- Email: [email protected]
Numerical Simulation of Hydraulic Fracturing Process in an Enhanced Geothermal Reservoir Using a Continuum Homogenized Approach
Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 191 (2017) 821 – 828
Symposium of the International Society for Rock Mechanics
Numerical Simulation of Hydraulic Fracturing Process in an Enhanced Geothermal Reservoir using a Continuum Homogenized Approach Johannes Will*, Stefan Eckardt, Animesh Ranjan Dynardo GmbH, Steubenstrasse 25, Weimar 99423, Germany
Abstract The current study presents a numerical modeling approach for three-dimensional simulation of hydro-shearing in jointed rocks for the generation of a man-made, multi-fracture heat exchanger in Hot Dry Rock (HDR) Geothermal reservoir. Various literatures have suggested the presence of in-situ fractured rock mass even in massive granite formations. Thereby, 3D numerical modelling is essential, since the prediction of fracture growth in 3D is key to investigation of different fracture designs and furthermore various operational parameters in order to optimize the heat exchanger design and the resulting energy production. The numerical approach incorporates the Dynardo’s approach of homogenized continuum method to simulate the hydro-shearing process in jointed rocks unlike vast majority of commercial and scientific approaches which use the discrete modelling technique. The main motivation of the continuum approach is the numerical efficiency of the 3D coupled hydraulicmechanical simulations of hydraulic fracturing process in comparison to other alternatives. The input parameters of the numerical model from the best available well log and reservoir data are calibrated from diagnostics measurements such as Micro-seismic events, Bottom Hole Pressure, etc to assign the correct level of forecast quality to the important mechanisms of hydraulic fracturing. The numerical procedure is applied to a prospective Granite reservoir in Thüringen, Germany within the purview of a German joint research project – optiRiss. The integrated approach involves ANSYS as a pre-processor and solver, Dynardo’s fracturing simulator on top of ANSYS, Tamino – a post-processing tool and optiSLang – an environment for optimization and uncertainty quantification. ©2017 2017The TheAuthors. Authors. Published by Elsevier © Published by Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the organizing committee of EUROCK 2017. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of EUROCK 2017 Keywords: Hot Dry Rock Geothermal Reservoir; Enhanced Geothermal Systems; Jointed Rocks; Calibration; ANSYS; multiPlas; optiSlang
* Corresponding author. Tel.: +49 (0) 3643 9008-30; fax: +49 (0) 3643 9008-39. E-mail address: [email protected]
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of EUROCK 2017
doi:10.1016/j.proeng.2017.05.249
822
Johannes Will et al. / Procedia Engineering 191 (2017) 821 – 828
1. Introduction Energy consumption in the world has seen an ever increasing upward trend since the early part of the 20th century. Still a major chunk of the total energy supply comes from non-renewable energy resources with approximately 66 % supplied only by crude oil, natural gas and coal reserves. The large share of these resources are not just restricted to developing economies such as China, Brazil, etc. but also economic powerhouses such as USA and the European Union [1]. Geothermal Energy provides tremendous benefits in terms of reducing dependence on fossil fuels, reducing greenhouse emissions and generating new economic and employment opportunities. Geothermal Power systems aim to extract the inexhaustible heat available beneath the earth's surface. Natural Geothermal springs are rare to find and hard to locate and in order to reduce dependence on naturally occurring hydrothermal reservoirs, Hot Dry Rock/Enhanced Geothermal Systems (EGS) provide a suitable alternative. EGS reservoirs are set-up by drilling wells beneath the earth's surface and creating a man-made permeable fracture network between the wells. In the process, Hydraulic Fracturing is a well-stimulation technique used for creating artificial heat exchanger by creating a network of permeable fractures between injection and production wells. During the last 15 years, Dynardo GmbH has developed a) Thermo-Hydro-Mechanical (THM) simulation environment based on ANSYS® implicit finite element code for parametric FEM modeling for geotechnical applications with successful applications in Dam Engineering [2], Hydraulic Fracturing of unconventional Oil, Gas reservoirs [3], Geothermal reservoirs [4] and Nuclear Waste disposals [5], b) Dynardo’s toolbox for parametric variation optiSLang® for sensitivity analysis and calibration of large number of reservoir parameters as well as engineering and operational conditions parameters and their influence on the final stimulated rock volume, the production and their uplift potentials. Since 2008, the THM simulation capabilities have been extended to 3D simulation of Enhanced Geothermal Systems or Hot Dry Rock Geothermal reservoirs. The Fracturing design in an EGS reservoir is different to fracturing design in an oil or gas reservoir. The process, more commonly referred to as Hydro-shearing [6] aims to generate mainly shear fractures between rocks by inducing shear failure in contrast to Hydraulic Fracturing in oil or gas reservoirs where tensile fractures are targeted, with injected fluid are used to break the rock and along with a proppant mixture are used to maintain the created openings. For EGS applications, similar to the numerical simulation procedure applied for oil or gas reservoir simulations, the homogenized continuum approach is used since it is far more efficient than other alternatives such as Discrete Element Modelling, XFEM, etc. The current study focusses on application of the aforementioned approach to numerical calibration of simulation parameters based on available data such as Bottom Hole Pressure (BHP) history or Micro-Seismic Events (MSE) Data and identification of the most influential parameters within an uncertain yet quantified design space. 2. Numerical Simulation The hydraulic fracturing simulator for the 3-dimensional simulation of the hydraulic fracturing process is based on coupled hydraulic-mechanical finite element analysis. The hydraulic fracturing simulator is based on the principle of continuum homogenization in both hydraulic and mechanical domains. In order to capture appropriate physical effects and material behavior in a reservoir stimulation process, a 3D model is recommended. The simulator, built on ANSYS Parametric Design Language (APDL) [7] framework, allows for parametric assignment of model variables which forms the backbone of reservoir calibration, uncertainty and operational conditions optimization studies.
