Skip to main content
SpringerLink
Log in

Rigorous modeling of gypsum solubility in Na–Ca–Mg–Fe–Al–H–Cl–H2O system at elevated temperatures

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Precipitation and scaling of calcium sulfate have been known as major problems facing process industries and oilfield operations. Most scale prediction models are based on aqueous thermodynamics and solubility behavior of salts in aqueous electrolyte solutions. There is yet a huge interest in developing reliable, simple, and accurate solubility prediction models. In this study, a comprehensive model based on least-squares support vector machine (LS-SVM) is presented, which is mainly devoted to calcium sulfate dihydrate (or gypsum) solubility in aqueous solutions of mixed electrolytes covering wide temperature ranges. In this respect, an aggregate of 880 experimental data were gathered from the open literature in order to construct and evaluate the reliability of presented model. Solubility values predicted by LS-SVM model are in well accordance with the observed values yielding a squared correlation coefficient (R 2) of 0.994. Sensitivity of the model for some important parameters is also checked to ascertain whether the learning process has succeeded. At the end, outlier diagnosis was performed using the method of leverage value statistics to find and eliminate the falsely recorded measurements from assembled dataset. Results obtained from this study indicate that LS-SVM model can successfully be applied in predicting accurate solubility of calcium sulfate dihydrate in Na–Ca–Mg–Fe–Al–H–Cl–H2O system over temperatures ranging from 283.15 to 371.15 K.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Abbreviations

AAE:

Average absolute error (%)

b :

Bias term

C :

Positive constant

CSA:

Coupled simulated annealing

EOR:

Enhanced oil recovery

H :

Hat matrix

\(K(x,x_{i} )\) :

Kernel function

LS-SVM:

Least-squares supported vector machine

m :

Molality

MSE:

Mean-squared error

NO:

Number of training objects

Q :

Solubility of CaSO4.2H2O (m)

R 2 :

Squared correlation coefficient

RMSE:

Root-mean-square error

R :

Residual

SDE:

Standard deviation error

x :

Inputs

X :

A two-dimensional matrix

ϕ(x):

Mapping function

t :

Transpose operator

T :

Temperature (K)

w :

A nonlinear function

y :

Outputs

ψ :

Relative weight of the summation of the regression errors

α :

Lagrange multipliers

σ 2 :

Squared bandwidth

References

  1. Amjad Z (1988) Calcium sulfate dihydrate (gypsum) scale formation on heat exchanger surfaces: the influence of scale inhibitors. J Colloid Interface Sci 123:523–536

    Google Scholar 

  2. Helalizadeh A (2002) Mixed salt crystallization fouling, PhD Thesis, Department of Chemical and Process Engineering, University of Surrey, UK

  3. Shih W-Y, Rahardianto A, Lee R-W, Cohen Y (2005) Morphometric characterization of calcium sulfate dihydrate (gypsum) scale on reverse osmosis membranes. J Memb Sci 252:253–263

    Google Scholar 

  4. Safari H, Jamialahmadi M (2014) Thermodynamics kinetics, and hydrodynamics of mixed salt precipitation in porous media: model development and parameter estimation. Transp Porous Med 101:477–505

    MathSciNet  Google Scholar 

  5. Safari H, Jamialahmadi M (2013) Estimating the kinetic parameters regarding barium sulfate deposition in porous media: a genetic algorithm approach, Asia-Pacific. J Chem Eng: n/a–n/a

  6. Jamialahmadi M, Muller-Steinhagen H (2008) Mechanisms of scale deposition and scale removal in porous media. Int J Oil Gas Coal Technol 1:81–108

    Google Scholar 

  7. Moghadasi J, Müller-Steinhagen H, Jamialahmadi M, Sharif A (2004) Model study on the kinetics of oil field formation damage due to salt precipitation from injection. J Petrol Sci Eng 43:201–217

