Modélisation d'un puits dans le cadre du projet GEOThermie haute énergie dans les Réservoirs Fracturés




Boillante 3 is the suitable one of the geothermal site that can produce a high demand of thermal energy. The Bouillante 3 has led to study the model of two-phase flow in production well. The empirical equations would identify the occurrence of the behaviour of producing geothermal wells in term of void fraction correlations with depth.



Global warming, like the majority of crises around the world, is a controversial topic.Geothermal energy considerable public concern has been placed on pioneering the sustainable energy sources. The Bouillante geothermal is one project that claims to be able to bring enormous benefits to the local communities. The Bouillante project invests considerable funds through BRGM and the joint ventures. Bouillante 3 becomes such a significant part of the modeling geothermal reservoirs simulations.

This project has led to greater understanding of the heat and pressure gradient inside geothermal well. Therefore, void fraction correlation would derive an emphasis term to simulate the characteristic physical model of Bouillante geothermal reservoirs.

Figure 1. shows that the typical type of geothermal in term of temperature level


The aim of this study is to take an account in detail of theoretical background of two-phase flow and validate of simulation with saturation temperature and static temperature from void fraction correlation analysis examined.





Enhanced Geothermal System

An Enhanced Geothermal System (EGS) is the process to generate electricity through "hydraulic stimulation". The geothermal power sources are stored as heat in hot fractured volcanic.

First of all, the EGS reservoir procedure will begin with identifying a geologic model of a potential site. The production area and the necessary properties like mechanical properties, the temperature gradient, and flow to extract the energy. The location should suitable for the geothermal reservoirs. 

Secondly, the majority of experienced geothermal drilling is to create a fracture network by injecting water at sufficient pressure or temperature differential. The hot water is pumped to the surface through the production well.

Lastly, the production well is carried the steam up to the surface from the bottom hole for driving a turbine, which in turn powers a generator for producing electricity.


Figure 3. illustrated schematic of another conceptual three-wells Enhanced Geothermal System (EGS) diagram modified from ANU Hot Rock Energy website.


Bouillante-3 wellbore

The Bouillante geothermal field is located on the island of Guadeloupe, Lesser Antilles. There are numerous surface manifestations such as hot springs, fumaroles and steaming ground which is suitable for geothermal energy. The French company BRGM had invested in the project of Bouillante geothermal field. The Bouillante field is constituted 7 wells but only 3 wells (s BO-4, BO-5 and BO-6)  are currently producing. Bouillante 3 was drilled in the year 1970 by EURAFREP but it was blocked. According to Bouillante 3 is far about 15 kilometres from the current active Soufrière volcano and about 600 m west of BO-2 as can be seen in the figure 2. and the power plant. 

Figure 2 shows the location map around the present power plant (Sanjuan et al., 2004)

Bouillante3 have been stimulating well for geothermal power plant again b BRGMWell BO-3 has 500 production level depth,  with the temperature   range between 250 - 260 ° C. The geothermal field of BO-3 is expected to produce the electricity generating capability about 24 MW with 150 tonne/hour of fluid and 30 tonne/hour of steam. 



Two-phase flow plays a predominant role in various industries especially geothermal reservoirs model, wellbore, and pipelines. The flow combines of phases which are gas/liquid, gas/solid, liquid/solid and immiscible fluids. The flow model can provide the fluid properties such as the temperature profile, the pressure gradient, and flow pattern. Due to the flow in the production well was evaluated the flow characteristics of the vertical pipe. The flow pattern in vertical upflow pipe is showed in the figure 3. 

Figure 3. Flow pattern in vertical upflow, the flow assurance site





The first step of the calculation was to obtain the temperature profile because temperature is the first initial value use for determination of exploration geothermal gradient mapping. There are several methods available for precisely  predicting temperature gradient along the production well. 

With a one-dimensional steady state, Carslaw and Jaeger (1959) was proposed to use the thermal conduction equation.

with the boundary conditions (z=0) are

T(0) = T0

The temperature profile can be determined by direct integration of the temperature gradient with the determination of other parameters.