Johannes Will et al. / Procedia Engineering 191 (2017) 821 – 828
Fig. 1. Coupled hydraulic-mechanical fracturing simulator.
The primary process-chain, as shown in Fig. 1, includes a sequentially coupled hydro-mechanical simulation with explicit update of coupling parameters. Non-linear mechanical analysis involves application of multi-surface plasticity for modelling fracture network activation in jointed rocks within homogenized continuum approach [8] while the hydraulic model is based on the assumption of laminar flow in multiple parallel joint systems [9]. The mechanical to hydraulic coupling is carried out using computation of fracture opening and closure resulting in anisotropic hydraulic jointed rock conductivity and varying permeability in the model. The hydraulic to mechanical coupling, on the other hand, is computed by determination of flow forces, depending on the pressure gradients within the jointed rock. The initialization of reservoir conditions, initial in situ strength, stress and pore pressure conditions are defined as model parameters. The fluid flow in the hydraulic model, being predominantly laminar in nature, is solved using Darcy’s law, which is a phenomenological description of the flow of fluid through a jointed rock. Darcy’s equation describes the flow through a homogenized fractured rock where the overall hydraulic conductivity is an aggregate super-imposition (see Fig 2a) of intact rock and jointed rock conductivities. The mechanical model employs the homogenized continuum approach, where jointed rocks are modelled within the strength definition in the mechanical domain as volume consisting of matrix material (intact rock) and up to 4 strength anisotropies (joints), which represent in situ (natural) joint systems (see Fig 2b). The multiple possible failure mechanisms of tensile and shear failure of intact rock and individual joint sets comes under the purview of multi – surface plasticity. Herewith, Dynardo’s multiPlas integration algorithm provides efficient numerical handling of multi-surface plasticity [8]. The strength conditions are modelled using a combination of isotropic Mohr-Coulomb and Rankine yield surface for the intact rock and anisotropic Mohr-Coulomb and tension cut-off yield surfaces for the jointed rock with a non-associated flow rule. A comprehensive description of the hydraulic and mechanical models along with their validation and comparison with analytical and other numerical approaches such as XFEM [9] has already been carried out. a)
b)
Fig.2. (a) Laminar fluid flow in one joint set with multiple activated joints; (b) The joint sets or the planes of weaknesses in jointed rocks.
823
824
Johannes Will et al. / Procedia Engineering 191 (2017) 821 – 828
3. Meiningen Suhl Reservoir Model The simulation of the heat exchanger generation in the Meiningen - Suhl reservoir model is based on a 3 Stage model. Post calculation of 3 stages in the reservoir model, the effect of further stages is extrapolated. The landing depth of the stimulation well is defined at 4500 m. A schematic is illustrated in Fig. 3a. The conglomerate formation beyond 3000 m is not modelled in the FE-environment in order to reduced FE mesh size, assuming that vertical fracture extension is no longer than 1500 m. Based on the reservoir permeability and in-situ stress and strength conditions, the stage design needs to be optimized. A 3D Finite Element model is developed and investigated in this study. Associated with the model, are reservoir and operational parameters employed during the simulation. Reservoir parameters denote specifications which are either characteristic to the reservoir layers, such as the initial stress state of the reservoir or the initial permeability. They also include the strength definitions of the intact or jointed rocks. Operational parameters, on the other hand, specify reservoir loading conditions or the operational characteristics of the well, fluid employed, etc. Table 1 illustrates some of the parameters used in the Meiningen – Suhl model to investigate their influence and optimize the well and the hydraulic fracturing design while Fig. 3b shows the well and stress orientation with respect to the defined joint orientations. a)
b)
Fig. 3. (a) A schematic of reservoir layers in Meiningen/Suhl (DBI Input Sheet, 2013 [11]); (b) Rose Diagram illustrating the respective angles of well orientation, joint sets and horizontal stress directions from each other.