    Google Scholar 

  8. Liu X, Jungang L, Qianya Z, Jinlai F, Yingli L, Jingxin S (2009) The analysis and prediction of scale accumulation for water-injection pipelines in the Daqing Oilfield. J Petrol Sci Eng 66:161–164

    Google Scholar 

  9. Yuan M (1989) Prediction of sulphate scaling tendency and investigation of barium and strontium sulphate solid solution scale formation. Heriot-Watt University, Edinburgh

    Google Scholar 

  10. Binmerdhah AB (2007) The study of scale formation in oil reservoir during water injection at high-barium and high-salinity formation water, M.Sc. thesis, Faculty of Chemical and Natural Resources Engineering, Universiti Teknologi Malaysia, Malaysia

  11. Bedrikovetsky PG, Mackay EJ, Silva RMP, Patricio FMR, Rosário FF (2009) Produced water re-injection with seawater treated by sulphate reduction plant: injectivity decline, analytical model. J Petrol Sci Eng 68:19–28

    Google Scholar 

  12. Li Z, Demopoulos GP (2005) Effect of NaCl, MgCl2, FeCl2, FeCl3, and AlCl3 on solubility of CaSO4 phases in aqueous HCl or HCl + CaCl2 Solutions at 298 to 353 K. J Chem Eng Data 51:569–576

    Google Scholar 

  13. Boerlage SFE, Kennedy MD, Bremere I, Witkamp GJ, Van der Hoek JP, Schippers JC (2002) The scaling potential of barium sulphate in reverse osmosis systems. J Memb Sci 197:251–268

    Google Scholar 

  14. Haarberg T, Selm I, Granbakken DB, Østvold T, Read P, Schmidt T (1992) Scale formation in reservoir and production equipment during oil recovery: an equilibrium model. SPE Prod Eng 7:75–84

    Google Scholar 

  15. Cameron FK, Seidell A (1900) Solubility of gypsum in aqueous solutions of certain electrolytes. J Phys Chem 5:643–655

    Google Scholar 

  16. Kumar A, Sanghavi R, Mohandas VP (2006) Experimental densities, speeds of sound, isentropic compressibilties and shear relaxation times of CaSO4·2H2O + CaCl2 + H2O and CaSO4·2H2O + NaCl + H2O systems at temperatures 30 and 35 °C. J Solution Chem 35:1515–1524

    Google Scholar 

  17. Kochetkova NV, Gavrilov NB, Dergacheva NP, Chudnenko KV, Krenev VA (2006) Physicochemical modeling of precipitating and dissolving of gypsum in chloride solutions. Russ J Inorg Chem 51:823–828

    Google Scholar 

  18. Kumar A, Sanghavi R, Mohandas VP (2007) Solubility Pattern of CaSO4·2H2O in the System NaCl + CaCl2 + H2O and Solution Densities at 35 °C: non-ideality and Ion Pairing. J Chem Eng Data 52:902–905

    Google Scholar 

  19. Kumar A, Shukla J, Dangar Y, Mohandas VP (2010) Effect of MgCl2 on the Solubility of CaSO4·2H2O in the Aqueous NaCl System and Physicochemical Solution Properties at 35 °C. J Chem Eng Data 55:1675–1678

    Google Scholar 

  20. Marshall WL, Slusher R, Jones EV (1964) Aqueous systems at high temperatures XIV. Solubility and thermodynamic relationships for CaSO4 in NaCl–H2O solutions from 40° to 200 °C., 0 to 4 Molal NaCl. J Chem Eng Data 9:187–191

    Google Scholar 

  21. Power WH, Fabuss BM, Satterfield CN (1966) Transient solubilities and phase changes of calcium sulfate in aqueous sodium chloride. J Chem Eng Data 11:149–154

    Google Scholar 

  22. Furby E, Glueckauf E, McDonald LA (1968) The solubility of calcium sulphate in sodium chloride and sea salt solutions. Desalination 4:264–276

    Google Scholar 

  23. Ostroff AG, Metler AV (1966) Solubility of calcium sulfate dihydrate in the system NaCl–MgCl2–H2O from 28° to 70° C. J Chem Eng Data 11:346–350

