# Development of a Thermodynamic Model for Wax Precipitation in Produced Crude Oil -- Case Study of Hydrocarbon Fluid from Niger-Delta, Nigeria

Thesis

Wax is often precipitated out of solution in waxy crude oil found in most oil reservoirs around the world, especially as the production of oil and gas has moved from on shore to more challenging terrains offshore. Waxes are composed primarily of paraffin which are saturated hydrocarbons. Wax precipitation and deposition pose production and transportation challenges in the area of flow assurance in the oil and gas industry which is not uncommon in the Niger Delta. This problem can affect system selection and operational procedures which has enormous cost implications. It is therefore important for producers to identify potential candidate wells/fields for organic solids precipitation and deposition. This can be done by understanding the composition and the paraffinic nature of the reservoir fluid mixture in prediction so that a production strategy can be designed to prevent or mitigate problems of wax precipitation and deposition. This research builds on thermodynamic principles to model wax precipitation using Niger-Delta petroleum fluids. Reservoir fluid characterization is very significant in modeling as it helps identify components of the mixture. Statistical methods are used for analyzing the molar distribution of components in petroleum fluids for the Heptanes plus components (C7+) which are usually lumped. Three probability distribution functions (Normal distribution, Exponential distribution and Weibull distribution) were used in analyzing the distribution of components in hydrocarbon fluid. Kolmogorov-Smirnov, Anderson-Darling, P-value, and L-RT statistical methods were then used to determine the goodness of fit of the distributions to petroleum fluid data. Exponential distribution is found to be the best fit for gas because gas components decline from C1 to the last heavy component, which is a continuous decline. Liquid hydrocarbon components usually increase from C1 to an intermediate component, for example C8 as shown in this study, and decline to the last heavy component. This makes exponential function unfit, for the entire distribution in liquid hydrocarbon. Weibull distribution is found to be the best fit for all hydrocarbon fluid (gas and liquid). A statistical model which can be used to determine goodness of fit for any number of data set at any desirable significance level, is developed using Kolmogorov- Smirnov test data. Minitab statistical analytical software is used to further analyze the fluid data using the Anderson-Darling test, P-value and the L-RT. Wax precipitation has a strong dependence on temperature. For wax prediction, a new correlation for predicting temperature of melting 𝑇𝑖 𝑓 of heavy ends is developed using fluid data from the Niger-Delta. The correlation is validated with experimentally determined melting point data. A reliable wax precipitation prediction model is desirable for the optimal production of reservoir fluids. The solid-liquid equilibrium parameter is important for developing a predictive thermodynamic model to determine the amount of wax precipitate and wax appearance temperature. The temperature dependent term is grouped as one and together with the composition dependent term, bivariate analysis is done. Bivariate analysis is used to mathematically remove correlations in the predictors such that the effects of these predictors on the response can be observed more clearly. A new set of independent predictor random variables is then developed with a reliable regression model whose R-square remains the same before and after removal of correlations. Multivariate analysis is also presented using multiple predictor on the equilibrium parameter, to better understand how each parameter affects the response. A Step by Step procedure of how this can be done is presented. A Correlation is also developed to determine the fluid component at various temperature and pressure. These components were then used to predict the wax appearance conditions of the fluid. This method is useful in determining the depth of wax appearance in the well bore.