825
Johannes Will et al. / Procedia Engineering 191 (2017) 821 – 828
Table 1. Reservoir & Operational Parameters for Meiningen/Suhl Reservoir Model. Parameter
Reference Value
Minimum Value
Maximum Value
Stage Distance [m]
100
100
200
Well Azimuth [°]
70
40
100
Well Dip [°]
0
-20
0
Pore Pressure Gradient [kPa/m]
10.66
5.00
11.00
Youngs’ Modulus [GPa]
78
6
85
Friction Angle [°]
41.8
35
42
Uniaxial Compressive Strength [MPa]
143
110
180
Dilatancy Angle [°]
20
15
25
Relative Joint Stength
0.16
0.10
0.30
Vertical Stress Ratio
0.8
0.75
0.85
Horizontal Stress Ratio
6.41
6.0
7.0
Slurry Volume [m3]
5000
2500
7500
Stimulation Rate [m3/s]
5
5
10
Horizontal Well Length [m]
1500
1000
10000
Dynamic Viscosity [cP]
1
1
1
Initial Pore Pressure Gradient [kPa/m]
10.66
10.66
10.66
3.1. Reservoir Calibration – Heat Exchanger Generation The fracturing or stimulation cycle is used to generate the heat exchanger, which serves as the primary energy source in the EGS process-chain. Simulation of the fracturing cycle gives a good initial impression about the accessible potential of the reservoir. Compared to most other reservoir simulators, where the characteristic dimension of the heat exchanger needs to be provided before-hand, Dynardo’s simulator with its capability to deal with the anisotropic in-situ stress conditions and anisotropic strength conditions of jointed rock, works directly on intrinsic reservoir parameters. In practice, a reservoir stimulation process could include generation of several fracture surfaces, located at fixed or varying distances from each other, connected, however, through a common well-bore. The fracture generation procedure employs pumping slurry at fixed timescales into each of these designated fracture generation locations, each represented by a stage. In the current study, a representative 1-Well, 3 Stage model is pumped with a stimulation rate of 0.0833 m3/s leading to a slurry volume of 500 cubic meter per stage. A fracture network is thereby generated which represents the design of the heat exchanger. In the calibration phase, the key parameters of the modelling approach like material strength, in situ conditions, natural joint sets, initial and maximum permeability of jointed rock mass or energy dissipation at pore pressure frontier are calibrated using one of the following approaches[12]: x Calibration of Fracture Initiation and Termination: An initialization study is carried out using initial in-situ stress state and pore – pressure gradient in the model. DFIT measurement based ISIP (Instantaneous Shut-In Pressure) results are used to define fracture initiation and fracture extension. x Calibration with Bottom Hole Pressure history – The simulated values of BHP are compared with available measured BHP, based on the actual fracturing process. Parameter calibration might include strength of rocks in perforated layers, maximum opening of activated fractures or energy losses x Calibration of Heat Exchanger Volume with Total Inflow Volume and leak-off – The generated heat exchanger volume is based on the mechanical openings of the generated fractures.
826
Johannes Will et al. / Procedia Engineering 191 (2017) 821 – 828
x Calibration of Heat Exchanger Volume with MSE – Micro-seismic data provides a time-line of spatial distribution of micro-earthquakes caused during hydraulic fracturing. As a base measurement tool, the spatial extension of the simulation model is compared with the distance of the micro-seismic event and the stage center. Fig. 4a shows the plastic elements corresponding to the generated fracture network of the 1 well, 3 stage model which represent the calibrated heat exchanger area. In Fig. 4b, the volume balances are illustrated. In the hydraulic model, the total in-flow volume must be equal to the volume stored in the model. Fluid is either stored in plastic elements, represented by storage in joints, or in elastic elements corresponding to leak-off volume. It is to be noted that the amount off leak-off volume is controlled by the initial permeability of the jointed rock. The plot shows that the volume balance in the hydraulic model is satisfied, i.e. the total inflow is equal to the sum of storage in joints and leak-off. Additionally, the fluid volume stored in the joints approximates to the total joint volume, which is calculated based on the mechanical openings, resulting in an efficiently calibrated reservoir. a)
b)
Fig. 4. (a) View of the Fracture Core representing the Heat exchanger generated during Hydraulic Stimulation; (b) Volume Balance in Reservoir – Meiningen/Suhl.
3.2. Uncertainty Quantification The sensitivity study is aimed at estimation of the variation of all relevant system responses as a result of variation of operational parameter and/or reservoir uncertainties. The design space is defined using windows of reservoir uncertainties and operational parameters, see Table 1. In order to identify the correlation structure between input variation and response variation, meta-modelling is performed and the predictive ability of the best possible generated meta-model for response variations is estimated using the software optiSLang [13] based on a variation forecast measure, known as Coefficient of Prognosis (CoP) [14]. The meta-model of optimal Prognosis (MOP) and the related CoP value for the generated heat exchanger area are highlighted in Fig. 5a. The CoP value for the heat exchanger area is equal to 85 % which implies an appreciable prognosability of the response variation as a result of input variation using the meta-model in the defined design space. The influential parameters, as seen in Fig. 5b, are a combination of operational parameters (Slurry Volume), well design parameters (Stage Distance, Horizontal Well Length and Stage Distance) and Reservoir Parameters (Friction Angle, in situ Stress Anisotropy - k0). The varying degrees of parameter influence on the heat exchanger area response are attributed to the corresponding percentage values shown in Fig. 5b. As a further implication, the heat exchanger area bears an inherent optimization potential in the designated space by utilization of optimum
Johannes Will et al. / Procedia Engineering 191 (2017) 821 – 828
operational and well design parameter values and by reducing the uncertainty of reservoir parameters due to measurements, when drilling the wells. a)
b)
Fig. 5. (a) Meta-model for Heat Exchanger Area based on Polynomial Regression; (b) COP for Heat Exchanger Area based on Polynomial Regression.
