Instead, the overall corrosion rate is calculated from two components : the reaction rate V_r and the mass transfer rate V_m.

V_r...reaction rate (mm/yr.) OUTPUT cell G37 Equation (11) from the 1995 paper,

V_m...mass transfer rate (mm/yr.) OUTPUT cell G38 Equation (10b) from the 1995 paper,

V_cor...corrosion rate (mm/yr.) OUTPUT cell G39 Equation (2) from the 1995 paper,

where V_cor is overall corrosion rate V_r is reaction rate

V_m is mass transfer rate

Outputs : 1995 De Waard Model

Reaction Rate

log₁₀V_r=6.23− 1119

T+273+0.0013 T+0.41log10(fCO2)−0.34pHact

Mass Transfer Rate

V_m=2.45U 0.8 d0.2 fCO2 Overall Corrosion Rate 1 V_cor = 1 V_r + 1 V_m

V_cor...merged corrosion rate (mm/yr.) OUTPUT G41

The merged rate simply takes the average of the 1993 and 1995 values. This allows CRYSTAL BALL to combine the probability distributions for the 1993 and 1995 rates so that one can see the lower and upper bounds on the expected corrosion rate.

The 1993 rate is regarded as the minimum. Velocity effects may increase this minimum rate as given by the 1995 value. The 1995 model is not accurate at low velocities so it is ignored whenever it falls below the 1993 value, and then the merged rate is the same as the 1993 rate.

The validity of any corrosion prediction model depends on how well it agrees with the measured corrosion rates in the field. However, the comparison is not always straightforward. This is because the models are developed from well characterised, clean and stable systems in the laboratory, and they are being applied to partially characterised, dirty, and variable systems in the field where the full operating history is not always known. This is no criticism of field activities. It is simply a fact of life of operations where the aim is to produce hydrocarbons, not to generate completely rigorous corrosion data.

The discrepancies between the models and r eal field corrosion data which do exist arise because there are parameters in the field which the model can not take account of effectively, or at all, e.g. surface coatings (scales, corrosion products, biomass), crude oil wetting, local hydrodynamics, weld metallurgy.

The industry generally regards the De Waard model as conservative compared to the field, i.e. it over-estimates the field corrosion rate. Much of this opinion is based on anecdotal and semi-quantitative evidence - often not published in the open literature - but it is confirmed by the occasional formal 1993 & 1995

Merged Corrosion Rate

V_cormerged=Vcor 1993_+V

cor1995 2

from a variety of sources which will be used to assess the Cassandra 98 spreadsheet presented here.

In the meantime Table 7 gives a comparison of the Cassandra 98 spreadsheet against new laboratory data; data which were not used in compiling the model. The final column shows whether the observed corrosion rate falls within 15% of the range encompassed by the 1993 and 1995 models and there is some agreement. However, the discrepancies show the pitfalls in trying to push the accuracy of the model too far. It is best used to gain order of magnitude estimates of corrosive situations rather than absolute corrosion rates to several decimal places.

Table 7: Comparison

of Model Predictions with Laboratory Data

BP 1993 0.1% NaCl, 3 litre flow loop (15 mm ID)

25 1.9 1 5 1.1 5.8 yes

25 1.9 0.27 2.2 0.5 1.9 yes

35 1.9 0.27 3.4 0.7 2 no

BP 1992 Forties brine, beaker test and 5 litre flow loop (15 mm ID)

50 0 0.88 2.5 1.5 0.1 no

50 1.2 0.88 2.5 1.5 3.2 yes

CAPCIS Flow Project Forties brine, flow loop (10 mm ID)

25 3.2 1 1.8 0.6 3.3 yes

50 1.1 0.88 3.8 1.5 3.2 yes

50 1.7 0.88 4.1 1.5 3.9 yes

50 2.5 0.88 2.5 1.5 4.4 yes

50 3.2 0.88 4 1.5 4.7 yes

CAPCIS Flow Project 3% NaCl, flow loop (10 mm ID)

25 3.2 1 6 1.2 7.7 yes 50 3.2 0.88 12.1 3.1 9.2 no 70 3.2 0.88 17.4 5.3 8.4 no 50 1.1 0.88 6.8 3.1 4.8 no 50 1.7 0.88 7.3 3.1 6.4 yes 50 2.5 0.88 8.6 3.1 8.1 yes

corrosion rate (mm/yr.)

