Chapter 1
Introduction

Abstract

Most of the fluid flows in the petroleum engineering are multiphase flows. For instance, the drilling fluid, during the common drilling of oil and gas wells, is a gas-solid phase. There are various macroscopic models for multiphase, such as the homogeneous flow model, the separated flow model, the drift-flux model and the statistical average model. These models are all based on the conservation laws of mass, momentum and energy. The basic parameters to describe a single phase flow are velocity, mass flow rate, and volumetric flow rate. Besides, in wellbore multiphase flow, the mass flow rate, volumetric fraction and velocity of each phase are also the important parameters. Although the mass proportion of gas-liquid phase is the same, the fluid behaviors change with the different gas-liquid distribution. Recognition of these characteristics is of great significance in multiphase flow study.

Keywords: drift-flux model; flow parameters; flow patterns; gas well drilling; homogeneous flow model; multiphase flow models; oil well drilling; separated flow model; statistical average model

A multiphase flow is a fluid flow that comprises more than one phase of matter. The phase defines the different chemical and physical properties of the matter, and the interface between different phases should be physically distinguished for multiphase flow. The same matter in different states, such as gas, liquid and solid, is considered as different phases. Insoluble chemicals with the same state are also considered as different phases. For instance, the fluid flow of ice and water, or vapor and water, is a multiphase flow. The fluid flow of oil and water is also a multiphase flow. However, the fluid flow of salt and water solution is not, because this solution is a homogeneous fluid without any physical interface between the two components.

The study of multiphase flow started at the beginning of the 20th century. Multiphase flow is widely applied in industry, such as in power generation, nuclear reactor technology, food production, chemical process, aerospace, automotive industries and petroleum engineering. From the 1970s, multiphase flows in the oil and gas wells especially became more and more important, because of the increasing dependence of world economy on petroleum, and the development of drilling and production engineering.

1.1 Multiphase flow in the well

Basically, most of the fluid flows in the petroleum engineering are multiphase flows. For instance, the drilling fluid, during the common drilling of oil and gas wells, is a gas-solid phase. Crude oil, during the production, is normally a gas-oil-water mixture. However, there are well-established methods to solve these fluid problems for conventional processing in petroleum engineering. In this book, we focus on the multiphase flow for unconventional processing, especially in drilling. These problems include underbalanced drilling, well control for kicking, well control for the acidic gas well, and the well control for deepwater drilling.

Underbalanced drilling uses low-density drilling fluid to keep the wellbore pressure lower than formation pore pressure, which protects the formation during the drilling. This demands very precise pressure control of the drilling fluid, otherwise disasters such as kicking and well collapse will easily happen. Injecting air to the drilling fluid is the most popular approach to lighten the drilling fluid. The prediction for this gas-liquid system in the complicated pressure and temperature conditions of the wellbore is challenging.

Safety is of key importance for the petroleum industry. Kicking and blowing are disasters that can damage the drilling facilities, and even kill the crews in many cases. These lead to serious social and economic losses. The early prediction of kicking, and well control when kicking or blowing happens, could efficiently prevent these losses.

In the 21st century, oil fields have been extended to offshore, where efficient lifting and multiphase transfer techniques are the common means for oil and gas development. How to increase the pumping efficiency and metering accuracy is related to multiphase flow theory. Therefore, the development of multiphase flow theory has a close relationship with petroleum engineering.

Due to the complexity of the multiphase flow, there are still many theoretical problems that have not been solved so far – such as flow regime transition, flow instability, flow similarity, phase interaction, propagation of sonic and electro-magnetic signals in multiphase flow, and so on. The development of multiphase flow theory is still in its early stages, and there is still a long way to go for the application of a perfect multiphase theory to practice.

1.2 Methods

1.2.1 Theoretical analysis

Based on different mathematical and physical principles, the theoretical study of the multiphase flow is classified into three different aspects: the classical macroscopic continuum mechanics; microscopic analysis, based on molecular dynamics; and mesoscopic studies. The multiphase flow problems introduced in this book mainly concern the macroscopic analysis.

There are various macroscopic models for multiphase, such as the homogeneous flow model, the separated flow model, the drift-flux model and the statistical average model. These models are all based on the conservation laws of mass, momentum and energy. They treat the interactions and the distribution of different phases with different methods. Details can be found in Section 1.5.

Microscopic analysis studies the scale of molecules, or so-called Molecule Dynamics (MD). The dynamics of every molecule in a study object have to be computed for this method. Because of limited computing capability, the simulation for complicated flow field is difficult to approach at the present time. So far, it only applies in micro-scale fluid dynamic problems.

Macroscopic continuum theory cannot be applied for some multi-scale and multiphase physical problems, while microscopic analysis is limited for the real application, due to limited computing capability. These multi-scale and multiphase fluid problems are quite challenging for the classical methods. However, there are novel methods, such as the so-called mesoscopic method, to build models in the scale between the microscopic and macroscopic method to make connection between them. The current mesoscopic methods include: Lattice cellular automata; the Lattice Boltzmann method; the Discretized Boltzmann model; the Gas kinetic scheme; and the Dissipative particle dynamics method.

1.2.2 Experimental study

The experimental study is the main method to discover the physical phenomena and to calibrate the theoretical results. There are two ways to approach the experiments for the petroleum industry: field observations and laboratory simulations. Field observation measures the existed fluid phenomena to analyze the laws of the flow and predict the changing of the flow. Laboratory simulation can manipulate the fluid conditions by which the phenomena can be reproduced. The flow phenomena can be generated on purpose, which helps in investigating characters and the properties of the complex flow. The observation and measurement of the velocity, flow rate, dimension, volume fraction, void fraction, temperature distribution, and so on, of each phase are very important in studying the flow, heat transfer, and mass transfer of the multiphase fluids.

The flow pattern formation and transition are important conditions for the fluid flow and heat transfer of the two-phase flow. Studies for the flow pattern and flow pattern transfer significantly depend on the experiments. With the experimental results, the characteristic parameters of the flow pattern and empirical formulas are obtained. Mathematical models of different flow patterns are built, based on the experimental study and theoretical analysis, and the characteristic parameters of the flow pattern and fluid properties are computed by these models. High-quality experimental data provide the basics for building the empirical models. Methods of measurement of the flow pattern include visual observation, high-speed cameras, holographic cameras, and electrical measurement.

There are two ways to measure the parameters of the flow rate: direct measurement and indirect measurement. Direct measurement includes: volumetric method, mass flow method, throttling method, turbine testing method, and so on. Indirect measurement includes: correlation method, mechanics method, thermal method, optical method, acoustics method, electromagnetic method, Nuclear Magnetic Resonance (NMR), and tracer method. Measurement methods for phase fraction include: quick closing valve method, conductometry, capacitance method, ray method, optical method, acoustics method, and microwave method. The bubble and droplet size of multiphase flow can be measured by the following methods: sieving method, photoelectric sedimentation method, capillary method, photographic method, light scattering method, ultrasonic attenuation method, and so on.

1.2.3 Numerical simulation

Numerical simulation, which is known as Computational Fluid Dynamics (CFD), digitally solves the existing flow models by a computing method. The results of the flow parameters can be illustrated with images or specific data curves. The basic idea of CFD is to solve the existing flow models, which are normally composed of partial differential...