# SPE Production & Operations Volume 24, Number 1, February 2009, pp. 165-170

SPE-108506-PA

### A Simple Mechanistic Model for Void-Fraction and Pressure-Gradient Prediction in Vertical and Inclined Gas/Liquid Flow

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DOI  10.2118/108506-PA http://dx.doi.org/10.2118/108506-PA

### Citation

• Khasanov, M., Khabibullin, R., Krasnov, V., Pashali, A., and Guk, V. 2009. A Simple Mechanistic Model for Void-Fraction and Pressure-Gradient Prediction in Vertical and Inclined Gas/Liquid Flow. SPE Prod & Oper  24 (1): 165-170. SPE-108506-PA.

### Discipline Categories

• 5.6 Multiphase Flow in Wells
• 5.7 Operations Management
• 5.3.1 Well Candidate Recognition

### Summary

A new mechanistic model for two-phase flow in vertical and inclined pipes was proposed on the basis of the drift-flux approach. The proposed model, unlike the other mechanistic models [Ansari et al. (1994); Xiao et al. (1990); Zhang et al.(2003)] that incorporate a system of nonlinear equations to solve, uses an explicit equation for liquid-holdup prediction, thus reducing computation time significantly. Coupled with some simplified assumptions on pressure/volume/temperature (PVT), such a simple form of a liquid-holdup-prediction formula enables an analytical integration of the pressure gradient in two-phase flow along the pipe. This procedure is used usually to speed up the calculation of bottomhole pressure (BHP) for a large number of wells for oil-production-optimization purposes (Khasanov et al. 2006).

The drift-flux approach can predict liquid holdup for bubbly flow quite accurately. However, for slug flow, it usually underestimates the void fraction. Because slug flow is the most common flow in producing wells, this leads to the pressure drop being overestimated significantly; this can be proved by comparing computational results to the experimental data and mechanistic models. Small gas bubbles in liquid slugs should be accounted for when predicting liquid holdup for slug flow more accurately. Gas in the slug body is considered by adding a proper term to the void-fraction expression. This term is based on the correlation for liquid holdup in the slug body. The model was evaluated with Rosneft's field data and the Tulsa University Fluid Flow Projects (TUFFP) databank. The model was evaluated by comparing it with three mechanistic models for multiphase flow.

### Introduction

The major tasks for every oil company are oil-production maximization and operational-costs reduction. This requires permanent well-production monitoring by selecting the most promising wells and performing operations on those wells to increase production (well-enhancement routines). The key objective of well-production monitoring is to control the productivity index and well potential for every well during the well lifecycle. This requires the well BHP to be determined. In some cases, direct measurement of BHP is either difficult or uneconomical; that is why BHP calculation is still a relevant problem.

The complexity of the pressure-gradient prediction grows out of the multiphase character of the mixture flowing through oil wells. The multiphase mechanistic models (those in Ansari et al. 1994; Xiao et al. 1990; Zhang et al. 2003) allow prediction of the pressure gradient with high accuracy. Such models together cover the whole range of pipe-inclination angles and input parameters. They are applicable for a detailed analysis, but because they usually incorporate a system of nonlinear equations to solve, the computation time can be quite long.

When an oil company operates thousands of wells, it is important for them to use their regular analysis to choose those wells the optimization of which would be most beneficial (Khasanov et al. 2006). For such cases, the use of mechanistic models can be rather difficult because their iterative procedures require lengthy computation times.

The purpose of this paper is to develop a simple mechanistic model for pressure-gradient prediction that (1) is applicable for the whole range of input data and (2) has a simple unified form of void-fraction expression for all considered flow patterns.

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### History

• Original manuscript received: 13 April 2007
• Meeting paper published: 27 June 2007
• Revised manuscript received: 15 August 2008
• Manuscript approved: 10 September 2008
• Published online: 2 March 2009
• Version of record: 26 February 2009