P. Egermann - Academia.edu (original) (raw)
Papers by P. Egermann
Reservoir simulations require relative permeability and capillary pressure curves as representati... more Reservoir simulations require relative permeability and capillary pressure curves as representative as possible of the studied case, especially in terms of reservoir conditions. Several methods can be used to determine these parameters and each one has its own advantages but also its own limitations, whatever the experimental conditions, ambient or reservoir. Within a SCAL study, the selection of the most appropriate method is thus very difficult for the reservoir engineer. The main objective of this paper is to compare two methods for capillary pressure measurement: the centrifuge technique, which is widely used under ambient conditions, and the semi-dynamic method (SDM), first presented in 1993, which can operate under reservoir conditions. The principle of the experimental and interpretation methods is recalled in the first part of the paper (Forbes' interpretation method for the centrifuge technique and a recently patented interpretation method for the semi-dynamic technique...
ECMOR XV - 15th European Conference on the Mathematics of Oil Recovery, 2016
The present paper proposes a new family of multiscale finite volume methods. These methods usuall... more The present paper proposes a new family of multiscale finite volume methods. These methods usually deal with a dual mesh resolution, where the pressure field is solved on a coarse mesh, while the saturation fields, which may have discontinuities, are solved on a finer reservoir grid, on which petrophysical heterogeneities are defined. Unfortunately, the efficiency of dual mesh methods is strongly related to the definition of up-gridding and down-gridding steps, allowing to define accurately pressure and saturation fields on both fine and coarse meshes and the ability of the approach to be parallelized. In the new dual mesh formulation we developed, the pressure is solved on a coarse grid using a new hybrid formulation of the parabolic problem. This type of multiscale method for pressure equation called Multiscale Hybrid-Mixed method (MHMM) has been recently proposed for finite elements and mixed-finite element approach [1]. We extend here the MH-Mixed Method to a Finite Volume discretization, in order to deal with large multiphase reservoir models. The pressure solution is obtained by solving a hybrid form of the pressure problem on the coarse mesh, for which unknowns are fluxes defined on the coarse mesh faces. Basis flux functions are defined through the resolution of a local finite volume problem, which accounts for local heterogeneity, whereas pressure continuity between cells is weakly imposed through flux basis functions, regarded as Lagrange multipliers. Such an approach is conservative both on the coarse and local scales and can be easily parallelized, which is an advantage compared to other existing finite volume multiscale approaches. It has also a high flexibility to refine the coarse discretization just by refinement of the Lagrange multiplier space defined on the coarse faces without changing nor the coarse nor the fine meshes. This refinement can also be done adaptively with respect to a posteriori error estimators. The method is illustrated by the application of single phase (well-testing) and multiphase flow in heterogeneous porous media at the field scale. [1] R. Araya, C. harder, D. Parades, F. Valentin, Multiscale Hybrid-Mixed Method, SIAM J. Numer. Anal. 51(6), 3505-3531, 2013.
All Days, 2000
Depressurization of a virgin or waterflooded oil reservoir results in the appearance of a solutio... more Depressurization of a virgin or waterflooded oil reservoir results in the appearance of a solution gas saturation. Above a saturation threshold, this gas becomes mobile and can be produced. Knowledge of the critical gas saturation (Sgc) and the subsequent relative permeabilities (Kr) in the far field and the near-wellbore region has a tremendous impact on gas and oil production forecasts. The present paper provides a new methodology to obtain representative Kr and Sgc values for a depressurization process. Specific experiments are presented in which under-saturated oil was injected upstream at a fixed rate whereas downstream the pressure was controlled in order to reproduce a drawdown. Evolution of pressure was recorded and in-situ gas saturations measured by CT-scanner. Two initial conditions were considered, fully oil saturated and at irreducible water saturation. Influence of the drawdown scheme was also explored. Transient evolution of the gas saturation profile in the core is c...
