Research on the Characterization and Prediction of Water Absorption Profiles Based on the Lorenz Curve

The water absorption profile refers to the distribution ratio of injected water for each layer of the water injection well. It is usually represented by a bar chart. This method can reflect the relative water absorption of each layer, but it cannot directly show the differences in water absorption performance among layers. Therefore, this method is only applicable when the differences of each small layer do not need to be evaluated. Aiming at the above problems, this paper considers using the Lorenz curve of the water absorption profile to depict the differences in water absorption of each small layer of the water injection well. The specific implementation steps are as follows: First, multiply the permeability of each layer corresponding to each well by the effective thickness to obtain the geological coefficient kh. Then, arrange the kh values in ascending order, accumulate the kh values, and calculate the percentage of the kh value of each small layer in the overall kh value. Finally, use the calculation results as the abscissa of the Lorenz curve of the water absorption profile of each well. After setting the abscissa, use a similar method to process the ordinate. Divide the relative water absorption capacity of each point by the effective thickness of the small layer where it is located to calculate the water absorption capacity of each layer. Then, also use the accumulation method to obtain the percentage of the overall relative water absorption capacity of each layer of each well to get the ordinate of the curve. Finally, draw a Lorenz curve to describe the water absorption profile. After completing the above steps, combine the collected production data, geological data, and test analysis data, and use the XGBoost algorithm to build a prediction model for the water absorption profile. The research results show that the error of the established prediction model is less than 10%. Compared with traditional methods, this method takes more factors into account and has higher prediction accuracy text.