4. Summary and Outlook The current study focuses on development of an integrated numerical simulation procedure for a Geo-thermal heat exchanger generation cycle. The objective of the simulation process chain is to provide forecast quality predictions for EGS reservoirs performance based on the continuum homogenized approach. A reference model based on reservoir conditions in Meiningen/Suhl, Thüringia, Germany has been developed. Reservoir calibration approaches have been discussed. In the absence of field data from drilling and fracture tests, the current reservoir has been calibrated based on the balance between Joint volume and Total Inflow Volume. Handling uncertainty quantification in EGS simulation has been further addressed in the current study. With optiSLang correlation analysis, the main reservoir parameters have been identified to additionally calibrate the influence of fracturing design parameter on the mechanism of fracture growth. Further extension of the EGS process chain to include the Energy-Production cycle, with a fluid-thermal coupling has already been implemented in the background although it is out of the scope of the current study [15].
Acknowledgements The authors would like to thank the Thüringer Aufbaubank for the financial support within the framework of the joint research project OPTIRISS. The authors would also like to express their heartful gratitude to Optiriss’ project partners, namely, the engineering team at Jena-GEOS, Department of Structural Geology, Institute for Geological Sciences at Friedrich-Schiller-Universität Jena, DBI - Institute of Gas Technology and the Department of Earth Sciences, TU Bergakadmie Freiberg for supporting the research work by providing valuable data and information.
827
828
Johannes Will et al. / Procedia Engineering 191 (2017) 821 – 828
References [1] F.R.L.R. Jelacic Allan, An Evaluation of Enhanced Geothermal Systems Technology, Technical Report - US Department of Energy, 2008. [2] B. Lange, F. Hering, R. Schlegel, G. Leyendecker, F. Ortega, HRB WALDBÄRENBURG: First RCC Dam Experience in Germany, in: 6th International Symposium on Roller Compacted Concrete (RCC) Dams, Zaragoza, October 2012. [3] J. Will, Optimizing of hydraulic fracturing procedure using numerical simulation, in: Weimar Optimization and Stochastic Days, Weimar, 2010. [4] J. Will, S. Eckardt, optiRiss - Simulation based Optimization and Risk Evaluation of Enhanced Geothermal Systems, in: Weimar Optimization and Stochastic Days, Weimar, 2015. [5] R. Schlegel, J. Will, M. Jobmann, Using Statistical Methods for Rock Parameter Identification to Analyse the THM Behaviour of Callovooxfordian Claystone, in: Second EAGE Workshop on Geomechanics and Energy, Celle, Germany, 2016. [6] P. Brenda, Geothermal Energy Resources, in: NARUC Winter Meeting, February 2010. [7] ANSYS Inc, ANSYS Mechanical, ANSYS Inc., Available: http://www.ansys.com/Products/Structures/ANSYS-Mechanical-Enterprise, [Online, September 2016]. [8] Dynardo GmbH, Dynamic Software and Engineering GmbH, multiPlas- Elastoplastic material models for Ansys, Dynardo GmbH, 2014, [Online], Available: http://www.dynardo.de/en/software/multiplas.html. [9 W. Wittke, Rock mechanics: theory and applications with case histories, The University of California: Springer, 1990, ISBN: 0387527192, 9780387527192. [10] S. Venkat, S. Eckardt, J. Will, Simulation of Penny Shaped Fracture using homogenized continuum approach, 2016. [11] H.J. Kretzschmar, M. Rafiee, MFRAC – Sensitivity study, DBI - interim report of the OPTIRISS project - modeling group (in German), DBI, Freiberg, April 2013 [12] J. Will, R. Schlegel, Simulation of Hydraulic Fracturing of Jointed Rock, in: Proceedings of European Conference on Fracture, Dresden, 2010. [13] J. Will, T. Most, Metamodell of Optimal Prognosis (MOP) - an Automatic Approach for User Friendly Parameter Optimization, in: Weimar Optimization and Stochastic Days, Weimar, 2009. [14] J. Will, T. Most, Sensitivity analysis using the Metamodel of Optimal Prognosis, in: Weimar Optimization and Stochastic Days, Weimar, 2011. [15] A. Ranjan, S. Eckardt, J. Will, Simulation of Fracture Design Generation, Production Characteristics and Temperature Development of a Hot Dry Rock Geothermal Reservoir, in: Weimar Optimization and Stochastic Days 2016, Weimar, 2016.
