The time necessary to initiate nucleation of crystals from a supersaturated solution is called "induction time" (Reddy, 1995). It is a function of the solution supersaturation, that is, the ratio of the ion activity product to the solubility product of the precipitating crystalline matter as demonstrated in this article by Reddy (1995) for calcium carbonate nucleation in the presence of magnesium ions. This article indicates that the induction time is lower for higher supersaturation.

Below the supersaturation value of about 10, the induction time for calcium carbonate nucleation is very long. In this region, the solution is at a "metastable" condition and, therefore, calcium carbonate crystals cannot be formed without the aid of a matching growth surface or substrate (Reddy, 1995). It can also be observed that the presence of magnesium ions increases the induction time for calcium carbonate nucleation and therefore has a retardation and/or inhibition effect.

Reddy (1995) explains the magnesium ion inhibition of calcium carbonate nucleation by adsorption of the magnesium ions and thus, the occupation of some crystal growth sites on the calcium carbonate crystal surface. For a quantitative interpretation of this phenomenon, Reddy (1986; 1995) resorts to a growth rate analysis and a Langmuir adsorption isotherm model using experimental data obtained by a seeded growth method. He expressed the crystal growth rate as being proportional to the surface available for crystal growth and the square of the driving force for precipitation:

where N represents the calcium carbonate crystal concentration in the solution in moles/liter, t denotes the time measured from the time of

initiation of the crystallization by seeding, s is the concentration of the seed added to provide the surface area for growth in mg/liter, and k is the crystal growth-rate constant. If N0 denotes the initial theoretical crystal concentration that would be produced by precipitation from a stable supersaturated solution at the time of seeding, the integration of Eq. 9-20 yields (Reddy, 1986):

The plot of the calcium carbonate growth data given by Reddy (1995) in this page confirms the validity of Eq. 9-21 and indicates that the presence of magnesium ions reduces the slopes of the straight lines and, thus the crystallization rate constant and inhibits the calcite formation. Reddy (1995) shows a rapid decline of the crystallization rate constant by the increasing magnesium ions presence. The plot of data according to the Langmuir model

given in this article by Reddy (1995) clearly indicates that the mechanism of the inhibition of the calcite crystal growth is the magnesium ion adsorption on the growth sites, where ka and kd denote the rate constants for adsorption and desorption of the magnesium ions at the growth sites, k0 and k are the crystallization growth-rate constants without and with the presence of magnesium ions, and TM 2+ is the total concentration of the magnesium ions present in the system.

Particle Growth and Dissolution in Solution

The particle growth is assumed to occur at a rate proportional to the surface, Ac, available for growth and the deviation of the saturation ratio from unity (Chang and Civan, 1992; Civan, 1996):

for which the initial amount of crystals present per unit bulk medium is given by

Relating the crystal shape to spherical shape, the mass and surface area of the crystalline particle is given, respectively, by:

in which C{ and C2 are the shape factors, pc, is the density, and Dc is the diameter. kc is a crystallization rate constant. Thus, Eqs. 9-23 through 9-26 lead to the following model in which the shape factors and the constant ( y 2 ) have been incorporated into the constant k'c:

For example, Dc = 5 urn, and k = k'c(Fs-l)/pc is equal to 1.4 and 10.3 um/s for calcium° carbonate crystal growth at 25 and 50°C, respectively, using the Dawe and Zhang (1997) data.


Arshad, A., & Harwell, J. H., "Enhanced Oil Recovery by Surfactant- Enhanced Volumetric Sweep Efficiency," SPE 14291, Annual Technical Conference and Exhibition of SPE, Las Vegas, Nevada, September 22- 25, 1985.

Atkinson, G., & Mecik, M., "The Chemistry of Scale Prediction," J. of Petroleum Science and Engineering, Vol. 17, No. 1/2, February 1997, pp. 113-121.

Chang, F. F., & Civan, F., "Predictability of Formation Damage by Modeling Chemical and Mechanical Processes," SPE 23793 paper, Proceedings of the SPE International Symposium on Formation Damage Control, February 26-27, 1992, Lafayette, Louisiana, pp. 293-312.

Chung, T.-H., "Thermodynamic Modeling for Organic Solid Precipitation," SPE 24851, Proceedings of the 67th Annual technical Conference and Exhibition of the SPE held in Washington, D.C., October 4-7, 1992, pp. 869-878.

Civan, F., "Correlation of the Pit Depth in Crystal Etching by Dissolution," J. of Colloid and Interface Science, Vol. 222, No. 1, pp. 156- 158, 2000.

Civan, F., "A Multi-Purpose Formation Damage Model," SPE 31101 paper, SPE Formation Damage Symposium, Lafayette, Louisiana, February 14-15, 1996, pp. 311-329.

Dawe, R. A. and Zhang, Y., "Kinetics of Calcium Carbonate Scaling Using Observations from Glass Micromodels," Journal of Petroleum Science and Engineering, Vol. 18, No. 3/4, pp. 179-187, 1997.

Dunn, K., Daniel, E., Shuler, P. J., Chen, H. J., Tang, Y, and Yen, T. F, "Mechanism of Surface Precipitation and Dissolution of Barite: A Morphology Approach," /. Colloid Interface Sci. Vol. 214, 1999, pp. 427-437.

Dunning, W. J., "General and Theoretical Introduction," Nucleation, Zettlemoyer, A.C. (Ed.), M. Dekker, Inc., New York, New York, 1969, pp. 1-67.

Hajash Jr., A., Carpenter, T. D., & Dewers, T. A., "Dissolution and Time-Dependent Compaction of Albite Sand: Experiments at 100°C and 160°C in pH-buffered Organic Acids and Distilled Water," Tectonophysics, Vol. 295, 1998, pp. 93-115.

