**John E. Oddo***Champion Technologies Inc. **Houston*

**Mason B. Tomson***Rice University **Houston*

- Fig.1 [300,902 bytes]
- Table 1 [154,792 bytes]
- Recommendated Equations [34,678 bytes]
- Recommendation Equation con't [20,586 bytes]

The calculations are accurate and useful for determining why failures have occurred, predicting future failures, determining chemical use rates, and selecting materials.

The calculations can be programmed in a spreadsheet to generate a comprehensive scale and corrosion model.

Because flowing pressures are required for accurate calculations, an algorithm to calculate flowing pressures must be developed in-house, or a commercial program can be obtained that can be combined with the prediction equations.

### Scale, corrosion model

Scale and corrosion continue to be serious and costly problems in gas and oil wells and production facilities. Algorithms that accurately predict the severity and location of scale deposition and corrosion allow one to develop and design early treatment programs and to determine if special materials need to be included in the installation. For effective corrosion prediction and treatment, one needs to recognize the relationships that exist between scale and corrosion. In a severely corrosive fluid environment, scales can form a protective coating over exposed surfaces, reducing or completely eliminating corrosion. This concept resulted in the Langelier saturation index that is used in methods for protecting water delivery pipelines.^{1}

The calculations discussed in this article are based on a unification of the revised scale prediction methods of Oddo and Tomson^{2-4 }and the CO_{2} corrosion prediction methods of de Waard and Lotz.^{5}

The prediction model uses produced water chemistry and production volume data, as well as flowing wellhead temperature and pressure, and bottom hole temperatures and pressures to estimate temperatures and shut-in and flowing pressures in a well to calculate the needed parameters.

The model will accept a downhole pump and can be used with wells containing rod and electrical submersible pumps.

The calculations are accurate and result in a scale/corrosion model that can be used to develop field treatment strategies and/or assist in material selection. As is true with the de Waard and Lotz methods, the corrosion calculations predict a "worst case" scenario.

Oddo and Tomson derived equations from the chemical properties of the needed components of mineral scales to determine the degree of saturation of the scale in the produced water at specific temperatures, pressures, and ionic strengths. As other authors have done, Langelier^{1} for example, the degree of saturation of a scale is given by the saturation index or the log_{10} of the ratio of the ion activity product of the scale components to the solubility product of that particular scale.

Oddo-Tomson defined a conditional solubility product that varied with temperature, pressure, and ionic strength to eliminate the need for activity coefficients in the calculations. The Oddo-Tomson saturation index is defined as the log_{10} of the product of the concentrations of the scale-forming components divided by the conditional solubility product.

The corrosion prediction equations used in this article are those of de Waard and Lotz.^{5} Reference 5 discusses a mechanism for carbon dioxide corrosion and includes data from which their equations were derived. Deviations to these equations used to developed the model presented in this article are noted.

### Predicting scale

For this model, the functional form of the equations, from References 2 and 3, used to calculate the needed solubility and stability constants has been changed from five or six terms to eight terms.Most of the scale-prediction equations have been completely revised. The predictions resulting from the revised equations have been compared to Pitzer-type calculations and have been found to be accurate. Generally, the equations are of the form:

-logwhere: (K_{10}(K_{c}) = a + bT + cT^{2}+ dP + eI^{0.5}+ fI + gI^{1.5}+ hTI^{0.5}

_{c}) is the conditional constant, T is temperature (°F.), P is pressure (psi), and I is the ionic strength of the produced water (molar).

Table 1 lists the parameters for the eight terms and their associated calculated constants. The equation box contains the rev ised equations for calculating the calcite saturation index (SI_{c}). The example box shows the saturation index calculation for gypsum. The other saturation indices for the sulfate scales are determined in the same manner except for a different conditional solubility equation and with the relevant metal cation.

### Corrosion prediction

De Waard and Lotz^{5}derived Equation 1 (see equation box) as a general prediction equation for the corrosion of carbon steel, where Vcor is the corrosion rate in mm/year. The equations necessary to calculate the parameters in Equation 1 are not shown in the table but will be discussed.

The results of Equation 1 are subsequently modified in their paper to account for other effects on the overall corrosion rate. The effects on these correction factors will be briefly described so that the reader can understand how the scale and corrosion-prediction algorithms have been combined.

### Deviations

The c in Equation 1 was defined by de Waard and Lotz to be a constant, c = 2.62 x 10^{6}. However, it was found that corrosion predictions in wells with relatively low flow rates were significantly underestimated with c equal to a constant.