T U fCO2 observed 93 95 correct?

"Henry's Law" describes the solubility of a gas in a liquid, pCO₂ = K_HX_CO2

where K_H is Henry's constant (bar/mole fraction) X_CO2 is mole fraction of CO₂dissolved in liquid

Henry's constants are dependant on both temperature and salinity and they are easily found for CO₂dissolved in pure water [e.g. 13]. The data for brines is less extensive [14-16]. Figure 7 is compiled using data from all these sources. The reduced number of points at higher salinity are still sufficient to show that the data in the 0-10% region can be reliably extrapolated up to ca 30% NaCl. Note that the 16 and 31% data at 75 and 100oC are actually for MgCl2 in the original paper but have been plotted in Figure 7 at the equivalent ionic strength of NaCl.

APPENDIX 1 : "Henry's Law" Constants for CO2 Dissolved in Brine

0 2000 4000 6000 8000 10000 12000 14000 0 5 10 15 20 25 30 35 [NaCl] %w/w Kh (bar/mol frac) 200 175 150 125 100 75 50 30 10 T (oC)

The lines in this figure can be represented by the following equations (to within ±15%),

Figure 7: Henry's

Law Constants as a Function of Salinity

where K_His Henry's constant (bar/mole fraction)

Cell AD31 in the spreadsheet uses these equations to calculate the true Henry's constant for the input values of T and TDS.

K_H(for 0−125°C )=(1.77 T+47.1) TDS

10000+(45.2 T+559 )

K_H(for 125−200°C )250 TDS

The value and purpose of predictive corrosion rate models should be neither overlooked nor exaggerated. The models (of which CO₂ models are one example) are tools for the Materials Engineer to use during materials selection studies. The models help to quantify the corrosion risk and to help assess the impact of various process or production scenarios. However, corrosion rate prediction models should always be used in conjunction with other tools such as life cycle costing as well as previous operational experience if the final materials selection is to offer the optimal balance between cost and reliability. As each project will have unique economic factors, materials selection should reflect these and the economic assessment will be as important as the corrosion modelling in the selection of the final materials. In-depth coverage of techniques such as life cycle costing and estimating values are beyond the scope of this document but both techniques are briefly covered in a previous publication [17].

Over the past few years, several design guidelines have been issued by BP for dealing with CO₂ corrosion risks. Each document deals with a specific application. This more general document summarises all previous guidelines but can not deal with the specific issues to the level of detail possible in the individual guidelines. The previously issued guidelines are listed in Table 8.

Table 8: Previously Issued Design Guidelines

A corrosion philosophy for the transport of wet oil and multiphase fluids containing CO₂

This was the first undertaking in recent years to document a BP approach to defining internal corrosion risks and the basic approach is still followed. It recommended the use of the de Waard and Milliams model to predict in-situ corrosion rates along with a 90% corrosion inhibitor efficiency. Much of the work is still valid but it is in the areas of high temperature scaling, corrosion inhibitor efficiencies and impact of various flow regimes that the

Report Title Authors Report Number Issue Date

A corrosion philosophy for the I D Parker ESR.93.ER.013 1/3/93 transport of wet oil and J Pattinson

multiphase fluids containing A S Green.

CO₂

A corrosion philosophy for I D Parker ESR.94.ER.016 28/8/94

the transport of wet J Pattinson

hydrocarbon gas containing A S Green.

CO₂

Assessment of a top of line D Paisley Branch Report 5/10/92

versus bottom of line corrosion J Pattinson No 124 421

ratio for use in the design of S Webster

wet natural gas pipelines

The application of pH D Paisley ESR.95.ER.042 10/4/95

moderation as a means of corrosion control for wet gas pipelines

The effects of low levels of D Paisley ESR.95.ER.073 22/6/95

hydrogen sulphide on carbon R Gourdin

dioxide corrosion: A review of industry practice and a guide to predicting corrosion rates

new guidelines differ. Most of the recommendations made in these guidelines have been reproduced or superseded in the present document and therefore the original guidelines are redundant.