ScienceDirect Procedia Engineering 191 (2017) 821 – 828
Symposium of the International Society for Rock Mechanics
Numerical Simulation of Hydraulic Fracturing Process in an Enhanced Geothermal Reservoir using a Continuum Homogenized Approach Johannes Will*, Stefan Eckardt, Animesh Ranjan Dynardo GmbH, Steubenstrasse 25, Weimar 99423, Germany
Abstract The current study presents a numerical modeling approach for three-dimensional simulation of hydro-shearing in jointed rocks for the generation of a man-made, multi-fracture heat exchanger in Hot Dry Rock (HDR) Geothermal reservoir. Various literatures have suggested the presence of in-situ fractured rock mass even in massive granite formations. Thereby, 3D numerical modelling is essential, since the prediction of fracture growth in 3D is key to investigation of different fracture designs and furthermore various operational parameters in order to optimize the heat exchanger design and the resulting energy production. The numerical approach incorporates the Dynardo’s approach of homogenized continuum method to simulate the hydro-shearing process in jointed rocks unlike vast majority of commercial and scientific approaches which use the discrete modelling technique. The main motivation of the continuum approach is the numerical efficiency of the 3D coupled hydraulicmechanical simulations of hydraulic fracturing process in comparison to other alternatives. The input parameters of the numerical model from the best available well log and reservoir data are calibrated from diagnostics measurements such as Micro-seismic events, Bottom Hole Pressure, etc to assign the correct level of forecast quality to the important mechanisms of hydraulic fracturing. The numerical procedure is applied to a prospective Granite reservoir in Thüringen, Germany within the purview of a German joint research project – optiRiss. The integrated approach involves ANSYS as a pre-processor and solver, Dynardo’s fracturing simulator on top of ANSYS, Tamino – a post-processing tool and optiSLang – an environment for optimization and uncertainty quantification. ©2017 2017The TheAuthors. Authors. Published by Elsevier © Published by Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of the organizing committee of EUROCK 2017. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of EUROCK 2017 Keywords: Hot Dry Rock Geothermal Reservoir; Enhanced Geothermal Systems; Jointed Rocks; Calibration; ANSYS; multiPlas; optiSlang
* Corresponding author. Tel.: +49 (0) 3643 9008-30; fax: +49 (0) 3643 9008-39. E-mail address: [email protected]
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of EUROCK 2017
doi:10.1016/j.proeng.2017.05.249
822
Johannes Will et al. / Procedia Engineering 191 (2017) 821 – 828
1. Introduction Energy consumption in the world has seen an ever increasing upward trend since the early part of the 20th century. Still a major chunk of the total energy supply comes from non-renewable energy resources with approximately 66 % supplied only by crude oil, natural gas and coal reserves. The large share of these resources are not just restricted to developing economies such as China, Brazil, etc. but also economic powerhouses such as USA and the European Union [1]. Geothermal Energy provides tremendous benefits in terms of reducing dependence on fossil fuels, reducing greenhouse emissions and generating new economic and employment opportunities. Geothermal Power systems aim to extract the inexhaustible heat available beneath the earth's surface. Natural Geothermal springs are rare to find and hard to locate and in order to reduce dependence on naturally occurring hydrothermal reservoirs, Hot Dry Rock/Enhanced Geothermal Systems (EGS) provide a suitable alternative. EGS reservoirs are set-up by drilling wells beneath the earth's surface and creating a man-made permeable fracture network between the wells. In the process, Hydraulic Fracturing is a well-stimulation technique used for creating artificial heat exchanger by creating a network of permeable fractures between injection and production wells. During the last 15 years, Dynardo GmbH has developed a) Thermo-Hydro-Mechanical (THM) simulation environment based on ANSYS® implicit finite element code for parametric FEM modeling for geotechnical applications with successful applications in Dam Engineering [2], Hydraulic Fracturing of unconventional Oil, Gas reservoirs [3], Geothermal reservoirs [4] and Nuclear Waste disposals [5], b) Dynardo’s toolbox for parametric variation optiSLang® for sensitivity analysis and calibration of large number of reservoir parameters as well as engineering and operational conditions parameters and their influence on the final stimulated rock volume, the production and their uplift potentials. Since 2008, the THM simulation capabilities have been extended to 3D simulation of Enhanced Geothermal Systems or Hot Dry Rock Geothermal reservoirs. The Fracturing design in an EGS reservoir is different to fracturing design in an oil or gas reservoir. The process, more commonly referred to as Hydro-shearing [6] aims to generate mainly shear fractures between rocks by inducing shear failure in contrast to Hydraulic Fracturing in oil or gas reservoirs where tensile fractures are targeted, with injected fluid are used to break the rock and along with a proppant mixture are used to maintain the created openings. For EGS applications, similar to the numerical simulation procedure applied for oil or gas reservoir simulations, the homogenized continuum approach is used since it is far more efficient than other alternatives such as Discrete Element Modelling, XFEM, etc. The current study focusses on application of the aforementioned approach to numerical calibration of simulation parameters based on available data such as Bottom Hole Pressure (BHP) history or Micro-Seismic Events (MSE) Data and identification of the most influential parameters within an uncertain yet quantified design space. 2. Numerical Simulation The hydraulic fracturing simulator for the 3-dimensional simulation of the hydraulic fracturing process is based on coupled hydraulic-mechanical finite element analysis. The hydraulic fracturing simulator is based on the principle of continuum homogenization in both hydraulic and mechanical domains. In order to capture appropriate physical effects and material behavior in a reservoir stimulation process, a 3D model is recommended. The simulator, built on ANSYS Parametric Design Language (APDL) [7] framework, allows for parametric assignment of model variables which forms the backbone of reservoir calibration, uncertainty and operational conditions optimization studies.
