Advances in the Flory–Huggins–Zuo Equation of State for Asphaltene Gradients and Formation Evaluation

Recent advances in the understanding of the molecular and colloidal structure of asphaltenes in crude oils are codified in the Yen–Mullins model of asphaltenes. The Yen–Mullins model has enabled the development of the industry’s first asphaltene equation of state for predicting asphaltene concentration gradients in oil reservoirs, the Flory–Huggins–Zuo equation of state (FHZ EOS). The FHZ EOS is built by adding gravitational forces onto the existing Flory–Huggins regular solution model that has been used widely to model the phase behavior of asphaltene precipitation in the oil and gas industry. For reservoir crude oils with a low gas/oil ratio (GOR), the FHZ EOS reduces predominantly to a simple form, the gravity term only, and for mobile heavy oil, the gravity term simply uses asphaltene clusters. The FHZ EOS has successfully been employed to estimate the concentration gradients of asphaltenes and/or heavy ends in different crude oil columns around the world, thus evaluating the reservoir connectivity, which has been confirmed by the subsequent production data. This paper reviews recent advances in applying the FHZ EOS to different crude oil reservoirs from volatile oil (condensate) to black oil to mobile heavy oil all over the world to address key reservoir issues, such as reservoir connectivity/compartmentalization, tar mat formation, non-equilibrium with a late gas charge, and asphaltene destabilization. The workflow incorporates the integration of new technology, downhole fluid analysis (DFA), coupled with the new scientific advances, the FHZ EOS and Yen–Mullins model. The combination proves a powerful new method of reservoir evaluation. Asphaltene or heavy end concentration gradients in crude oils are treated using the FHZ EOS, explicitly incorporating the size of resin molecules, asphaltene molecules, asphaltene nanoaggregates, and/or asphaltene clusters. All of the parameters in the FHZ EOS are related to DFA measurements, such as compositions, GOR, density, etc. The variations of gas and oil properties with depth are calculated by the classical cubic equation of state (EOS) based on DFA compositions and GOR using specifically developed delumping, characterizing, and oil-based drilling mud (OBM) contamination correcting techniques. Field case studies have proven the value and simplicity of this asphaltene or heavy end treatment. Heuristics can be developed from results corresponding to estimation of asphaltene gradients. Perylene-like resins with the size of ∼1 nm are dispersed as molecules in high-GOR volatile oils with high fluorescence intensity and virtually no asphaltenes (0 wt % asphaltene). Heavy asphaltene-like resins with the size of ∼1.3 nm are molecularly dissolved in volatile oil at a very low asphaltene content. Asphaltene nanoaggregates with the size of ∼2 nm are dispersed in stable crude oil at a bit higher asphaltene content. Asphaltene clusters are found in mobile heavy oil with the size of ∼5 nm at even higher asphaltene content (typically >8 wt % based on stock tank oil). Two types of tar mats are identified by the FHZ EOS: one with a large discontinuous increase in asphaltene content versus depth typically at the base of an oil column (corresponding to asphaltene phase transition) and one with a continuous increase in asphaltene content at the base of a heavy oil column simply by extending the oil column in the downdip direction because of an exponential increase in viscosity with asphaltene content. All of these studies are in accordance with the observations in the Yen–Mullins model within the FHZ EOS analysis.