Frederick H. WaltersUniversity of Southwestern Louisiana

Lafayette

An empirical statistical model has been developed to obtain the corrosion rate of tubulars in gas condensate wells.

This correlation includes four surface parameters: chloride content, wellhead pressure, percent erosional velocity, and pH.

### MODELING CORROSION

Corrosion models can have several degrees of understanding and complexity as follows:

- A black box model (as in neural networks) has inputs that enter the black box and provide an output. No known relationship or equation relates the parameters to the output.
- Statistical models can be developed from existing data, but are limited to the range of data used and the number of situations included.
- Quadratic models with interaction terms are obtained from experimental design, where parameters and their values are controlled, along with response surface methodology.
- Computer models, a level above the other models, incorporate many factors, including flow and temperature characteristics.1 3

Empirical models have used correlations with C02 partial pressure,4 C02 partial pressure and temperature, water production rate, and the Copra relationship.6 All of these models are limited in nature.

As an alternative, this study examined 13 surface parameters from which 4 were chosen for the correlation.

### PARAMETERS

Field data from 21 gas-condensate wells were collected. The actual corrosion rates were obtained from caliper data or actual time to failure.

The field data can be divided into four groups.

- Production rates
- Well completion data
- Reservoir, wellhead, and separator pressure and temperature
- Production fluid composition.

Not all data were available for each well.

The wells selected represent a broad spectrum of gas condensate wells located on three continents. For further information on the wells see Reference 3.

The 13 parameters examined and their ranges are:

- C02 partial pressure, 5.6 187 psi
- Water production rate, 4 52 b/d
- Gas production rate, 0.79 38.6 MMscfd
- Iron production rate, 0.013 1.39 lb/day
- pH measured, 4.6 7.63
- pH calculated,7 2.6 6.03
- Alkalinity, 0.61 686 ppm
- Chloride content, 22066,500 ppm
- Wellhead temperature, 90 220 F.
- Wellhead pressure, 305-7,180 psig
- Actual velocity, 8.36-54.77 fps
- Percent erosional velocity, 16.6 123.2
- Velocity difference, 7.42 42.2 fps.

### ANALYSIS

The data were transformed by taking the natural logarithms of the raw data. Stepwise regression and stepwise robust regression were performed using Number Cruncher, a statistical program.

Table 1 shows the results of the stepwise linear regression of the natural logarithmical transformed data, as well as robust linear regression of the four factor case. Models were developed using three to seven parameters. The parameter order is C13, C11, C9, C15, C4, C6, and C7.

Perfect correlation exists when R2, Table 1, is equal to 1. At this point no other factors need to be added to the equation because the other factors are either taken care of by the factors already included or are not significant.

The best fit is obtained from the four parameter model that includes pH calculated, pressure, chloride concentration, and percent erosional velocity. Table 2 shows the measured corrosion rate and the values calculated from each model.

Robust regression minimizes the effect of outliers, and this is the technique used in Model 3 because two wells have high values and two others have low values. A linear model using the raw data was developed and discussed in Reference 3. The model included pH, iron production, velocity difference, and percent erosional velocity.

The pH is a major factor in both sets of models. Flow characteristics such as percent erosional velocity are difficult to model in the laboratory but are important in the models discussed.

The pH was calculated using the relationship developed by Oddo and Tomson.7

The logarithmic linear model can be transformed to the exponential equation:

CR,m v = 3.57 x 1010

(C1 )0.271 (P)0.48 (% V)0.826/ (pH)18.43

### ACKNOWLEDGMENTS

The help of James Garber (University of Southwestern Louisiana corrosion center) and Cedric Adams (Baker Performance Chemicals) is gratefully acknowledged.

### REFERENCES

- Fang, C.S., Garber, J.D., Perkins, R.S., and Rienhardt, J.R., "Computer model of a gas condensate well containing carbon dioxide," Paper 465, Corrosion 89, NACE meeting, New Orleans, 1989.
- Fang, C.S., Garber, J.D., Perkins, R.S., and Rienhardt, J.R., "Gas condensate wells computer model Phase 111," Paper 44, Corrosion 90, NACE meeting, Los Vegas, Nev., 1990.
- Adams, C.D., Garber, J.D., Walters, F.H., and Singh, C., "Verification of computer modeled tubing life predictions by field data," Paper 82, Corrosion 93, NACE meeting, New Orleans, 1993.
- Rhodes, J., and Clark, W., Ind. Engr. Chem., Vol. 28, No. 1078, 1936.
- Bradburn, J., "Water production: An index to corrosiveness," C02 Corrosion in Oil and Gas Production, NACE, 1983.
- Hausler, R.H., and Garber, J.D., "The COPRA correlation revisited," Paper 45, Corrosion 90, Los Vegas, Nev., 1990.
- Oddo, J.E., and Tomson, M.B., "Simplified calculation of CaCO3 Saturation at high temperature and pressure in brine solutions," JPT, July 1992, pp. 1583 90.

*Copyright 1994 Oil & Gas Journal. All Rights Reserved.*