The details of the parameters were used for calculating the temperature shown in Table 1.
Table 1 the initial measured of Bouillante 3 
The predicted temperature gradient of the BO-3 production well is shown in figure 3. The graph indicates the relation wall temperature from the surface down to the bottom hole of the reservoirs. The temperature range at 500 m depth is around 260 C.
Figure 3. The predicted wall temperature of the BO-3 
Figure 4 The comparison temperature profile with depth in each Bouillante

Two-Phase Flow Pressure Drop


Generally, the total pressure drop (∆Ptotal )   of a fluid depends on the kinetic and potential energy which total pressure drop can be expressed in term of a static pressure drop( ∆Pstatic), the momentum pressure drop (∆Pmom) and the friction pressure drop ( ∆Pfrict). 

The static pressure drop equation is related to the vary in elevation of the vertical depth. 

where z is the depth of the production well. The homogeneous density  is


The Lockhart and Martinelli correlation (1949) void fraction can be obtained from the steam quality of x as

This method shows the relation between the void fraction, density and viscosity  which are 

varied in the production well.

The momentum pressure drop is a covariant of the steam quality term.

The method of Lockhart and Martinelli correlation (1949) is the original well-known method that used for two-phase prediction.In order to calculate the friction  pressure is derived from the correlation of the Lockhart and Martinelli model. 

The function is estimated based on a two-phase multiplier for the liquid phase (l) and vapor phase(g), respectively

for ∆pg can be applied with (x2)

The friction factor can be defined in terms of Reynold number by Blasius equation:

where is Reynold number is


The viscosity is calculated based on the quality average between two-phase flow  which is obtained from 

The single -phase friction of the liquid fl and the steam fg are corresponded with two-phase multipliers



Liquid Gas C
Turbulent Turbulent 20
Laminar Turbulent 12
Turbulent Laminar 10
Laminar Laminar 5

Table 1. Values of C

where is Xtt is the Martinelli parameter for both phase in the turbulent regimes defined as

The correlation of Lockhart and Martinelli is applicable to the vapor quality range 0<x<1.

The most problematic term is vapor quality (x) which can be obtained from heat flux correlation. 

where the heat flux( q)  is 

The heat flux is based on the enthalpy of two-phase flow which proposed by Gunger et Winterton (1986) 

All these relation depend on temperature, pressure, and void fraction. 

Figure 5 shows the pressure in term of the changing of depth.

The graph indicates that the variation of pressure versus the well depth from the land surface to the bottom hole. The trend of the pressure was upward while the increasing of the well depth. To sum up, it was expected to have the decreasing trend of pressure as  a function of depth taking the significant effects of the saturation temperature.

Figure 5 The predicted temperature and the saturation temperature 

It is obvious that the predicted temperature was willing to archive the saturation point at 250 C with very close to the bottom hole as shown in figure 5. On the other hand, the analysis of vapor quality (x) reported in figure 6 showed that error vapor quality (x) calculation along the saturation pressure. It provided the exceeding vapor quality values over 1. Generally, the vapor quality should not get more than 1.    

Figure 6. the saturation temperature contribution in the production well as a function of vapor quality (x)












1. The model of BO-3 is capable of the two-phase modeling with a various friction, friction correction factor and void fraction correlation
2. The predicted temperature shows that it can achieve the saturation phase  at temperature above 250 C

3. A measure of each void fraction performs in simulating the pressure and temperature profile  shows the uncertainty analysis and sensitivity.

4. Inaccurate prediction can be caused by the use of physical properties of water that do not represent actual thermodynamic behavior of geothermal fluid


Sanjuan B., Le Nindre Y.M., Menjoz A., Sbai A., Brach M., Lasne E. (2004) - Travaux de recherche liés au développement du champ géothermique de Bouillante (Guadeloupe). Rapport BRGM/RP-53136-FR, 166 p.

Wolverine turbine, INC engineering thermal innovation, Engineering data book III, Chapter 13 Two-phase pressure droup, 13-1.

Sergio P., Ferro and Goldschmit - A numerical model for multiphase flow on oil production wells, Center for industrial reserch, Tenaris. 

B.J. Azzopardi- Multiphase flow. Chemical engineering and chemical process technology-Vol.I- Multiphase flow

Halldora GTudmunsdottire, Magnus Thor Jonsson and Halldor Palsson(2013) -The wellbore simulation flowell. Proceesing, Thirty-Eighth Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, February 11-13,  SGP-TR-198

​Lockhart, R.W. and Martinelli, R.C. (1949).- Proposed Correlation of Data for isothermal Two-phase, Two component flow in pipes, Chemical engineering progress symposium series, 45:39-48

Compliation et interprétations des données thermique de Bouillante, BRGM/RP-52452-FR