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.
Similar content being viewed by others
References
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)
Bern CR (2009) Soil chemistry in lithologically diverse datasets: the quartz dilution effect. Appl Geochem 24:1429–1437
Buccianti A (2011) Isometric log-ratio co-ordinates and their simple use in water geochemistry. Bol Geol Min 122:453–458
Buccianti A, Magli R (2011) Metric concepts and implications in describing compositional changes for world river’s water chemistry. Comput Geosci 37:670–676
Buccianti A, Pawlowsky-Glahn V (2005) New perspectives on water chemistry and compositional data analysis. Math Geol 37:703–727
Carpenter AB (1978) Origin and chemical evolution of brines in sedimentary basins. Circ-Okla Geol Surv 79:60–77
Chayes F (1960) On correlation between variables of constant sum. J Geophys Res 65:4185–4193
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
Davis SN, Whittemore DO, Fabryka-Martin J (1998) Uses of chloride/bromide ratios in studies of potable water. Ground Water 36:338–350
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
Egozcue J, Pawlowsky-Glahn V, Mateu-Figueras G, Barceló-Vidal C (2003) Isometric logratio transformations for compositional data analysis. Math Geol 35:279–300
Egozcue JJ, Pawlowsky-Glahn V (2005) Groups of parts and their balances in compositional data analysis. Math Geol 37:795–828
Filzmoser P, Hron K, Reimann C (2009a) Principal component analysis for compositional data with outliers. Environmetrics 20:621–632
Filzmoser P, Hron K, Reimann C, Garrett R (2009b) Robust factor analysis for compositional data. Comput Geosci 35:1854–1861
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.
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
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
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
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
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
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
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
Nativ R (1996) The brine underlying the Oak Ridge Reservation, Tennessee, USA: characterization, genesis, and environmental implications. Geochim Cosmochim Acta 60:787–801
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
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
Pawlowsky-Glahn V, Egozcue JJ (2001) Geometric approach to statistical analysis on the simplex. Stoch Environ Res Risk Assess 15:384–398
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
Price PH, Hare CE, McCue JB, Hoskins HA (1937) Salt brines of West Virginia. West Virginia Geological Survey Report VIII, 203 pp
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
Rollinson HR (1993) Using geochemical data: evaluation, presentation, interpretation. Longman, Singapore
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
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
Acknowledgements
This research was funded by the U.S. Geological Survey Energy Resources Program. The authors would also like to acknowledge Lin Ma (University of Texas at El Paso), Jennifer McIntosh (University of Arizona, U.S. Geological Survey), Ricardo Olea (U.S. Geological Survey), Josep Antoni Martín Fernández (Universitat de Girona), and two anonymous journal reviewers for providing critical comments and corrections to this paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Engle, M.A., Rowan, E.L. Interpretation of Na–Cl–Br Systematics in Sedimentary Basin Brines: Comparison of Concentration, Element Ratio, and Isometric Log-ratio Approaches. Math Geosci 45, 87–101 (2013). https://doi.org/10.1007/s11004-012-9436-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11004-012-9436-z