In this article, c is made a function of the Reynolds Number (Equation 2) and is correlated with the corrosion equations by setting c equal to the de Waard value of 2.62 x 10^{6} at a Reynolds Number (Re) of 0.0.

The c value then increases with the square of Re.

With c defined in this manner, the corrosion equations gave reasonable results for wells with low flow rates, and the cVmass term becomes negligible at higher flow rates as required and noted by de Waard and Lotz.

The dynamic viscosity needed for the Re calculation was obtained from the kinematic viscosity Equation 8.6 This equation differs slightly from the equation used by de Waard and Lotz.

The kinematic viscosity obtained was corrected for the ionic strength of the water using data from Reference 7, pp. 24-17. A new kinematic viscosity was then calculated from the corrected dynamic viscosity for use in the corrosion equation.

Oil viscosity was also included in the Re calculations for the field examples discussed in this article. Oil viscosity was estimated by the method of Beggs and Robinson.^{8}

The value of 1,710 in the temperature term of Equation 3 was calculated to be 1,543 in the general corrosion equation by de Waard and Lotz. However, this value seemed to overestimate the corrosion rate in well systems with a high Re.

In the model presented in this article, the previously derived value of 1,710 (see de Waard and Lotz) was used in the corrosion equation. It may very well be that the value of 1,543 is more correct, but more corrosion rate data are needed to test the model.

In the original derivation, pHact was intended to be measured or calculated using methods not described in the paper. In the model developed by Oddo and Tomson,2 3 the pH at any point in the system can be calculated using the scale-prediction algorithms. The calculated pH is used in this article as pH_{act}.

This is not a small issue based on the practical difficulties involved with obtaining meaningful pH values in a pressured flowing system, especially, downhole.

The parameter [H_{2}CO_{3}] can be calculated using equations available in the de Waard and Lotz paper. However, all of the parameters necessary to make this calculation, the fugacity coefficient, the partial pressure of CO_{2}, and the Henry's Law constant, are available in the scale prediction calculations.

The scale-prediction calculations for these variables were used because they are functions of temperature, pressure, and ionic strength. The value obtained in the de Waard and Lotz paper is a function of temperature only.

### Correction factors

The results of the general corrosion equation (Equation 1) are multiplied by correction factors. These decrease the amount of corrosion predicted. Neither the corrections for glycol or inhibition^{5}are included in this discussion, or in the derived model.

### Scale deposition

Protective films formed by mineral scale deposition have long been known to reduce or eliminate corrosion in pipes. FeCO_{3}or Fe

_{3}O

_{4}film deposition is accounted for in the de Waard and Lotz paper with Equation 12, where F is a general correction factor with a value of 0.0scale<1.0 and f

_{g}p(b)co

_{2}is the fugacity of co

_{2}in bars.

The fugacity coefficient, f_{g}, the mole fraction of co_{2} and the total pressure at any point are calculated when obtaining the saturation index for calcite scale and are used in this equation to obtain a value for f_{scale}.

In addition to FeCO_{3} or Fe_{3}O_{4} deposition, calcite scale deposits will also reduce or eliminate corrosion. another scale-correction factor is introduced to account for the effects of calcium carbonate scale on the overall corrosion rate.

The same approach taken in the previous discussion will be applied. A correction factor, fcalcite, is defined with values of 0.0

When sic is 0.4 or higher, fcalcite is set equal to 0.0 because this value, based on field experience, is when calcite Scale will deposit in a nonturbulent production system.

Local turbulence caused by a choke, a no-go nipple, etc. will increase the scaling tendency locally.

If calcite-scale deposition is taking place, the corrosion rate should be 0.0. fcalcite is set equal to 1.0 when sic is equal to or less than -0.4 and is a linear function from 0.0 to 1.0, depending on sic.

More information is needed regarding the transition zone between definite scaling with no corrosion, and corrosion not influenced by the saturation of scaling materials.

It is obvious that any other bulk massive scale should also inhibit corrosion, for example barite. however, more information regarding the controlling si values for definite scale deposition of these other scales is needed. Correction terms for other scales could be included in the model.

Foil is a factor to correct the corrosion rate in low water cut oil wells. When this occurs, the water is assumed to be entrained in the oil phase and not available to react with the tubing.

De Waard and Lotz set this term equal to zero when the water cut is less than 30% and the liquid velocity is greater than 1 m/sec, and to 1.0 when these conditions are not met.