Proceedings of SPE Annual Technical Conference and Exhibition, 2006
It has been long recognized that interfacial interactions (interfacial tension, wettability, capi... more It has been long recognized that interfacial interactions (interfacial tension, wettability, capillarity and interfacial mass transfer) govern fluid distribution and behavior in porous media. Therefore the interfacial interactions between CO2, brine and reservoir oil and/or gas should have an important influence on the effectiveness of any CO2 storage operation. As a model, the interfacial tension of the pure water-CO2 system has been studied intensively. Nevertheless, to our knowledge, no interfacial tension (IFT) equilibrium data for brine-CO2systems are available at reservoir conditions for different salinities, temperatures and pressures. In this paper, we present experimental IFT brine-CO2data obtained at high pressures (45 to 255 bar), high temperatures (27 to 100°C) and different salt concentrations (5,000 to 150,000 ppm of NaCl) using the axi-symmetric drop shape analysis technique (ADSA) for a rising drop case. Special attention was paid in developing a procedure to achieve true thermodynamic equilibrium. The themodynamic conditions were selected in order to cover the most practical CO2 storage cases of interest, liquid and supercritical CO2. A correlation was developped on the basis of the Parachor model, the salt effect and a regression fit of more than a hundred IFT experimental values obtained in this study. This correlation yields a Brine-CO2IFT prediction at reservoir conditions with a mean absolute deviation of 2.5%. We also present correlations to determine the IFT increase due to salt concentration. The existence of a plateau in the brine-CO2IFT values, independent of the temperature and the pressure and only dependent on the salt concentration, has been demonstrated from the experimental data for temperatures between 27 to 71°C and pressures above 150 bar. These pressure and temperature values can be easily found in many geological sites considered as prospects for CO2storage. The linear dependency of the IFT increase with molal NaCl concentration has also been demonstrated.
Proceedings of SPE Annual Technical Conference and Exhibition, 2006
The injection of carbon dioxide in oil and gas reservoirs (Enhanced Hydrocarbon Recovery, EHR) or... more The injection of carbon dioxide in oil and gas reservoirs (Enhanced Hydrocarbon Recovery, EHR) or in aquifers is a promising way to cope with the short-medium term issue of greenhouse gas emission mitigation. Although CO2-EHR projects represent the best economical opportunities, the CO2 injection projects in deep aquifers offer the largest capacity potential for long-term CO2 storage. The design of a CO2 injection project mainly depends on the results of reservoir models. To be predictive, the numerical tools have to be parameterized to adequately model the multiphase flow behavior (relative permeability curves) and the phase exchanges between the injected fluids and the fluids in place (thermodynamic equilibrium). In the particular case of the CO2 injection, the potential rock/fluid interactions with the host formation must also be studied carefully as a function of the thermodynamic conditions, the fluid compositions, the rock mineralogy but also the flow regime (i.e. the distance to the well bore). This paper presents an integrated workflow based on experiments and numerical simulations to determine in a comprehensive and robust manner the appropriate parameters at the core scale for a CO2 injection in aquifer. CO2 injection experiments were conducted under reservoir conditions. Experiment were carried out on companion plugs under several thermodynamic conditions and with different fluid systems (different brine salinities) in order to collect data (production curves and differential pressure evolution as a function of time) over a wide range of CO2 storage conditions. Then, these experiments were modeled using a compositional simulator dedicated to CO2 geological storage. Using this approach, we show that an unique set of parameters enables modeling of CO2 injection for various thermodynamic conditions and fluid systems. Therefore, such approach leads to predictive simulations at the core scale, which contributes to the accuracy of the performance prediction of the CO2 injection at the reservoir scale, if the main geological features (heterogeneities) are included into the large scale model.
Petrophysics, 2014
Three-phase flow data play a major role in the design of various E&P applications (gas injection,... more Three-phase flow data play a major role in the design of various E&P applications (gas injection, WAG, SAGD) and also in the context of gas storage activity (additional oil related to the conversion of depleted oil fields). Intermediate to oil-wet carbonate reservoirs comprise huge global oil reserves, and hence it is very important to characterize three-phase flow data to reduce current uncertainties. This work is an experimental contribution to share new data sets of three-phase relative permeability (kr) obtained under drainage conditions (gas saturation increase) on different intermediate to oil-wet carbonate rock-types of two giant Middle East reservoirs. In each case, the ternary diagrams have been obtained through the numerical interpretation of displacement experiments conducted at various initial saturation conditions (from Swi to Sorw). Three-phase kr tables (functions of two saturations Sg and Sw) have been adjusted by trial-and-error method until a good history match was...
This paper addresses the problem of modeling transient production curves during a centrifuge expe... more This paper addresses the problem of modeling transient production curves during a centrifuge experiment. Modern accurate measurement techniques used to monitor fluid saturation versus time while spinning indicate that capillary equilibrium is difficult to define and that a stability criterion for changing the centrifuge speed is needed. Such a criterion is very often set empirically, based on individual experience. This approach can lead to errors in the capillary pressure curves that are not detected by capillary pressure interpretation algorithms. We propose a mathematical model using two exponential functions to fit the measured production curves. The bi-exponential model is necessary because of the existence of two typical time scales, that are different by a factor of ten. They are interpreted as the signature of viscous and capillary-controlled flow. For constantly accelerating centrifuge experiments, a model using two strechted exponential functions is proposed. The bi-expone...
