Mathematical Geosciences

, Volume 45, Issue 1, pp 87–101 | Cite as

Interpretation of Na–Cl–Br Systematics in Sedimentary Basin Brines: Comparison of Concentration, Element Ratio, and Isometric Log-ratio Approaches

Article

Abstract

Mathematicians and geochemists have long realized that compositional data intrinsically exhibit a structure prone to spurious and induced correlations. This paper demonstrates, using the Na–Cl–Br system, that these mathematical problems are exacerbated in the study of sedimentary basin brines by such processes as the evaporation or dissolution of salts owing to their high salinities. Using two published datasets of Na–Cl–Br data for fluids from the Appalachian Basin, it is shown that log concentration and Na/Br versus Cl/Br methods for displaying solute chemistry may lead to misinterpretation of mixing trends between meteoric waters (for example shallow drinking water aquifers) and basinal brines, partially due to spurious mathematical relationships. An alternative approach, based on the isometric log-ratio transformation of molar concentration data, is developed and presented as an alternative method, free from potential numerical problems of the traditional methods. The utility, intuitiveness, and potential for mathematical problems of the three methods are compared and contrasted. Because the Na–Cl–Br system is a useful tool for sourcing solutes and investigating the evolution of basinal brines, results from this research may impact such critical topics as evaluating sources of brine contamination in the environment (possibly related to oil and gas production), evaluating the behavior of fluids in the reservoir during hydraulic fracturing, and tracking movement of fluids as a result of geologic CO2 sequestration.

Keywords

Brine Isometric log-ratio Compositional data analysis Appalachian Basin Produced Water 