In this article, the factor is increased linearly from 0.0 to 1.0 for 15-30% water cuts (equation 14). This factor may seriously underestimate corrosion in gas condensate wells, because the model assumes that the input oil production exists in all parts of the well.

In fact, the condensate fraction is decreasing with depth and pressure and the relative water production is increasing.

In condensate wells, the factor may not be necessary because as the condensate fraction increases, the water may not be entrained in the condensate phase. in that case, water would be available to corrode the well tubulars.

Obviously, a correction term could be included in the model to determine the amount of condensate formed. This would correct the corrosion rate.

### Field Applications

To apply the model in the field, some additional information is required. temperatures and pressures in the well system need to be estimated at various intervals in the well.In the model, temperature is calculated with a linear temperature well bore gradient. this can introduce serious errors in some systems involving massive carbonates, for example. However, in most cases this assumption should not dramatically affect the overall scale and corrosion predictions.

The bottom hole pressure is calculated from the input pressure gradient. this number is required to calculate bottom hole %CO_{2} in the gas phase if %CO_{2} at surface is unknown.

Even if %CO_{2} is known at the surface, it is wise to run the model without inputting a %CO_{2} and alter the water chemistry (total alkalinity) to calculate a %CO_{2} at the surface, which is consistent with the measured value.

This procedure will tend to reduce errors in the alkalinity measurements, especially if the alkalinity of the weak organic acids is not measured and is unknown. Unfortunately, the contribution of the weak organic acids to the total alkalinity is not commonly measured. however, for accurate calcite scale and corrosion prediction, a value for the weak organic acid alkalinity is required or the total alkalinity must be altered by the previous procedure if the %CO_{2} is known with confidence for that particular well.

A good estimate of the weak organic acid alkalinity can be easily obtained in the field or in the laboratory while measuring total alkalinity. The fraction of the total alkalinity due to bicarbonate can then be calculated as a function of temperature and pressure for each point of interest in the system.

The value required by calcite scale prediction algorithms is the true bicarbonate alkalinity. (See Oddo-Tomson^{3} for a complete discussion.) For these reasons, poor results will be obtained from the model by forcing a %CO_{2} measured value on a water chemistry that does not include a measurement of the contribution to the total alkalinity of weak acids other than bicarbonate.

In this case, it is better to alter the total alkalinity until a calculated %CO_{2} is obtained that is consistent with the measured value.

If a measured %CO_{2} value is not available, it is imperative to obtain the alkalinity due to other weak acids. It is also unwise to use field average values for the %CO_{2} in a particular well. poor results will generally be obtained.

Flowing pressures in the well were calculated from the weight of the produced gas and liquid column and the wellhead pressure. The flowing tubing pressure is calculated from the wellhead, downhole, and also from the bottom hole conditions up the well bore to the wellhead pressure.

When convergence is obtained to less than 1.0 psi at intervals in the well bore, the pressure is accepted as an accurate estimate of the flowing pressure. The produced fluid column weights are corrected at intervals in the well bore for the temperature and pressure effects on water density,^{9} solution gas and oil density,^{10} and gas expansion.

Pressure drop in the well bore due to flow is calculated using a combination of equations 15 and 16.

The model calculates a bubble point pressure using the solution-gas calculations if a bubble point will be encountered in the well. the bubble point pressures calculated in the model were consistent with the bubble point pressures estimated from the lasater correlation.^{11} calculated flowing pressures are used for scale and corrosion calculations because those pressures are operative during flow.

Required input into the model is shown in the example box. Fig. 1a shows the scale and corrosion predictions graphically for example 1.

### Example 1

The first example (see example box) is a well with an electrical submersible pump (ESP) set near the level of the perforations. The model predicts that the fluids are corrosive below the pump and into the ESP.As is common in an ESP, fluid temperature increases from one end of the pump to the other. At the output side of the pump, the system is scaling relative to calcite due to the 50° f. increase in temperature, in spite of the pressure increase. As temperature decreases in the upper part of the well, the system becomes corrosive, and serious corrosion is predicted for the upper parts of the well.

The most serious corrosion is at about 1,600 ft.

Scale is predicted in the flow lines after the choke and in the heater treater. Note that the fluid level in this well is a negative number, indicating that the well will flow at the surface without a pump.

In the field, the ESP failed after less than 3 months in the hole. when the tubing and pump were pulled from the hole, serious corrosion was found at the input side of the pump and in the tubing further up the hole. the most severe corrosion was in the region of about 1,500 ft.

The ESP failed due to calcite scale deposition in the pump section. the most severe deposition was in the mid and upper (hottest) sections of the pump.