A corrosion philosophy for the transport of wet hydrocarbon gas containing CO₂

This was a companion document to the guidelines on wet oil and multiphase systems. The basic approach was similar but this document dealt with the specific wet gas application. Most of the recommendations made in these guidelines have been reproduced or superseded in the present document and therefore the original guidelines are redundant.

Assessment of a top of line versus bottom of line corrosion ratio for use in the design of wet natural gas pipelines

Wet natural gas pipelines operating under stratified flow have two distinct corrosion environments : (a) the bottom of line which is continually wetted by condensed water, hydrate inhibitor and hydrocarbons, and (b) the top of line which is wetted intermittently by condensing liquids. The corrosion rate at the top of the line is lower than that at the bottom due to the more limited exposure to corrosive species. Predicting this rate is done by predicting the bottom of line rate using models in the normal way and applying a moderating factor for the top of line rate. Up to 1992, BP used a factor of 0.3, i.e. the top of line corrosion rate was predicted to be 30% of the bottom of line rate. When inhibitors are used to control the bottom of line rate, the top of line corrosion rate becomes the limiting rate as inhibitors are assumed not to protect against condensing corrosion. This report reviewed the top of line factor and recommended the adoption of a moderating factor of 0.1. For inhibitor efficiencies up to 90%, the top of line corrosion rate is therefore not the limiting rate. This approach is no longer valid since BP have moved away from the direct use of inhibitor efficiencies, as described later in this report. However, the assumption that top of line rates are 1/10th of the predicted uninhibited bottom of line rates can still be used. For applications were the 'top of line' corrosion rate is the faster rate (using the 0.1 moderating factor) then a more detailed evaluation should be carried out. Such a scenario does not lend itself to the use of simplified guidelines.

The application of pH moderation as a means of corrosion control for wet gas pipelines

This technique is not widely applicable but may find niche applications in highly corrosive wet gas lines utilising recycled glycol for hydrate control. It is covered in more detail on p75 but if this technique is of interest the full guideline document should be reviewed.

The effects of low levels of hydrogen sulphide on carbon dioxide corrosion: A review of industry practice and a guide to predicting corrosion rates

This document summarised how low levels of H₂S influence corrosion rates dominated by CO₂. The conclusion was that H₂S at levels below the NACE criteria for sulphide stress corrosion cracking (ref MR0175, NACE Publications) reduces general metal loss rates but can promote pitting. The pitting proceeds at a rate determined by the CO₂ partial pressure and therefore CO₂-based models are still applicable at low levels of H₂S. Where the H₂S concentration is greater or equal to the CO₂ value, or greater than 1 mole%, the corrosion mechanism may not be controlled by the CO₂and therefore CO₂based models may not be appropriate.

Summary of Previous Guidelines

In summary, the old guidelines are generally still applicable. What has changed is BP’s views on the reliability and performance of corrosion inhibitors as well as the availability of updated models incorporating flow affects. The old guidelines defined a corrosion inhibitor efficiency of 90% with no scope for variation. There were also stringent velocity restrictions for use under multiphase conditions which restricted the energy of slug flow to below 20 Pa, later raised to 100 Pa. In light of favourable field data, this approach is now seen as too pedantic and inhibitor availabilities are seen as a better way of describing the role of inhibitors. These differences in approach are covered in more detail in the following sections. Furthermore, the corrosion rate prediction model (p5-30) does not cover some aspects that are important during design and these are covered in the next section.

The modelling approach outlined in this document deals with all the inputs (mole% CO₂, temperature etc.) on a deterministic basis. However, each input will have a level of uncertainty associated with it and this can have important effects on the outcome. One way to deal with this it to calculate a range of output values, (in this case the predicted corrosion rate) across the whole range of input values. Where the model is dealing with several inputs (temperature, pressure, CO₂ mole %, pH, scaling factor), this can be time consuming. Also, the value of these inputs will not all vary in a uniform manner. Some will behave uniformly while others may behave in a normal or log-normal manner.

