Analytical Models for Liquid Loading in Multifractured Horizontal Gas Wells

Liquid loading is a key issue in gas reservoirs with horizontal wells and multiple hydraulic fractures, especially for shale-gas reservoirs. Field results show that only 15-30% of the original fracturing fluid is recovered. Most liquid is trapped in the rock matrix near the fracture face and induced fractures. Water flow-back from reservoir to wellbore and liquid loading from wellbore to surface are two main factors affecting the recovery of the original fracturing fluid. Significant efforts have been made to understand the effect of liquid loading on well performance, and some models have been proposed to describe the liquid loading. However, these models ignore the effect of liquid-drop size and its shape change with size. The falling liquid is nearly spherical in shape when its diameter is smaller than 2 mm, but when larger than 2 mm, it will change to be a half-hamburger in shape. Hence, ignoring the liquid-drop size and its shape change with size will lead to inaccurate calculations of the critical liquid-loading-flow rate. In this study, we conduct several groups of experiments to examine the liquid-droplet-shape change with liquid-droplet size in a gas-flow wellbore with different inclined angles. Similar to the falling liquid in air, larger liquid droplets are half-hamburger in shape (like the top half of the bun, flat on bottom and round on top). On the basis of this phenomenon, we propose analytical models to describe the critical liquid loading in vertical, slanted, and horizontal wellbores by considering the size and shape of liquid drops. Also, we validate this model by use of field data from the Daniudi gas field, and apply the proposed model to evaluate the liquid-loading problem in the Marcellus shale. Results show that the ratio of the liquid-drop height/width is a strong function of the liquid-drop width. Both the maximum and minimum ratios are determined: The maximum is unity, representing the shape of a sphere; the minimum is 0.3765; and the liquid drop is unstable when the ratio is less than 0.3765. In addition, the liquid drop with the minimum ratio is most easily loaded and produced from the vertical wellbore of gas wells. The key coefficient of B in the model of critical liquid-loading-flow velocity-v(g) = B[sigma(rho(l)-rho(g))/rho(2)(g)](0.25)-is a function of the width of the liquid drop. The range of B is quantified as from 1.54 to 2.5. In the slanted wellbore of gas wells, the critical liquid-loading gas-flow velocity is related to the angle beta, the slant angle, and the width of the liquid droplet. In the horizontal wellbore of gas wells, the critical liquid-loading gas-flow velocity is a function of the width of the liquid droplet. The models proposed in this work can accurately calculate the critical liquid-loading-flow rate for multifractured horizontal gas wells. This study can provide critical insights into the understanding of the liquid flowback and its effect on well productivity in gas reservoirs.