Scale also occurred in the surface facilities, as predicted by the model.

The iron concentration in the produced water was 35 mg/l. and was consistent with the corrosion occurring in the well when compared to the sandstone calculated iron concentration of 3 mg/l.

The sandstone calculated iron concentration is derived for sandstone reservoirs from the comparative solubilities of iron and calcium carbonate, the calcium concentration, and the overall water chemistry. The calculation does not work well in carbonate reservoirs because they can be seriously deficient in iron relative to calcium due to the depositional environment.

### Example 2

Example 2 illustrates the importance of correcting the total alkalinity for the contributions of other weak acids.Fig. 1b shows the scale and corrosion profile of the second example. The well is produced with a rod pump set 4,000 ft above the perforations. the well produces 50 mcfd, 25 bo/d, and 200 bw/d from a depth of 8,500 ft.

The fluids are corrosive in the entire well, with the worst corrosion near the pump. however, the model assumes the same tubing size to the perforations. because there is no tubing set below the pump, the actual corrosion rate in the 6-in. casing below the pump is much less than that shown in Fig. 1a.

A separate calculation can be run with 6-in. tubing to show the corrosion rate below the pump. In addition, when entering the tubing id in the calculations, the rod diameter must be subtracted from the tubing id.

The well depicted by Fig. 1b must be treated with corrosion inhibitor every 2 weeks, or failures will occur within 1-2 months after a workover. As the model shows, the most serious corrosion is near the pump, and it is less in the shallower portion of the hole.

Scale has not been detected in this well. This is consistent with the model predictions.

The barite saturation index increases to 0.49 at the wellhead, but this is not sufficient to precipitate barite scale. Laboratory experiments done at rice university suggest that the saturation index necessary to precipitate barite scale is much higher than the 0.4 si used for calcite and is in the region of sib ? 0.9.12

Fig. 1c shows the same well profile, but all of the alkalinity was attributed to bicarbonate, ignoring the alkalinity due to other weak acids. In addition, the calculated %CO_{2} in the gas phase was ignored and the measured value of 3.4% was input. Note the dramatic increase in scaling tendency and the decrease in the corrosion rate.

The fact that the scaling tendency is so high in a high-fluid well downhole at the perforations should be a clue that there is a problem with the input data. The total alkalinity was 1,586 mg/l., while the (ignored) alkalinity due to other weak acids was 1,013 mg/l.

Fig. 1d shows the same well profile as Figs. 1b and c, also ignoring the alkalinity due to weak acids other than bicarbonate. However, in this example no %CO_{2} was input into the model. the model calculates a %co2 in the gas phase of 20.5%. The result is a predicted corrosion rate over 2.5 times as high as would be calculated with the other weak acids included in the calculations.

### Example 3

Fig. 1e is for a rod pumped well in west texas that produces from a carbonate formation. The formation has been waterflooded with water having a high sulfate concentration.The well produces 130 mcfd, 54 bo/d, and 110 bw/d from 6,500 ft. the pump is set at 3,132 ft.

Two types of mineral scale are produced from the well. calcium sulfate scale is deposited shallow in the reservoir, in the perforations, and deep in the well bore. Calcium carbonate scale is deposited from the wellhead down to about 1,000 ft.

The well is corrosive from the pump to about 1,500 ft and must be treated with corrosion inhibitor. In addition to the corrosion treatment, the well is squeezed periodically to inhibit scale deposition.

The model correctly predicts the scale and corrosion profiles in the well. The model predicts anhydrite scale as the thermodynamically predicted calcium sulfate phase, but it is known that gypsum often forms kinetically when anhydrite is predicted thermodynamically.^{13}

The calcium sulfate si threshold for scale deposition can also be shown to be lower than that for calcite scale in laboratory work done at rice university.^{12} the value appears to be about 0.2, but more work is needed to improve the accuracy of the value. however, this value appears to correctly predict calcium sulfate scale deposition.

### Example 4

Fig. 1f depicts a gas well offshore Louisiana. The well produces 4 mmcfd and 300 bw/d. from a depth of 15,000 ft. As is common in deep gas wells, the well bore scales with calcium carbonate at the perforations and in the production tubing, deep in the well bore.The scale problem in this well was so bad that the tubing was bridged completely with calcite scale near the perforations. The scale in the well was treated with acid pumped through coiled tubing. Acid was flushed into the formation to bring the well back into production.

The well is corrosive in the upper 10,000 ft with the most severe corrosion taking place in the upper 4,500 ft.