    Google Scholar 

  24. Wu X, He W, Guan B, Wu Z (2010) Solubility of calcium sulfate dihydrate in Ca–Mg–K chloride salt solution in the range of (348.15 to 371.15) K. J Chem Eng Data 55:2100–2107

    Google Scholar 

  25. Spencer RJ, Møller N, Weare JH (1990) The prediction of mineral solubilities in natural waters: a chemical equilibrium model for the Na–K–Ca–Mg–Cl–SO4–H2O system at temperatures below 25°C. Geochim Cosmochim Acta 54:575–590

    Google Scholar 

  26. Monnin C, Galinier C (1988) The solubility of celestite and barite in electrolyte solutions and natural waters at 25°C: a thermodynamic study. Chem Geol 71:283–296

    Google Scholar 

  27. Møller N (1988) The prediction of mineral solubilities in natural waters: a chemical equilibrium model for the Na-Ca-Cl-SO4-H2O system, to high temperature and concentration. Geochim Cosmochim Acta 52:821–837

    Google Scholar 

  28. Monnin C (1999) A thermodynamic model for the solubility of barite and celestite in electrolyte solutions and seawater to 200°C and to 1 kbar. Chem Geol 153:187–209

    Google Scholar 

  29. Monnin C (1990) The influence of pressure on the activity coefficients of the solutes and on the solubility of minerals in the system Na–Ca–Cl–SO4–H2O to 200 °C and 1 kbar and to high NaCl concentration. Geochim Cosmochim Acta 54:3265–3282

    Google Scholar 

  30. Harvie CE, Weare JH (1980) The prediction of mineral solubilities in natural waters: the Na–K–Mg–Ca–Cl–SO4–H2O system from zero to high concentration at 25° C. Geochim Cosmochim Acta 44:981–997

    Google Scholar 

  31. Oddo JE, Tomson MB (1994) Why scale forms and how to predict it. SPE Prod Oper 9:47–54

    Google Scholar 

  32. Mohammadi AH, Richon D (2007) Thermodynamic modeling of salt precipitation and gas hydrate inhibition effect of salt aqueous solution. Ind Eng Chem Res 46:5074–5079

    Google Scholar 

  33. Pitzer K (1975) Thermodynamics of electrolytes V. effects of higher-order electrostatic terms. J Solut Chem 4:249–265

    Google Scholar 

  34. Pitzer KS (1973) Thermodynamics of electrolytes. I. Theoretical basis and general equations. J Phys Chem 77:268–277

    Google Scholar 

  35. Wang P, Oakes CS, Pitzer KS (1997) Thermodynamics of aqueous mixtures of magnesium chloride with sodium chloride from 298.15 to 573.15 K. New measurements of the enthalpies of mixing and of dilution. J Chem Eng Data 42:1101–1110

    Google Scholar 

  36. Phutela RC, Pitzer KS, Saluja PPS (1987) Thermodynamics of aqueous magnesium chloride, calcium chloride, and strontium chloride at elevated temperatures. J Chem Eng Data 32:76–80

    Google Scholar 

  37. Pitzer KS, Olsen J, Simonson JM, Roy RN, Gibbons JJ, Rowe L (1985) Thermodynamics of aqueous magnesium and calcium bicarbonates and mixtures with chloride. J Chem Eng Data 30:14–17

    Google Scholar 

  38. Pitzer KS, Peiper JC, Busey RH (1984) Thermodynamic properties of aqueous sodium chloride solutions. J Phys Chem Ref Data 13:1–102

    Google Scholar 

  39. Rogers PSZ, Pitzer KS (1981) High-temperature thermodynamic properties of aqueous sodium sulfate solutions. J Phys Chem 85:2886–2895

    Google Scholar 

  40. Shi W, Kan AT, Fan C, Tomson MB (2012) Solubility of barite up to 250 °C and 1500 bar in up to 6 m NaCl Solution. Ind Eng Chem Res 51:3119–3128

