Productivity Prediction of Multilateral Horizontal Wells in Low-Permeability Gas Reservoirs Under Two-Phase Flow Conditions

The productivity of multilateral horizontal wells will decrease rapidly after water breakthrough, which brings challenges to accurately predict production. In this paper, a semi-analytical model for predicting the productivity of multilateral horizontal wells considering two-phase flow is established based on the principle of conformal transformation and superposition of potential functions. The model considers the effects of various factors such as gas slippage effect and reservoir stress sensitivity. Compared to the conventional productivity prediction model, the model can not only consider variable mass flow in horizontal wellbore, but also different combinations of multiple branches. The results of field case and sensitivity analysis show that the productivity of multilateral wells decreases with the increase of gas-water volume ratio and reservoir stress sensitivity coefficient, and increases with the increase of gas slippage coefficient and the angle between branch wellbore and main wellbore. The presented model can help to better understand the flow characteristics of water-producing multilateral horizontal wells and accurately calculate the productivity, which is of great significance for the development of low-permeability gas reservoirs. 1. INTRODUCTION Multilateral wells are widely used in complex reservoirs with the improvement of drilling and completion technology (Ouyang and Aziz, 2001; Tabatabaei and Ghalambor, 2011; Hassan et al., 2017). Compared to conventional vertical wells, multilateral horizontal wells can create more contact area with reservoir and effectively increase gas well productivity, making it an attractive option for efficient exploitation of low permeability reservoirs (Wang et al., 2015; Zhou et al., 2016). The research on horizontal well productivity began in the 1950s. Many attempts have been made to characterize the productivity of horizontal wells, and several models have been presented. Analytic models are widely accepted because they are very convenient to use. Borisov (1984) proposed a production capacity model for horizontal wells in steady state. The assumptions of the model are: the formation is homogeneous and isotropic, the drain boundary is elliptical, the fluid is incompressible, and the formation damage caused by drilling and completing the well is ignored. The analytical model has more assumptions and is not realistic, so its use is limited.