Methods for Rapid Prediction of Salt Quality and Influent-Water Quality Effects on Hardness Leakage in Steamflood Water
Authors: Chen James C.T. 
Published: December 2007

Summary
Counter current regeneration of two-stage sodium zeolite softeners has been employed successfully in reducing hardness leakage level of steam flooding water to less than 1 ppm when raw water contains as much as 5,000 ppm of the total dissolved solids (TDS). Hardness leakage is caused by sodium displacement of calcium and magnesium from the bottom of the exchanger bed. The calcium and magnesium are left over because of either incomplete regeneration or impurities in the regenerant. Brine containing high calcium and magnesium content used for regeneration may be the primary cause of hardness leakage. This paper presents methods for making rapid calculations, for which a convenient operational model does not already exist. The figures relate the hardness leakage as a function of salt quality and influent water quality and present solutions for predicting the leakage level, salt quality requirement, or the treatability of raw water required for steam flooding projects.

Introduction
Counter current regeneration of two-stage sodium zeolite softeners has been employed successfully in reducing the hardness leakage level of the steam flooding water to less than 1 ppm even when raw water contains as much as 5,000 ppm of the TDS. However, the bane containing higher calcium and magnesium content used for regeneration may be the primary cause of hardness leakage. Data provided by resin manufacturers have related the hardness leakage as a function of rinse requirements or influent hardness concentration. Little information is available regarding hardness leakage attributable to the hardness concentration in the brine. The impact of salt quality on hardness leakage may be estimated by the equivalent fraction form expressed in Eq. 4, which is presented later. However, tedious trial-and-error calculations must be performed to find the impact of salt quality on the hardness leakage level. This paper attempts to find an equation and to derive figures that may relate the hardness leakage level directly to the qualities of both raw water and salt to be used. To achieve these objectives, a brief review of ion-exchange softening process is in order and is presented next.

Mathematical Development
The exchange of calcium and magnesium ion with sodium in a sulfonic-acid cation exchange resin can be represented as
..........(1)
or, since only the cations are actually involved in the exchange and generalizing for the exchange between a monovalent ion and a divalent ion, we get
........................(2)
where the superscript bar indicates the ion in the resin phase while A+ and B++ indicate the ions in solution. The mass action expression for this reaction is
..................(3)
The square brackets indicate molar concentrations and the term K is the selectivity coefficient for the reaction. The mass action expression is more manageable when put in terms of equivalent fractions. If the total ionic concentration of the solution is C, then the equivalent fraction of ion A+ in solution is X A = [A+]/C and the equivalent fraction of ion B++ in solution is XB=[B++]/C. Since only two exchangeable ions are present in solution, we have XA + XB = 1. Similarly, in the resin phase, we have XA = [A+]/C, XB = [B++]/C, and XA + XB = 1. In brine solution, we also have XA=[A+]/C, XB=[B++]/C, and XA+XB=1. When Eq. 3 is converted to the equivalent fraction form, we have
........(4)
Leakage is caused by sodium displacement of calcium and magnesium from the bottom of the exchanger bed. The calcium and magnesium are either left over because of incomplete regeneration or impurities in the regenerant.
JPT
P. 793^