    Google Scholar 

  41. Raju KUG, Atkinson G (1989) Thermodynamics of scale mineral solubilities. 2. Strontium sulfate(s) in aqueous sodium chloride. J Chem Eng Data 34:361–364

    Google Scholar 

  42. Raju K, Atkinson G (1988) Thermodynamics of scale mineral solubilities. 1. Barium sulfate(s) in water and aqueous sodium chloride. J Chem Eng Data 33:490–495

    Google Scholar 

  43. Harvie CE, Møller N, Weare JH (1984) The prediction of mineral solubilities in natural waters: the Na–K–Mg–Ca–H–Cl–SO4–OH–HCO3–CO3–CO2–H2O system to high ionic strengths at 25°C. Geochim Cosmochim Acta 48:723–751

    Google Scholar 

  44. Pabalan RT, Pitzer KS (1987) Thermodynamics of concentrated electrolyte mixtures and the prediction of mineral solubilities to high temperatures for mixtures in the system Na–K–Mg–Cl–SO4–OH–H2O. Geochim Cosmochim Acta 51:2429–2443

    Google Scholar 

  45. Monnin C (1995) Thermodynamic properties of the Na–K–Ca–Ba–Cl–H2O System to 473.15 K and solubility of barium chloride hydrates. J Chem Eng Data 40:828–832

    Google Scholar 

  46. Eakin BE, Mitch FJ (1988) Measurement and correlation of miscibility pressures of reservoir oils, SPE annual technical conference and exhibition, (1988 Copyright 1988. Society of Petroleum Engineers, Houston

    Google Scholar 

  47. Gharagheizi F, Eslamimanesh A, Farjood F, Mohammadi AH, Richon D (2011) Solubility parameters of nonelectrolyte organic compounds: determination using quantitative structure–property relationship strategy. Ind Eng Chem Res 50:11382–11395

    Google Scholar 

  48. Cristianini N, Shawe-Taylor J (2000) An introduction to support vector machines: and other kernel-based learning methods. Cambridge University Press, Cambridge

    Google Scholar 

  49. Suykens JAK, Vandewalle J (1999) Least squares support vector machine classifiers. Neural Process Lett 9:293–300

    MathSciNet  Google Scholar 

  50. Baylar A, Hanbay D, Batan M (2009) Application of least square support vector machines in the prediction of aeration performance of plunging overfall jets from weirs. Expert Syst Appl 36:8368–8374

    Google Scholar 

  51. Byvatov E, Fechner U, Sadowski J, Schneider G (2003) Comparison of support vector machine and artificial neural network systems for drug/nondrug classification. J Chem Inf Comput Sci 43:1882–1889

    Google Scholar 

  52. Scholkopf BS, Smola AJ (2002) Learning with kernels: support vector machines, regularization, optimization and beyond. MIT press, Cambridge

  53. Vapnik V (1995) The nature of statistical learning theory. Springer, New York

    MATH  Google Scholar 

  54. Moser G, Serpico SB (2009) Modeling the error statistics in support vector regression of surface temperature from infrared data. Geosci Remote Sens Lett IEEE 6:448–452

    Google Scholar 

  55. Suykens JAK (2001) Support vector machines: a nonlinear modelling and control perspective. Eur J Control 7:311–327

    MATH  Google Scholar 

  56. Smola AJ, SchoLkopf B (2004) A tutorial on support vector regression. Stat Comput 14:199–222

    MathSciNet  Google Scholar 

  57. Haifeng W, Dejin H (2005) Comparison of SVM and LS-SVM for regression, neural networks and brain, 2005. ICNN&B ‘05. International Conference on 2005, pp 279–283

  58. Farasat A, Shokrollahi A, Arabloo M, Gharagheizi F, Mohammadi AH (2013) Toward an intelligent approach for determination of saturation pressure of crude oil. Fuel Process Technol 115:201–214

