Results in Engineering (Jun 2023)
Experimental investigation of holdup fraction using the trapezoidal rule, Simpson's rule and the average offset formula in perforated horizontal wellbore
Abstract
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).