Johannes Will et al. / Procedia Engineering 191 (2017) 821 – 828
Fig. 1. Coupled hydraulic-mechanical fracturing simulator.
The primary process-chain, as shown in Fig. 1, includes a sequentially coupled hydro-mechanical simulation with explicit update of coupling parameters. Non-linear mechanical analysis involves application of multi-surface plasticity for modelling fracture network activation in jointed rocks within homogenized continuum approach [8] while the hydraulic model is based on the assumption of laminar flow in multiple parallel joint systems [9]. The mechanical to hydraulic coupling is carried out using computation of fracture opening and closure resulting in anisotropic hydraulic jointed rock conductivity and varying permeability in the model. The hydraulic to mechanical coupling, on the other hand, is computed by determination of flow forces, depending on the pressure gradients within the jointed rock. The initialization of reservoir conditions, initial in situ strength, stress and pore pressure conditions are defined as model parameters. The fluid flow in the hydraulic model, being predominantly laminar in nature, is solved using Darcy’s law, which is a phenomenological description of the flow of fluid through a jointed rock. Darcy’s equation describes the flow through a homogenized fractured rock where the overall hydraulic conductivity is an aggregate super-imposition (see Fig 2a) of intact rock and jointed rock conductivities. The mechanical model employs the homogenized continuum approach, where jointed rocks are modelled within the strength definition in the mechanical domain as volume consisting of matrix material (intact rock) and up to 4 strength anisotropies (joints), which represent in situ (natural) joint systems (see Fig 2b). The multiple possible failure mechanisms of tensile and shear failure of intact rock and individual joint sets comes under the purview of multi – surface plasticity. Herewith, Dynardo’s multiPlas integration algorithm provides efficient numerical handling of multi-surface plasticity [8]. The strength conditions are modelled using a combination of isotropic Mohr-Coulomb and Rankine yield surface for the intact rock and anisotropic Mohr-Coulomb and tension cut-off yield surfaces for the jointed rock with a non-associated flow rule. A comprehensive description of the hydraulic and mechanical models along with their validation and comparison with analytical and other numerical approaches such as XFEM [9] has already been carried out. a)
b)
Fig.2. (a) Laminar fluid flow in one joint set with multiple activated joints; (b) The joint sets or the planes of weaknesses in jointed rocks.
823
824
Johannes Will et al. / Procedia Engineering 191 (2017) 821 – 828
3. Meiningen Suhl Reservoir Model The simulation of the heat exchanger generation in the Meiningen - Suhl reservoir model is based on a 3 Stage model. Post calculation of 3 stages in the reservoir model, the effect of further stages is extrapolated. The landing depth of the stimulation well is defined at 4500 m. A schematic is illustrated in Fig. 3a. The conglomerate formation beyond 3000 m is not modelled in the FE-environment in order to reduced FE mesh size, assuming that vertical fracture extension is no longer than 1500 m. Based on the reservoir permeability and in-situ stress and strength conditions, the stage design needs to be optimized. A 3D Finite Element model is developed and investigated in this study. Associated with the model, are reservoir and operational parameters employed during the simulation. Reservoir parameters denote specifications which are either characteristic to the reservoir layers, such as the initial stress state of the reservoir or the initial permeability. They also include the strength definitions of the intact or jointed rocks. Operational parameters, on the other hand, specify reservoir loading conditions or the operational characteristics of the well, fluid employed, etc. Table 1 illustrates some of the parameters used in the Meiningen – Suhl model to investigate their influence and optimize the well and the hydraulic fracturing design while Fig. 3b shows the well and stress orientation with respect to the defined joint orientations. a)
b)
Fig. 3. (a) A schematic of reservoir layers in Meiningen/Suhl (DBI Input Sheet, 2013 [11]); (b) Rose Diagram illustrating the respective angles of well orientation, joint sets and horizontal stress directions from each other.