Calculating the impact of all these variables is time consuming, unless a programme such as Crystal Ball is used. This is an add-in to Excel and handles the variability by performing a Monte Carlo analysis. Any number of iterations can be performed and the output is displayed in terms of a probability, rather than as a discreet value. In general, a minimum of 1,000 iterations, involving tens of thousands of individual calculations are required to show the effects of the variability in input data. A modern PC can perform such a task in a minute or two.

The important factors to consider are the range and type of distribution assumed for each variable. If process data are available, this will form an ideal basis for determining the range and type of distribution but if this is lacking, some assumptions will have to be made.

Using distributions to define variables in a predictive model can have significant effects on the outcome.

Engineering design traditionally uses worst case inputs so that the final design will be safe under all foreseeable combinations of events. This approach has also been adopted when predicting corrosion rates, where pressure and temperature etc. are used as inputs to the models. In the past this approach was the only viable one as predicting the enormous range of possible outcomes for all variables would have been too time consuming but it can result in substantial over-design. Metal loss corrosion processes do not lead to sudden failure due to a combination of variables over short time periods

Worst Case Design

Important Factors not Covered by the Corrosion Model

The Probabilistic Approach to

(unlike high pressure which can lead to an instantaneous failure) but rather reflect a combination of varying conditions over a longer time period. Using the worst case values is therefore not a sensible approach, if a range of more realistic values can be handled.

In defining a range of likely operating variables such as temperatures and pressures, the design values will form the maximum for the respective distributions but lower values should be included. Defining this range will require inputs from the Process and Reservoir Engineers. Due to the nature of the uncertainty, such that all values within the range are as likely as each other, Uniform distributions are probably the most appropriate for these variables.

The yield strength and wall thickness of linepipe are other examples of the type of variables that can be treated in this manner. The linepipe properties are important if using corrosion models to calculate mean time to failure. Rather than using the minimum values for each, based on the specified material and the variation allowed within the specification, typical distributions can be defined for each value. Such variables tend to be distributed normally around a mean with the specified minimum properties defining a lower bound.

Many variables in corrosion rate predictions, such as the level of CO₂in the gas phase, are based on “best guess” or on limited well test data. No attempt is made to define the uncertainty in these data and this is a major limitation of deterministic modelling. In defining the distributions of such variables, the mean value should be based on the best guess or well test data in a similar way to the deterministic approach. However, a range of possible values should be considered. In the absence of any other information, the distribution of values is likely to be symmetrical around the mean with the greatest probability associated with values close to the mean. The Normal distribution is a familiar example of this type and should be used.

It should be noted that using a symmetrical distribution, such as a Normal distibution, does not correspond to using a single value equal to the mean if the variable under consideration has a non-linear relationship with the outcome. For example, the corrosion rate prediction model used by BP states that:

Non-Linear Relationships

Therefore, the corrosion rates associated with the CO₂partial pressure values in the Normal distribution that are greater than the mean value are closer to the mean corrosion rate than those associated with the values below the mean CO₂ partial pre s s u re. In other words, defining symmetrical distributions for variables whose influence is described by a power < 1 produces a non-symmetrical distribution of outcomes (predicted corrosion rates). The mean value of this distribution will be lower than the single value calculated using the mean of the input variable.

The same applies to all symmetrical distributions, including Uniform distributions. In the previous section on 'worst case design', the uncertainties regarding operating temperature and pressure were discussed. In both cases, Uniform Distributions were used to define the range of possible values. In corrosion rate modelling, both these inputs have non-linear relationships with the outcome (predicted corrosion rate). The effect of pressure is moderated by a fugacity coefficient related to the non-ideality of CO₂. Therefore, considering a range of pressures distributed symmetrically around a mean value will tend to reduce the predicted corrosion rate.