A true permeability log is obtainable for the first time just a few days after drilling a well.
Assessing representative threshold capillary properties of fine grained rocks is very important i... more Assessing representative threshold capillary properties of fine grained rocks is very important in the context of the reservoir production, the basin modeling and the geological storage (natural gas or CO2) This paper presents an innovative approach to measuring representative values of threshold capillary pressure under in-situ conditions based on the analysis of a dynamic displacement of the non-wetting fluid in the sample. When the injection is conducted at a constant pressure drop (higher than the threshold capillary pressure), the pressure profile within the core can be divided into three parts : the upstream invaded region, the front zone with a pressure jump associated with the threshold capillary pressure and the virgin region still saturated with the brine. Just before the non-wetting phase contacts the inlet face of the core, the brine production rate corresponds to Darcy's law using the overall pressure drop and the absolute permeability value. When the non-wetting fl...
This paper presents results from a laboratory study comparing different techniques to measure per... more This paper presents results from a laboratory study comparing different techniques to measure permeabilities below 10 microDarcy such as tight reservoir and cap rock. Permeabilities were measured with gas using three different methods. An unsteady-state method based on the pressure fall off technique and a conventional steady-state method were used to measure permeabilities in conventional plugs of 70 mm length, 40 mm diameter. An unconventional method, was also implemented through a new permeameter device (Darcygas). The technique consists in setting rock fragments or a small plug in a small cell and studying the response to a pressure pulse. This method has the advantage to require very small pieces of rock (like drill cuttings) without any conditioning. Moreover, the measurement is extremely fast since the relaxation time is proportional to the square of the sample size. Once all the measurements were corrected from Klinkenberg effects, the permeabilities measured with the three ...
65th EAGE Conference & Exhibition
Petrophysics – The SPWLA Journal of Formation Evaluation and Reservoir Description
3rd EAGE North African/Mediterranean Petroleum and Geosciences Conference and Exhibition, 2007
Oil & Gas Science and Technology – Revue de l’Institut Français du Pétrole, 2010
Proceedings of SPE Annual Technical Conference and Exhibition, 1999
SPE European Petroleum Conference, 2000
Reservoir simulations require relative permeability and capillary pressure curves as representati... more Reservoir simulations require relative permeability and capillary pressure curves as representative as possible of the studied case, especially in terms of reservoir conditions. Several methods can be used to determine these parameters and each one has its own advantages but also its own limitations, whatever the experimental conditions, ambient or reservoir. Within a SCAL study, the selection of the most appropriate method is thus very difficult for the reservoir engineer. The main objective of this paper is to compare two methods for capillary pressure measurement: the centrifuge technique, which is widely used under ambient conditions, and the semi-dynamic method (SDM), first presented in 1993, which can operate under reservoir conditions. The principle of the experimental and interpretation methods is recalled in the first part of the paper (Forbes' interpretation method for the centrifuge technique and a recently patented interpretation method for the semi-dynamic technique...
ECMOR XV - 15th European Conference on the Mathematics of Oil Recovery, 2016
The present paper proposes a new family of multiscale finite volume methods. These methods usuall... more The present paper proposes a new family of multiscale finite volume methods. These methods usually deal with a dual mesh resolution, where the pressure field is solved on a coarse mesh, while the saturation fields, which may have discontinuities, are solved on a finer reservoir grid, on which petrophysical heterogeneities are defined. Unfortunately, the efficiency of dual mesh methods is strongly related to the definition of up-gridding and down-gridding steps, allowing to define accurately pressure and saturation fields on both fine and coarse meshes and the ability of the approach to be parallelized. In the new dual mesh formulation we developed, the pressure is solved on a coarse grid using a new hybrid formulation of the parabolic problem. This type of multiscale method for pressure equation called Multiscale Hybrid-Mixed method (MHMM) has been recently proposed for finite elements and mixed-finite element approach [1]. We extend here the MH-Mixed Method to a Finite Volume discretization, in order to deal with large multiphase reservoir models. The pressure solution is obtained by solving a hybrid form of the pressure problem on the coarse mesh, for which unknowns are fluxes defined on the coarse mesh faces. Basis flux functions are defined through the resolution of a local finite volume problem, which accounts for local heterogeneity, whereas pressure continuity between cells is weakly imposed through flux basis functions, regarded as Lagrange multipliers. Such an approach is conservative both on the coarse and local scales and can be easily parallelized, which is an advantage compared to other existing finite volume multiscale approaches. It has also a high flexibility to refine the coarse discretization just by refinement of the Lagrange multiplier space defined on the coarse faces without changing nor the coarse nor the fine meshes. This refinement can also be done adaptively with respect to a posteriori error estimators. The method is illustrated by the application of single phase (well-testing) and multiphase flow in heterogeneous porous media at the field scale. [1] R. Araya, C. harder, D. Parades, F. Valentin, Multiscale Hybrid-Mixed Method, SIAM J. Numer. Anal. 51(6), 3505-3531, 2013.