References

  1. Aitchison J (1986) The statistical analysis of compositional data. Monographs on statistics and applied probability. Chapman & Hall, London. (Reprinted in 2003 with additional material by The Blackburn Press) CrossRefGoogle Scholar
  2. Bern CR (2009) Soil chemistry in lithologically diverse datasets: the quartz dilution effect. Appl Geochem 24:1429–1437 CrossRefGoogle Scholar
  3. Buccianti A (2011) Isometric log-ratio co-ordinates and their simple use in water geochemistry. Bol Geol Min 122:453–458 Google Scholar
  4. Buccianti A, Magli R (2011) Metric concepts and implications in describing compositional changes for world river’s water chemistry. Comput Geosci 37:670–676 CrossRefGoogle Scholar
  5. Buccianti A, Pawlowsky-Glahn V (2005) New perspectives on water chemistry and compositional data analysis. Math Geol 37:703–727 CrossRefGoogle Scholar
  6. Carpenter AB (1978) Origin and chemical evolution of brines in sedimentary basins. Circ-Okla Geol Surv 79:60–77 Google Scholar
  7. Chayes F (1960) On correlation between variables of constant sum. J Geophys Res 65:4185–4193 CrossRefGoogle Scholar
  8. Chi G, Savard MM (1997) Sources of basinal and Mississippi Valley-type mineralizing brines: mixing of evaporated seawater and halite-dissolution brine. Chem Geol 143:1–5 CrossRefGoogle Scholar
  9. Davis SN, Whittemore DO, Fabryka-Martin J (1998) Uses of chloride/bromide ratios in studies of potable water. Ground Water 36:338–350 CrossRefGoogle Scholar
  10. Dresel PE, Rose AW (2010) Chemistry and origin of oil and gas well brines in western Pennsylvania. Pennsylvania Geological Survey, Open-File Oil and Gas Report 10-01.0 Google Scholar
  11. Egozcue J, Pawlowsky-Glahn V, Mateu-Figueras G, Barceló-Vidal C (2003) Isometric logratio transformations for compositional data analysis. Math Geol 35:279–300 CrossRefGoogle Scholar
  12. Egozcue JJ, Pawlowsky-Glahn V (2005) Groups of parts and their balances in compositional data analysis. Math Geol 37:795–828 CrossRefGoogle Scholar
  13. Filzmoser P, Hron K, Reimann C (2009a) Principal component analysis for compositional data with outliers. Environmetrics 20:621–632 CrossRefGoogle Scholar
  14. Filzmoser P, Hron K, Reimann C, Garrett R (2009b) Robust factor analysis for compositional data. Comput Geosci 35:1854–1861 CrossRefGoogle Scholar
  15. Hanor JS (1994) Origin of saline fluids in sedimentary basins. In: Parnell J (ed) Geofluids: origin, migration and evolution of fluids in sedimentary basins. Special publications. Geological Society, London, pp 151–174. Google Scholar
  16. 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 CrossRefGoogle Scholar
  17. Hron K, Templ M, Filzmoser P (2010) Imputation of missing values for compositional data using classical and robust methods. Comput Stat Data Anal 54:3095–3107 CrossRefGoogle Scholar
  18. Kharaka YK, Hanor JS (2007) Deep fluids in the continents: I. Sedimentary basins. In: Holland HD, Turekian KK (eds) Surface and ground water, weathering, and soils. Treatise on geochemistry, vol 5. Elsevier, Amsterdam, 48 pp Google Scholar
  19. Mateu-Figueras G, Pawlowsky-Glahn V, Egozcue JJ (2011) The principle of working on coordinates. In: Pawlowsky-Glahn V, Buccianti A (eds) Compositional data analysis: theory and applications. Wiley, Chichester, pp 31–42 Google Scholar
  20. McCaffrey MA, Lazar B, Holland HD (1987) The evaporation path of seawater and the coprecipitation of Br and K+ with halite. J Sediment Res 57:928–937 Google Scholar
  21. Miesch AT (1969) The constant sum problem in geochemistry. In: Merriam DF (ed) Computer applications in the earth sciences. Plenum Press, New York, pp 161–176 CrossRefGoogle Scholar
  22. Monnin C (1989) An ion interaction model for the volumetric properties of natural waters: density of the solution and partial molal volumes of electrolytes to high concentrations at 25 °C. Geochim Cosmochim Acta 53:1177–1188 CrossRefGoogle Scholar
  23. Nativ R (1996) The brine underlying the Oak Ridge Reservation, Tennessee, USA: characterization, genesis, and environmental implications. Geochim Cosmochim Acta 60:787–801 CrossRefGoogle Scholar
  24. Otero N, Tolosana-Delgado R, Soler A, Pawlowsky-Glahn V, Canals A (2005) Relative vs absolute statistical analysis of compositions: a comparative study of surface waters of a Mediterranean river. Water Res 39:1404–1414 CrossRefGoogle Scholar
  25. Palarea-Albaladejo J, Martín-Fernández JA, Olea RA (2011) Non-detect bootstrap method for estimating distributional parameters of compositional samples revisited: a multivariate approach. In: Proceedings of the 4th international workshop on compositional data analysis, San Feliu de Guixols, Spain, pp 1–9 Google Scholar
  26. Pawlowsky-Glahn V, Egozcue JJ (2001) Geometric approach to statistical analysis on the simplex. Stoch Environ Res Risk Assess 15:384–398 CrossRefGoogle Scholar
  27. Pearson K (1897) On a form of spurious correlation which may arise when indices are used in the measurement of organs. Proc R Soc Lond 60:489–502 Google Scholar
  28. Price PH, Hare CE, McCue JB, Hoskins HA (1937) Salt brines of West Virginia. West Virginia Geological Survey Report VIII, 203 pp Google Scholar
  29. Rittenhouse G (1967) Bromine in oil-field waters and its use in determining possibilities of origin of these waters. Am Assoc Pet Geol Bull 51:2430–2440 Google Scholar
  30. Rollinson HR (1993) Using geochemical data: evaluation, presentation, interpretation. Longman, Singapore Google Scholar
  31. Walter LM, Stueber AM, Huston TJ (1990) Br–Cl–Na systematics in Illinois Basin fluids: constraints on fluid origin and evolution. Geology 18:315–318 CrossRefGoogle Scholar
  32. Zherebtsova IK, Volkova NN (1966) Experimental study of behavior of trace elements in the process of natural solar evaporation of Black Sea water and Sasyk-Sivash brine. Geochem Int 3:656–670 Google Scholar

Copyright information

© International Association for Mathematical Geosciences 2012

Authors and Affiliations

  1. 1.U.S. Geological Survey956 National CenterRestonUSA
  2. 2.Department of Geological SciencesUniversity of Texas at El PasoEl PasoUSA

Personalised recommendations