Oilfield scale formation represents a very significant flow assurance challenge to the oil and gas industry, with increasing water production worldwide and higher oil prices. Scale Inhibitor (SI) squeeze treatment is the most widespread method to combat downhole scaling. In order to predict SI squeeze treatments accurately for further optimisation, it is necessary to simulate the SI retention in the formation, which may be described by pseudo-adsorption isotherms. While these are often derived from core flood experiments, sometimes they are not appropriate for modelling well treatments because the core tests on which they are based cannot fully represent field scale processes. In practice, the parameters of an analytic form of the isotherm equation are modified by trial and error by an experienced practitioner until a match is obtained between the prediction and the return profile of the first treatment in the field.
The main purpose of this paper is to present a Stochastic Hill Climbing Algorithm for automatic isotherm derivation. The performance of the algorithm was evaluated using data from three field cases. Two success criteria were defined: firstly, ability to match a single historical treatment and secondly, ability to predict subsequent successive treatments. To test for the second criterion, a candidate isotherm was derived from the first treatment in a well that was treated with the same chemical package on consecutive occasions, and then the predictions using the suggested solution were compared with the observed scale inhibitor concentration return profiles from the subsequent treatments. In all the calculations, performance of the isotherms suggested by the Hill Climbing algorithm and isotherms derived by trial and error were compared. The results demonstrate that the Hill Climber Algorithm is a very effective technique for deriving an isotherm to enable accurate modelling of scale inhibitor squeeze treatments.