    Google Scholar 

  59. Fazavi M, Hosseini SM, Arabloo M, Shokrollahi A, Amani M (2013) Applying a smart technique for accurate determination of flowing oil/water pressure gradient in horizontal pipelines. J Dispers Sci Technol

  60. Hemmati-Sarapardeh A, Shokrollahi A, Tatar A, Gharagheizi F, Mohammadi AH, Naseri A (2013) Reservoir oil viscosity determination using an intelligent approach. Fuel 116:39–48

    Google Scholar 

  61. Rafiee-Taghanaki S, Arabloo M, Chamkalani A, Amani M, Zargari MH, Adelzadeh MR (2013) Implementation of SVM framework to estimate PVT properties of reservoir oil. Fluid Phase Equilib 346:25–32

    Google Scholar 

  62. Shokrollahi A, Arabloo M, Gharagheizi F, Mohammadi AH (2013) Intelligent model for prediction of CO2–Reservoir oil minimum miscibility pressure. Fuel 112:375–384

    Google Scholar 

  63. Arabloo M, Shokrollahi A, Gharagheizi F, Mohammadi AH (2013) Towards a predictive model for estimating dew point pressure in gas condensate systems. Fuel Process Technol (in Press)

  64. Pelckmans K, Suykens JAK, Van Gestel T, De Brabanter J, Lukas L, Hamers B, De Moor B, Vandewalle J (2002) LS-SVMlab: a matlab/c toolbox for least squares support vector machines, Tutorial. KULeuven-ESAT, Leuven

    Google Scholar 

  65. Corana A, Marchesi M, Martini C, Ridella S (1987) Minimizing multimodal functions of continuous variables with the simulated annealing algorithm. ACM Trans Math Softw 13:262–280

    MATH  MathSciNet  Google Scholar 

  66. Xavier-de-Souza S, Suykens JAK, Vandewalle J, Bolle D (2010) Coupled simulated annealing. IEEE Trans Syst Man Cybern Part B Cybern 40:320–335

    Google Scholar 

  67. Butler JN (1964) Ionic equilibrium: a mathematical approach. Addison-Wesley, Reading

    Google Scholar 

  68. Rousseeuw PJ, Leroy AM (2005) Robust regression and outlier detection. Wiley, Hoboken

    Google Scholar 

  69. Gramatica P (2007) Principles of QSAR models validation: internal and external. QSAR Comb Sci 26:694–701

    Google Scholar 

  70. Rousseeuw PJ, Leroy AM (2005) Robust regression and outlier detection. Wiley, Hoboken

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Petroleum Engineering, Petroleum University of Technology, Ahvaz, Iran

    Hossein Safari & Mohammad Jamialahmadi

  2. Thermodynamics Research Unit, School of Chemical Engineering, University of KwaZulu-Natal, Howard College Campus, King George V Avenue, Durban, 4041, South Africa

    Farhad Gharagheizi & Amir H. Mohammadi

  3. Department of Chemical Engineering, Buinzahra Branch, Islamic Azad University, Buinzahra, Iran

    Farhad Gharagheizi

  4. Institut de Recherche en Génie Chimique et Pétrolier (IRGCP), Paris Cedex, France

    Amir H. Mohammadi

  5. Department of Gas Engineering, Petroleum University of Technology, Ahvaz, Iran

    Alireza Samadi Lemraski

  6. Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran

    Milad Ebrahimi

Authors
  1. Hossein Safari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Farhad Gharagheizi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alireza Samadi Lemraski
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mohammad Jamialahmadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Amir H. Mohammadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Milad Ebrahimi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Hossein Safari or Amir H. Mohammadi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Safari, H., Gharagheizi, F., Lemraski, A.S. et al. Rigorous modeling of gypsum solubility in Na–Ca–Mg–Fe–Al–H–Cl–H2O system at elevated temperatures. Neural Comput & Applic 25, 955–965 (2014). https://doi.org/10.1007/s00521-014-1587-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-014-1587-z

Keywords

Search

Navigation