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This study aimed to investigate the holdup fraction in a perforated horizontal well. This article examined the surface of flow patterns (bubble, dispersed bubble, elongated dispersed bubble/slug, plug, stratified wave, half-slug, stratified wave flow, and stratified transition wave/semi-stratified flow). Numerical methods include the trapezoidal rule, Simpson's rule, and the mean displacement formula used to calculate the liquid surface area under a curve for irregular shapes. The average ratio of the flow pattern surface areas by the trapezoidal rule, the Simpsons rule and the average displacement formula were 81.3%, 79.8% and 81.14%, respectively. In addition, the surface area of the liquid phase (holdup fraction) which increases with bubble flow is 108.6 cm 2 and decreases with semi-stratified flow was 51.9 cm 2. However, the ratio of the liquid surface area that increased with Case A (bubble flow) was 32%, and it decreased by 15% with Case L (semi-stratified flow) due to the increased air-phase flow (void fraction). Water phase flow (holdup fraction) was kept constant. The percent error minimum of the liquid surface was 9.42%, 11%, and 9.50% by the Trapezoidal Rule, Simpsons Rule, and Average Displacement Formula occurring in Case A (bubble flow), respectively. In contrast, the maximum values of the surface defect percentage were 56.58%, 57.25%, and 56.75%, respectively, occurring in Case L (semi-stratified flow).

To address the issue of horizontal well production affected by the distribution of perforation density in the wellbore, a numerical model for simulating two-phase flow in a horizontal well is established under two perforation density distribution conditions (i.e. increasing the perforation density at inlet and outlet sections respectively). The simulation results are compared with experimental results to verify the reliability of the numerical simulation method. The behaviors of the total pressure drop, superficial velocity of air-water two-phase flow, void fraction, liquid film thickness, air production and liquid production that occur with various flow patterns are investigated under two perforation density distribution conditions based on the numerical model. The total pressure drop, superficial velocity of the mixture and void fraction increase with the air flow rate when the water flow rate is constant. The liquid film thickness decreases when the air flow rate increases. The liquid and air productions increase when the perforation density increases at the inlet section compared with increasing the perforation density at the outlet section of the perforated horizontal wellbore. It is noted that the air production increases with the air flow rate. Liquid production increases with the bubble flow and begins to decrease at the transition point of the slug-stratified flow, then increases through the stratified wave flow. The normalized liquid flux is higher when the perforation density increases at the inlet section, and increases with the radial air flow rate. [ABSTRACT FROM AUTHOR]