Uncertainty Quantification of Pseudo-Adsorption Isotherm History Matching

Abstract

Scale Inhibitor Squeeze treatments are some of the most common techniques to prevent oilfield mineral scale deposition in oil producers. A squeeze treatment design's effectiveness and lifespan is determined by the scale inhibitor (SI) retention, which can be described using a pseudo-isotherm adsorption, commonly derived from coreflooding experiments, although in some certain circumstances a new isotherm will need to be re-derived to match the field return concentration profile, once the treatment is deployed and samples are collected to measure SI return concentration. This new isotherm is used to design the next treatment. The objective of this manuscript is to quantify the uncertainty, which depends of the number of samples analyzed. In any inverse problem, there might not be a unique solution, which is in our context a pseudo-isotherm matching the return concentration profile. As a consequence, there will be a certain level of uncertainty predicting the next squeeze treatment lifetime. Solving this inverse problem in Bayesian formulation, incorporating the prior information, and the likelihood involving the return concentration profile, it is possible to quantify the posterior distribution, and therefore calculate the uncertainty range, commonly known as P90/P50/P10, based on the Randomized Maximum Likelihood (RML) approach. The P90/P50/P10 was calculated as a function of the number of samples available, differentiating from the early production and late production. The results suggest that there is a correlation between the P90/P50/P10 interval and the number of samples, i.e. the differences between the P10 and P90 in terms of the forecast squeeze lifetime was wider the smaller number of samples. The methodology proposed may be used to determine the number of samples required to reduce the level of uncertainty predicting the lifetime of the next squeeze treatment. Although taking more samples may increase the cost per barrel for a treatment, the ability to predict accurately treatment lifetime will be more cost effective in the long term, as production might not be affected.