The effect of temperature on predicted corrosion rates is strongly non-linear. At higher temperatures, the role of protective corrosion products or scales can be important. There is a great deal of uncertainty in the effects of these scales but the bounds of the expected values can be defined using existing models. One approach would be to use a log normal distribution, defined as follows:

1. The de Waard & Milliams unscaled rate (upper bound), 2. The de Waard & Milliams fully scaled rate (lower bound),

3. A modal value equivalent to the standard BP approach that uses the scaling temperature to calculate the corrosion rate for all temperatures above this.

Again, the outcome of considering a range of temperatures symmetrically distributed around a mean will tend to be a lower corrosion rate estimation than found by calculating a single value at the mean temperature.

Each input into a corrosion rate prediction should be considered and a range of possible outcomes defined. By consideration of the way in which the

Summary of Inputs to a Monte Carlo

1. Where variations would be due to nature, such as the difference in CO₂ levels around the field, a Normal Distribution should be used with a mean equivalent to the best guess. Figure 7 shows an example of a Normal Distribution describing the expected variation in CO₂ levels, centred around a mean of 5%.

Figure 7: An Example of a Normal

Distribution for the concentration of CO2 in a gas. The Mean Value is 5 mole% with a range of 3 to 7 mole%.

2. Where an input may vary over a wide range but would be expected to be skewed around the 'best guess' or predicted value, a Log Normal Distribution should be used. The effects of high temperature scaling would be an example of this type of distribution, or the pit depth at which inhibitors fail to control corrosion. Figure 8 shows the Log Normal Distribution used to describe the critical pit depth with a modal value of 8 mm and a range of 5 to 12mm.

Figure 8: An Example of a Log Normal Distribution describing the critical pit depth.

Figure 9: An Example of a Uniform

Distribution Describing the Flowline Operating Pressur e

3. Where a value may occur equally often within the defined range e.g flowline operating pressure, a Uniform Distribution should be used, i.e. all values are equally likely to occur. Figure 9 shows how a range of flowline operating pressures can be described. In this case the range of 1,000 to 1,200 psi has been used.

Table 9 summarises the assumptions used in a recent probabilistic study into mean time to failure, based on CO2 corrosion risks. As the study looked at failure mechanisms as well as corrosion rates, some of the factors apply to the linepipe steel while others apply to the CO2 prediction model. The 'Standard Value' corresponds to the value that would be used in a deterministic study. The Table does not attempt to fully define the distributions in a statistical sense but more information is available from the authors if required.

Linepipe Wall thickness e.g. 0.75" Mean = 0.75" Normal SD = 0.01

Linepipe Yield Stress SMYS Mean = 70 ksi Normal e.g. 65 ksi SD = 2.5 ksi

Linepipe Flow Stress - - - - 1.15 x Yield Stress Normal

Fluids CO₂Content 5 mole% Mean = 5% Normal SD = 0.72

Fluids Temperature 110oC 85 - 110oC Uniform

Fluids Pressure 1,200 psi 1,000 - 1,200 psi Uniform

Corrosion Water pH Cormed * Cormed * Normal

model prediction ± 0.25 units

Corrosion Corrosion rate >Rate at scaling Unscaled to Log Normal

model scaling ToC temperature fully scaled

Inhibitor Inhibitor 90% 65 - 95% Log Normal

efficiency availability

Inhibitor Critical pit depth 8 mm 5 - 12 mm Log Normal

efficiency

Inhibitor Inhib. effic. > 0% 0 - 90% Uniform

efficiency critical pit depth

Table 9:Summary of Variables Modelled, the Values that would be Assigned Using a Standard Approach, and the Range of Values Used in the Example Study

Component Variable 'Standard Range Used Distribution

in study Value'

Note * Cormed is a software programme which can predict in-situ pH values of oilfield brines.

Figure 10 shows the output from a Monte Carlo simulation, using 20,000 iterations to determine the distribution in outcomes (predicted corrosion rate) due to the variation in inputs detailed above. The most likely corrosion rate is circa 1 mm/yr. While there is a possibility that higher or lower rates occur, the probability of such rates decreases the further they are from the most likely outcome.