Holstad, A., "Mathematical Modeling of Diagenetic Processes in Sedimentary Basins," Mathematical Modeling of Flow Through Porous Media," Bourgeat, A. P., Carasso, C., Luckhaus, S., and Mikelic, A., (Eds.), World Scientific Publ. Co. Pte. Ltd., 1995, pp. 418-428.

Hunkeler, F. and Bohni, H., "Determination of Pit Growth Rates on Aluminum Using a Metal Foil Technique," Corrosion, Vol. 37(11), 1981, pp. 645-650.

Labrid, J., "Modeling of High pH Sandstone Dissolution," Proceedings of the International Technical Meeting held jointly by the Petroleum Society of CIM and the SPE in Calgary, June 10-13, 1990, pp. 81/1-21.

Leetaru, H. E., "Reservoir Characteristics and Oil Production in the Cypress and Aux Vases Formations at Storms Consolidated Field in White County, Illinois," Illinois Petroleum Series 150, 1996, Department of Natural Resources, Illinois State Geological Survey, 47 p.

Leontaritis, K. J., Amaefule, J. O., & Charles, R. E., "A Systematic Approach for the Prevention and Treatment of Formation Damage Caused by Asphaltene Deposition," SPE 23810 paper, Proceedings of the SPE International Symposium on Formation Damage Control, Lafayette, Louisiana, February 26-27, 1992, pp. 383-395.

Liu, X., & Ortoleva, P., "A General-Purpose, Geochemical Reservoir Simulator," SPE 36700 paper, Proceedings of the 1996 SPE Annual Technical Conference and Exhibition, Denver, Colorado, October 6-9, 1996, pp. 211-222.

Liu, X., Ormond, A., Bartko, K., Li, Y., & Ortoleva, P., "A Geochemical Reaction-Transport Simulator for Matrix Acidizing Analysis and Design," J. of Petroleum Science and Engineering, Vol. 17, No. 1/2, February 1997, pp. 181-196.

Majors, J., "Crystallization and the Bottom Line," Chemical Processing, Vol. 62, No. 2, 1999, pp. 55-59.

Merino, E., & Dewers, T., "Implications of Replacement for Reaction-Transport Modeling," Journal of Hydrology, Vol. 209, 1998, pp. 137-146.

Oddo, J. E., & Tomson, M. B., "Why Scale Forms and How to Predict It," SPE Production Facilities, February 1994, pp. 47-54.

Ortoleva, P., Chadam, J., Merino, E., & Sen, A., "Geochemical Self-Organization II: The Reactive-Infiltration Instability," Amer. J. ScL, Vol. 287, 1987, pp. 1008-1040.

Putnis, A., & McConnell, J. D. C., Principles of Mineral Behaviour, Blackwell Scientific Publ., Boston, 1980.

Raines, M. A., & Dewers, T. A., "Mixed Transport/Reaction Control of Gypsum Dissolution Kinetics in Aqueous Solutions and Initiation of Gypsum Karst," Chemical Geology, Vol. 140, 1997, pp. 29-48.

Raines, M. A., & Dewers, T. A., "Mixed Kinetics Control of Fluid-Rock Interactions in Reservoir Production Scenarios," J. of Petroleum Science and Engineering, Vol. 17, No. 1/2, February 1997, pp. 139-155.

Reddy, M. M., "Effect of Magnesium Ion on Calcium Carbonate Nucleation and Crystal Growth in Dilute Aqueous Solutions at 25° Celsius, in Studies in Diageneses, Denver, F. A. Mumpton (Ed.), Colorado, U.S. Geological Survey," Bulletin 1578, 1986, pp. 169-182.

Reddy, M. M., "Carbonate Precipitation in Pyramid Lake, Nevada, Probable Control by Magnesium Ion," in Mineral Scale Formation and Inhibition (Z. Amjad, ed.), Plenum Press, New York, 1995, pp. 21-32.

Rege, S. D., & Fogler, H. S., "Competition Among Flow, Dissolution and Precipitation in Porous Media," AIChE J., Vol. 35, No. 7, 1989, pp. 1177-1185.

Richardson, S. M., & McSween, H. Y, Geochemistry: Pathways and Processes, Prentice Hall, Inc., New York, New York, 1989.

Ring, J. N., Wattenbarger, R. A., Keating, J. F., & Peddibhotla, S., "Simulation of Paraffin Deposition in Reservoirs," SPE Production & Facilities, February 1994, pp. 36-42.

Roberts, B. E., "The Effect of Sulfur Deposition on Gaswell Inflow Performance," SPE Reservoir Engineering, May 1997, pp. 118-123.

Schneider, G. W., "A Geochemical Model of the Solution-Mineral Equilibria Within a Sandstone Reservoir," M.S. Thesis, The University of Oklahoma, 1997, 157 p.

Stumm, W., & Morgan, J. J., Aquatic Chemistry: Chemical Equilibria and Rates in Natural Waters, John Wiley and Sons, New York, New York, 1996.

Todd, B. J., Willhite, G. P., & Green, D. W., "A Mathematical Model of In-situ Gelation of Polyacrylamide by a Redox Process," SPE Reservoir Engineering, February 1993, pp. 51-58.

Walton, A. G., "Nucleation in Liquids and Solutions," Nucleation, Zettlemoyer, A. C. (Ed.), M. Dekker, Inc., New York, New York, 1969, pp. 225-307.

Zhu, T., & Tiab, D., "Improved Sweep Efficiency by Selective Plugging of Highly Watered Out Zones by Alcohol Induced Precipitation," JCPT, Vol. 32, No. 9, November 1993, pp. 37-43.