Developing Live Oil Property Models With Global Fluid Database Using Symbolic Regression
Authors:   Halliburton, Chen Songhua , Jones Christopher Michael ,   Halliburton, Dai Bin ,   Halliburton, Shao Wei ,   Halliburton
Published: September 2024

Global equations for predicting GOR, API gravity, and saturated viscosity from downhole testing and sampling measurements have been developed using a symbolic regression (SR) machine-learning method. The performance analysis confirms that these new models outperform the existing empirical and neural network-based models with the relative error approaching a similar level of the direct downhole measurements. They are sufficiently robust to be a reliable QC tool to be used globally. The genetic-programming-based SR method has been applied to a global fluid sample database consisting of nearly 700 samples collected from more than 500 wells located in many parts of the world to obtain solution GOR, API gravity, and saturated viscosity prediction equations. The database consists of environmental parameters such as pressure and temperature measurements, measured fluid properties such as fluid density ρ(T), methane density ρ_CH4 (P,T), saturated compressibility γ_sat, methane and oil compressibilities, γ_CH4 (P,T) and γ_oil (P,T), among others, as well as the target live oil properties of solution gas-oil ratio GOR, saturated viscosity μ_sat, and API gravity. Pair plots and correlation heatmaps are used first to assess the relevancy of the input variables with the targets and, from which, narrow down the input variable pools. The random nature of genetic evolution processes embedded in SR ensures a nonsubjective selection of the input variables to the target prediction equations. By varying termination conditions, fitness functions, and/or by including or excluding conditional-branch-enabling math operators, multiple predict equations are obtained. Subsequently, the best models are determined based on statistical measures of error, the absence of outliers from the prediction equations, and their honoring to the physics of the input variable dependencies. The SR-generated solution GOR prediction equations are compared with the benchmark Standing equation and also the neural-network-based prediction model. The optimal equation from SR yields the relative error, computed with RMSE/range, of approximately 5%. This is significantly lower than that from the use of a Standing equation or neural-network-based prediction, as the latter two yield a relative error of about 20%. The 5% relative error approaches the current downhole GOR measurement performance uncertainty, indicating that the GOR prediction equation generated using our SR workflow indeed reached its optimal limit. Similarly, the prediction equations for API gravity and saturated viscosity are also performed highly satisfactorily, with relative errors in the range of 10 to 12%. Considering the performance is based on the large, diverse global fluid database, such performance is remarkably robust. The prediction equations are to be used routinely in operations, mainly as a QC tool to identify potential invalid GOR or API measurements and as a substitution when no valid direct measurements are available. •	A comparison of prediction equations trained with and without methane density and compressibility data indicated that including these methane properties improves the overall performance over the entire GOR range. •	Unlike the Standing equation, these new equations require no bubblepoint pressure, a quantity that is difficult to obtain downhole accurately.