Again, the model correctly predicts the scale/corrosion profile. No barite scale has been found in this well, but barite scale was recovered downstream due to a water incompatibility problem.

The iron concentration in the produced water was 204 mg/l. The high iron concentration is consistent with the corrosion occurring in the well, especially when compared to the calculated sandstone iron concentration of 7.2 mg/l.

This example also demonstrates the importance of calculating flowing pressures in the well bore when predicting scale or corrosion. the bottom hole shut-in pressure during production will not predict scaling at the reservoir level and will generate a poor scale corrosion profile.

### Example 5

Fig. 1g is the scale corrosion profile of a gas and oil well onshore louisiana. The well produces 2.9 mmcfd, 1,100 bo/d, and 300 bw/d from a depth of 15,522 ft. The flowing tubing pressure is 2,000 psi at the wellhead.The scale corrosion profile is similar to example 4, but the scaling tendency is less at the perforations because of the increased pressure caused by the greater weight of the fluid column.

The well has a positive scaling tendency over its entire length. This decreases the corrosion that might be expected. However, due to the high flowing tubing pressure, the well is corrosive with the most severe corrosion taking place at the wellhead. again, the model is consistent with the field experience.

Production declines in this well were attributed to scale near the perforations. An acid job brought the well back to full production.

A scale squeeze should be performed on this well to eliminate scale deposition in the future.

### References

- Langelier, W.G., "The Analytical Control of Anti-Corrosion Water Treatment," Journal AWWA, Vol. 28, 1936, p. 1,500.
- Oddo, J.E., and Tomson, M.B., "Simplified Calculation of CaCO3 Saturation at High Temperatures and Pressures in Brine Solutions," JPT, Vol. 34, 1982, pp. 1583-90.
- Oddo, J.E., and Tomson, M.B., "Why Scale Forms and How to Predict It.," SPE Production and Facility Journal, February 1994, pp. 47-54.
- HE, S.L., KAN, A.T., Tomson, M.B., and Oddo, J.E., "A New Interactive Software for Scale Prediction, Control and Management," Paper No. SPE 38801, SPE Annual Technical Conference and Exhibition, San Antonio, 1997.
- De Waard, C., and Lotz, U., "Prediction of CO
_{2}Corrosion of Carbon Steel," Paper No. 69, Corrosion 93, NACE, Houston, 1993. - Swindells, J.F., Handbook of Chemistry and Physics, The Chemical Rubber co., 1970.
- Bradley, H.B., Petroleum Engineering Handbook, SPE, Richardson, Tex., 1989.
- Beggs, H.D., and Robinson, J.R., "Estimating the Viscosity of Crude Oil Systems," JPT, September 1975, pp. 1140-41.
- Kell, G.S., "Volume Properties of Ordinary Water," J. of Chem and Eng. Data, Vol. 12, 1967, pp. 67-68.
- Vasquez, M., and Beggs, H.D., "Correlations for Fluid Physical Property Prediction," JPT, June, 1980, pp. 968-70.
- Lasater, J.A., "Bubble Point Pressure Correlation," Trans., AIME, Vol. 213, 1958, pp. 379-81.
- Tomson, M.B., Rice University, Unpublished Data, 1997.
- Cowan, J.C., and Weintritt, D.J., Water Formed Scale Deposits, Gulf Publishing Co., 1976, p. 586.

### Books

An Introduction to Saline Lakes on the Qinghai-Tibet Plateau, by Zheng Mianping. Published by Kluwer Academic Publishers, P.O. Box 989, 3300 Az Dordrecht, The Netherlands. 294 pp., $207. This book deals with the temporal-spatial evolution of the plateau saline lakes and the prospects for inorganic salts and organic resources and their exploitation and protection, as well as the relationships between saline lakes and global changes.### The Authors

John E. Oddois senior technical advisor with Champion Technologies Inc., Houston. He is involved in scale/corrosion control and water treatment. Oddo has a BS in geology from the University of Akron, an MS in geology from Toledo University, and a PhD from Rice University. He is a certified petroleum geologist and a member of AAPG, SPE, and NACE.

Mason B. Tomsonis a professor in the environmental science and engineering department at Rice University. He has studied water and brine chemistry throughout his career. Tomson has a BS in chemistry from Southwestern State College in Oklahoma and a PhD from Oklahoma State University. He is a member of the American Chemical Society, National Water Well Association, and NACE.

*Copyright 1998 Oil & Gas Journal. All Rights Reserved.*