What Alkalinity is and Why it is Needed for pH Calculations in Oilfield Waters - Description of a Rapid and Robust Algorithm

Abstract Knowing pH inside the production equipment is necessary to evaluate the risk for scale formation or corrosion. Measuring pH is not an option in most systems, and one therefore must rely on a calculated pH. Formulating the necessary set of equations needed to calculate pH in a system is straightforward but solving it will become very complex as soon as the water contains more than one acid or base, and most oilfield waters will contain both CO2, H2S, several organic acids and possibly acidic or basic production chemicals. Solving pH analytically will then be an impossible task and solving it numerically can also be very challenging unless a very good start estimate is available. Also, if the electro neutrality equation, which is one of the fundamental equations for aqueous systems, is used, one will find that the uncertainty in the analyzed concentrations of several of the main ions is much larger than the concentration of the ions one need to calculate to find pH. To overcome these problems, alkalinity of the water can be measured, and the alkalinity equation can be used to calculate pH numerically. In this paper, it will be shown that if alkalinity is defined and measured correctly, the alkalinity equation can be used to calculate pH numerically by combining Newton-Raphson and bisection iteration. The method is very robust and does not require a start estimate for pH, it will always converge to the correct solution. By using the alkalinity equation as the working equation, the system can easily be expanded to include multiple acids and bases without any significant increase in complexity because each acid/base system is treated separately and added to the working equation as simple terms. The method can easily be implemented in computer codes or spreadsheet models.