All Days, 2000
Depressurization of a virgin or waterflooded oil reservoir results in the appearance of a solutio... more Depressurization of a virgin or waterflooded oil reservoir results in the appearance of a solution gas saturation. Above a saturation threshold, this gas becomes mobile and can be produced. Knowledge of the critical gas saturation (Sgc) and the subsequent relative permeabilities (Kr) in the far field and the near-wellbore region has a tremendous impact on gas and oil production forecasts. The present paper provides a new methodology to obtain representative Kr and Sgc values for a depressurization process. Specific experiments are presented in which under-saturated oil was injected upstream at a fixed rate whereas downstream the pressure was controlled in order to reproduce a drawdown. Evolution of pressure was recorded and in-situ gas saturations measured by CT-scanner. Two initial conditions were considered, fully oil saturated and at irreducible water saturation. Influence of the drawdown scheme was also explored. Transient evolution of the gas saturation profile in the core is c...
Proceedings of SPE Annual Technical Conference and Exhibition, 2006
It has been long recognized that interfacial interactions (interfacial tension, wettability, capi... more It has been long recognized that interfacial interactions (interfacial tension, wettability, capillarity and interfacial mass transfer) govern fluid distribution and behavior in porous media. Therefore the interfacial interactions between CO2, brine and reservoir oil and/or gas should have an important influence on the effectiveness of any CO2 storage operation. As a model, the interfacial tension of the pure water-CO2 system has been studied intensively. Nevertheless, to our knowledge, no interfacial tension (IFT) equilibrium data for brine-CO2systems are available at reservoir conditions for different salinities, temperatures and pressures. In this paper, we present experimental IFT brine-CO2data obtained at high pressures (45 to 255 bar), high temperatures (27 to 100°C) and different salt concentrations (5,000 to 150,000 ppm of NaCl) using the axi-symmetric drop shape analysis technique (ADSA) for a rising drop case. Special attention was paid in developing a procedure to achieve true thermodynamic equilibrium. The themodynamic conditions were selected in order to cover the most practical CO2 storage cases of interest, liquid and supercritical CO2. A correlation was developped on the basis of the Parachor model, the salt effect and a regression fit of more than a hundred IFT experimental values obtained in this study. This correlation yields a Brine-CO2IFT prediction at reservoir conditions with a mean absolute deviation of 2.5%. We also present correlations to determine the IFT increase due to salt concentration. The existence of a plateau in the brine-CO2IFT values, independent of the temperature and the pressure and only dependent on the salt concentration, has been demonstrated from the experimental data for temperatures between 27 to 71°C and pressures above 150 bar. These pressure and temperature values can be easily found in many geological sites considered as prospects for CO2storage. The linear dependency of the IFT increase with molal NaCl concentration has also been demonstrated.
Proceedings of SPE Annual Technical Conference and Exhibition, 2006
The injection of carbon dioxide in oil and gas reservoirs (Enhanced Hydrocarbon Recovery, EHR) or... more The injection of carbon dioxide in oil and gas reservoirs (Enhanced Hydrocarbon Recovery, EHR) or in aquifers is a promising way to cope with the short-medium term issue of greenhouse gas emission mitigation. Although CO2-EHR projects represent the best economical opportunities, the CO2 injection projects in deep aquifers offer the largest capacity potential for long-term CO2 storage. The design of a CO2 injection project mainly depends on the results of reservoir models. To be predictive, the numerical tools have to be parameterized to adequately model the multiphase flow behavior (relative permeability curves) and the phase exchanges between the injected fluids and the fluids in place (thermodynamic equilibrium). In the particular case of the CO2 injection, the potential rock/fluid interactions with the host formation must also be studied carefully as a function of the thermodynamic conditions, the fluid compositions, the rock mineralogy but also the flow regime (i.e. the distance to the well bore). This paper presents an integrated workflow based on experiments and numerical simulations to determine in a comprehensive and robust manner the appropriate parameters at the core scale for a CO2 injection in aquifer. CO2 injection experiments were conducted under reservoir conditions. Experiment were carried out on companion plugs under several thermodynamic conditions and with different fluid systems (different brine salinities) in order to collect data (production curves and differential pressure evolution as a function of time) over a wide range of CO2 storage conditions. Then, these experiments were modeled using a compositional simulator dedicated to CO2 geological storage. Using this approach, we show that an unique set of parameters enables modeling of CO2 injection for various thermodynamic conditions and fluid systems. Therefore, such approach leads to predictive simulations at the core scale, which contributes to the accuracy of the performance prediction of the CO2 injection at the reservoir scale, if the main geological features (heterogeneities) are included into the large scale model.