825
Johannes Will et al. / Procedia Engineering 191 (2017) 821 – 828
Table 1. Reservoir & Operational Parameters for Meiningen/Suhl Reservoir Model. Parameter
Reference Value
Minimum Value
Maximum Value
Stage Distance [m]
100
100
200
Well Azimuth [°]
70
40
100
Well Dip [°]
0
-20
0
Pore Pressure Gradient [kPa/m]
10.66
5.00
11.00
Youngs’ Modulus [GPa]
78
6
85
Friction Angle [°]
41.8
35
42
Uniaxial Compressive Strength [MPa]
143
110
180
Dilatancy Angle [°]
20
15
25
Relative Joint Stength
0.16
0.10
0.30
Vertical Stress Ratio
0.8
0.75
0.85
Horizontal Stress Ratio
6.41
6.0
7.0
Slurry Volume [m3]
5000
2500
7500
Stimulation Rate [m3/s]
5
5
10
Horizontal Well Length [m]
1500
1000
10000
Dynamic Viscosity [cP]
1
1
1
Initial Pore Pressure Gradient [kPa/m]
10.66
10.66
10.66
3.1. Reservoir Calibration – Heat Exchanger Generation The fracturing or stimulation cycle is used to generate the heat exchanger, which serves as the primary energy source in the EGS process-chain. Simulation of the fracturing cycle gives a good initial impression about the accessible potential of the reservoir. Compared to most other reservoir simulators, where the characteristic dimension of the heat exchanger needs to be provided before-hand, Dynardo’s simulator with its capability to deal with the anisotropic in-situ stress conditions and anisotropic strength conditions of jointed rock, works directly on intrinsic reservoir parameters. In practice, a reservoir stimulation process could include generation of several fracture surfaces, located at fixed or varying distances from each other, connected, however, through a common well-bore. The fracture generation procedure employs pumping slurry at fixed timescales into each of these designated fracture generation locations, each represented by a stage. In the current study, a representative 1-Well, 3 Stage model is pumped with a stimulation rate of 0.0833 m3/s leading to a slurry volume of 500 cubic meter per stage. A fracture network is thereby generated which represents the design of the heat exchanger. In the calibration phase, the key parameters of the modelling approach like material strength, in situ conditions, natural joint sets, initial and maximum permeability of jointed rock mass or energy dissipation at pore pressure frontier are calibrated using one of the following approaches[12]: x Calibration of Fracture Initiation and Termination: An initialization study is carried out using initial in-situ stress state and pore – pressure gradient in the model. DFIT measurement based ISIP (Instantaneous Shut-In Pressure) results are used to define fracture initiation and fracture extension. x Calibration with Bottom Hole Pressure history – The simulated values of BHP are compared with available measured BHP, based on the actual fracturing process. Parameter calibration might include strength of rocks in perforated layers, maximum opening of activated fractures or energy losses x Calibration of Heat Exchanger Volume with Total Inflow Volume and leak-off – The generated heat exchanger volume is based on the mechanical openings of the generated fractures.
826
Johannes Will et al. / Procedia Engineering 191 (2017) 821 – 828
x Calibration of Heat Exchanger Volume with MSE – Micro-seismic data provides a time-line of spatial distribution of micro-earthquakes caused during hydraulic fracturing. As a base measurement tool, the spatial extension of the simulation model is compared with the distance of the micro-seismic event and the stage center. Fig. 4a shows the plastic elements corresponding to the generated fracture network of the 1 well, 3 stage model which represent the calibrated heat exchanger area. In Fig. 4b, the volume balances are illustrated. In the hydraulic model, the total in-flow volume must be equal to the volume stored in the model. Fluid is either stored in plastic elements, represented by storage in joints, or in elastic elements corresponding to leak-off volume. It is to be noted that the amount off leak-off volume is controlled by the initial permeability of the jointed rock. The plot shows that the volume balance in the hydraulic model is satisfied, i.e. the total inflow is equal to the sum of storage in joints and leak-off. Additionally, the fluid volume stored in the joints approximates to the total joint volume, which is calculated based on the mechanical openings, resulting in an efficiently calibrated reservoir. a)
b)
Fig. 4. (a) View of the Fracture Core representing the Heat exchanger generated during Hydraulic Stimulation; (b) Volume Balance in Reservoir – Meiningen/Suhl.
3.2. Uncertainty Quantification The sensitivity study is aimed at estimation of the variation of all relevant system responses as a result of variation of operational parameter and/or reservoir uncertainties. The design space is defined using windows of reservoir uncertainties and operational parameters, see Table 1. In order to identify the correlation structure between input variation and response variation, meta-modelling is performed and the predictive ability of the best possible generated meta-model for response variations is estimated using the software optiSLang [13] based on a variation forecast measure, known as Coefficient of Prognosis (CoP) [14]. The meta-model of optimal Prognosis (MOP) and the related CoP value for the generated heat exchanger area are highlighted in Fig. 5a. The CoP value for the heat exchanger area is equal to 85 % which implies an appreciable prognosability of the response variation as a result of input variation using the meta-model in the defined design space. The influential parameters, as seen in Fig. 5b, are a combination of operational parameters (Slurry Volume), well design parameters (Stage Distance, Horizontal Well Length and Stage Distance) and Reservoir Parameters (Friction Angle, in situ Stress Anisotropy - k0). The varying degrees of parameter influence on the heat exchanger area response are attributed to the corresponding percentage values shown in Fig. 5b. As a further implication, the heat exchanger area bears an inherent optimization potential in the designated space by utilization of optimum
Johannes Will et al. / Procedia Engineering 191 (2017) 821 – 828
operational and well design parameter values and by reducing the uncertainty of reservoir parameters due to measurements, when drilling the wells. a)
b)
Fig. 5. (a) Meta-model for Heat Exchanger Area based on Polynomial Regression; (b) COP for Heat Exchanger Area based on Polynomial Regression.
4. Summary and Outlook The current study focuses on development of an integrated numerical simulation procedure for a Geo-thermal heat exchanger generation cycle. The objective of the simulation process chain is to provide forecast quality predictions for EGS reservoirs performance based on the continuum homogenized approach. A reference model based on reservoir conditions in Meiningen/Suhl, Thüringia, Germany has been developed. Reservoir calibration approaches have been discussed. In the absence of field data from drilling and fracture tests, the current reservoir has been calibrated based on the balance between Joint volume and Total Inflow Volume. Handling uncertainty quantification in EGS simulation has been further addressed in the current study. With optiSLang correlation analysis, the main reservoir parameters have been identified to additionally calibrate the influence of fracturing design parameter on the mechanism of fracture growth. Further extension of the EGS process chain to include the Energy-Production cycle, with a fluid-thermal coupling has already been implemented in the background although it is out of the scope of the current study [15].
Acknowledgements The authors would like to thank the Thüringer Aufbaubank for the financial support within the framework of the joint research project OPTIRISS. The authors would also like to express their heartful gratitude to Optiriss’ project partners, namely, the engineering team at Jena-GEOS, Department of Structural Geology, Institute for Geological Sciences at Friedrich-Schiller-Universität Jena, DBI - Institute of Gas Technology and the Department of Earth Sciences, TU Bergakadmie Freiberg for supporting the research work by providing valuable data and information.
827
828
Johannes Will et al. / Procedia Engineering 191 (2017) 821 – 828
References [1] F.R.L.R. Jelacic Allan, An Evaluation of Enhanced Geothermal Systems Technology, Technical Report - US Department of Energy, 2008. [2] B. Lange, F. Hering, R. Schlegel, G. Leyendecker, F. Ortega, HRB WALDBÄRENBURG: First RCC Dam Experience in Germany, in: 6th International Symposium on Roller Compacted Concrete (RCC) Dams, Zaragoza, October 2012. [3] J. Will, Optimizing of hydraulic fracturing procedure using numerical simulation, in: Weimar Optimization and Stochastic Days, Weimar, 2010. [4] J. Will, S. Eckardt, optiRiss - Simulation based Optimization and Risk Evaluation of Enhanced Geothermal Systems, in: Weimar Optimization and Stochastic Days, Weimar, 2015. [5] R. Schlegel, J. Will, M. Jobmann, Using Statistical Methods for Rock Parameter Identification to Analyse the THM Behaviour of Callovooxfordian Claystone, in: Second EAGE Workshop on Geomechanics and Energy, Celle, Germany, 2016. [6] P. Brenda, Geothermal Energy Resources, in: NARUC Winter Meeting, February 2010. [7] ANSYS Inc, ANSYS Mechanical, ANSYS Inc., Available: http://www.ansys.com/Products/Structures/ANSYS-Mechanical-Enterprise, [Online, September 2016]. [8] Dynardo GmbH, Dynamic Software and Engineering GmbH, multiPlas- Elastoplastic material models for Ansys, Dynardo GmbH, 2014, [Online], Available: http://www.dynardo.de/en/software/multiplas.html. [9 W. Wittke, Rock mechanics: theory and applications with case histories, The University of California: Springer, 1990, ISBN: 0387527192, 9780387527192. [10] S. Venkat, S. Eckardt, J. Will, Simulation of Penny Shaped Fracture using homogenized continuum approach, 2016. [11] H.J. Kretzschmar, M. Rafiee, MFRAC – Sensitivity study, DBI - interim report of the OPTIRISS project - modeling group (in German), DBI, Freiberg, April 2013 [12] J. Will, R. Schlegel, Simulation of Hydraulic Fracturing of Jointed Rock, in: Proceedings of European Conference on Fracture, Dresden, 2010. [13] J. Will, T. Most, Metamodell of Optimal Prognosis (MOP) - an Automatic Approach for User Friendly Parameter Optimization, in: Weimar Optimization and Stochastic Days, Weimar, 2009. [14] J. Will, T. Most, Sensitivity analysis using the Metamodel of Optimal Prognosis, in: Weimar Optimization and Stochastic Days, Weimar, 2011. [15] A. Ranjan, S. Eckardt, J. Will, Simulation of Fracture Design Generation, Production Characteristics and Temperature Development of a Hot Dry Rock Geothermal Reservoir, in: Weimar Optimization and Stochastic Days 2016, Weimar, 2016.