Petrophysics, 2014
Three-phase flow data play a major role in the design of various E&P applications (gas injection,... more Three-phase flow data play a major role in the design of various E&P applications (gas injection, WAG, SAGD) and also in the context of gas storage activity (additional oil related to the conversion of depleted oil fields). Intermediate to oil-wet carbonate reservoirs comprise huge global oil reserves, and hence it is very important to characterize three-phase flow data to reduce current uncertainties. This work is an experimental contribution to share new data sets of three-phase relative permeability (kr) obtained under drainage conditions (gas saturation increase) on different intermediate to oil-wet carbonate rock-types of two giant Middle East reservoirs. In each case, the ternary diagrams have been obtained through the numerical interpretation of displacement experiments conducted at various initial saturation conditions (from Swi to Sorw). Three-phase kr tables (functions of two saturations Sg and Sw) have been adjusted by trial-and-error method until a good history match was...
This paper addresses the problem of modeling transient production curves during a centrifuge expe... more This paper addresses the problem of modeling transient production curves during a centrifuge experiment. Modern accurate measurement techniques used to monitor fluid saturation versus time while spinning indicate that capillary equilibrium is difficult to define and that a stability criterion for changing the centrifuge speed is needed. Such a criterion is very often set empirically, based on individual experience. This approach can lead to errors in the capillary pressure curves that are not detected by capillary pressure interpretation algorithms. We propose a mathematical model using two exponential functions to fit the measured production curves. The bi-exponential model is necessary because of the existence of two typical time scales, that are different by a factor of ten. They are interpreted as the signature of viscous and capillary-controlled flow. For constantly accelerating centrifuge experiments, a model using two strechted exponential functions is proposed. The bi-expone...
A true permeability log is obtainable for the first time just a few days after drilling a well.
Assessing representative threshold capillary properties of fine grained rocks is very important i... more Assessing representative threshold capillary properties of fine grained rocks is very important in the context of the reservoir production, the basin modeling and the geological storage (natural gas or CO2) This paper presents an innovative approach to measuring representative values of threshold capillary pressure under in-situ conditions based on the analysis of a dynamic displacement of the non-wetting fluid in the sample. When the injection is conducted at a constant pressure drop (higher than the threshold capillary pressure), the pressure profile within the core can be divided into three parts : the upstream invaded region, the front zone with a pressure jump associated with the threshold capillary pressure and the virgin region still saturated with the brine. Just before the non-wetting phase contacts the inlet face of the core, the brine production rate corresponds to Darcy's law using the overall pressure drop and the absolute permeability value. When the non-wetting fl...
This paper presents results from a laboratory study comparing different techniques to measure per... more This paper presents results from a laboratory study comparing different techniques to measure permeabilities below 10 microDarcy such as tight reservoir and cap rock. Permeabilities were measured with gas using three different methods. An unsteady-state method based on the pressure fall off technique and a conventional steady-state method were used to measure permeabilities in conventional plugs of 70 mm length, 40 mm diameter. An unconventional method, was also implemented through a new permeameter device (Darcygas). The technique consists in setting rock fragments or a small plug in a small cell and studying the response to a pressure pulse. This method has the advantage to require very small pieces of rock (like drill cuttings) without any conditioning. Moreover, the measurement is extremely fast since the relaxation time is proportional to the square of the sample size. Once all the measurements were corrected from Klinkenberg effects, the permeabilities measured with the three ...
65th EAGE Conference & Exhibition
Petrophysics – The SPWLA Journal of Formation Evaluation and Reservoir Description
3rd EAGE North African/Mediterranean Petroleum and Geosciences Conference and Exhibition, 2007
Oil & Gas Science and Technology – Revue de l’Institut Français du Pétrole, 2010
Proceedings of SPE Annual Technical Conference and Exhibition, 1999
SPE European Petroleum Conference, 2000