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LIST OF FIGURES... IV LIST OF TABLES ... X INTRODUCTION ...1 CHAPTER 1. INTRODUCTION TO MULTI-MEDIUM FRACTURED/HETEROGENEOUS KARSTIC RESERVOIRS : THE EXPERIMENTAL HYDROGEOLOGICAL SITE (EHS) ...7

1.1. Introduction 222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222223 1.2. Karstic/Heterogeneous aquifers 22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222223 1.3. Origin of fractures and their impact on flow 2222222222222222222222222222222222222222222222222222222222222222222222222222222222222244 1.4. Construction of a geological model of a heterogeneous/fractured reservoir2222222222222222222222222224

1.4.1. Discrete models5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555C+

1.4.2. Equivalent homogenous models555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555CD

1.5. Presentation of heterogeneity parameters in the geostatistical models of reservoirs 2222222224 1.6. The Experimental Hydrogeological Site (EHS) : a heterogeneous fractured reservoir22222222245

1.6.1. (Hydro-)geological frame work

555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555C-1.6.2. Stratigraphy and depositional sequences.55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555C)

1.6.3. Structural features - tectonic history - fracturing features555555555555555555555555555555555555555555555555555555555555555555555CE

1.6.4. Diagenetic fingerprints- Evidence of the karstic nature of the aquifer5555555555555555555555555555555555555555555555555+D

1.6.5. Previous studies and analysis using pumping data at EHS555555555555555555555555555555555555555555555555555555555555555555+)

1.7. Conclusion22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222

CHAPTER 2. APPROACHES AND TOOLS FOR MODELLING, SIMULATING AND CALIBRATING THE HYDODYNAMICS OF AN UNDERGROUND RESERVOIR...35

2.1. Introduction 222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222 6 2.2. The reservoir modelling workflow 22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222 7

2.2.1. Geostatistical and Geological modelling55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555DF

2.2.2. Flow modelling555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555G,

2.2.3. History matching555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555GC

2.2.4. Optimization methods555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555G+

2.3. Workflow tools and methodologies 2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222288

2.3.1. Geostatistical modelling using HERESIM methodology555555555555555555555555555555555555555555555555555555555555555555555555HH

2.3.2. Flow modelling using SIMTESTW simulator

5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555H-2.3.3. Petrophysical inversion using WELGEM methodology5555555555555555555555555555555555555555555555555555555555555555555555555H)

2.3.4. Gradual deformation using CONDOR sotftware package555555555555555555555555555555555555555555555555555555555555555555555HE

CHAPTER 3. PRELIMINARY STUDIES AND GEOSTATISTICAL MODELLING OF

THE SITE 63

3.1. Introduction 222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222 8

3.1.1. Preliminary pumping data analysis55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555-H

3.1.2. Flowmeter data analysis and interpretation555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555-E

3.1.3. Imaging data555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555-E

3.1.4. Core derived petrophysical parameters555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555-E

3.2. Building a geostatistical model of the site 2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222264

3.2.1. Reference 3D grid555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555)C

3.2.2. Modelling features555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555)+

3.2.3. Variogram of model

5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555)-3.2.4. The petrophysical modelling5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555))

3.2.5. Resulting Geostatistical model of the EHS5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555)F

3.3. Conclusion222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227

CHAPTER 4. DESIGN AND APPLICATION OF A SEQUENTIAL METHODOLOGY FOR CALIBRATING THE HYDRODYNAMIC MODEL OF A

HIGHLY-HETEROGENEOUS RESERVOIR...85

4.1. Introduction 22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222276 4.2. Preliminary tests 22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222276 4.3. Design of a sequential calibration methodology 22222222222222222222222222222222222222222222222222222222222222222222222222222273 4.4. Flow model: application to the EHS2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222239 4.5. Selected well data for model calibration22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222235 4.6. Preliminary calibration of the flow boundary conditions 2222222222222222222222222222222222222222222222222222222222222223 4.7. Petrophysical inversion2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222223 4.8. Gradual deformation of facies 22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222237

4.9. Local gradual deformation of facies 22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222494 4.10. Predictability of the resulting model22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222495 4.11. CONCLUSION222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222249

CHAPTER 5. ANALYSIS AND DISCUSSION ...109

5.1. Introduction 2222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222444 5.2. Analysis of inversion as regard the schedule of steps in the sequential calibration 2222222222244

5.2.1. Gradual deformation followed by petrophysical inversion5555555555555555555555555555555555555555555555555555555555555555555CC+

5.2.2. Combining (global) gradual deformation and petrophysical inversion in a single calibration phase

CCH

5.3. Impact of the parameterization on the calibration performance 222222222222222222222222222222222222222222222222447 5.4. Optimization efficiency and computation times 22222222222222222222222222222222222222222222222222222222222222222222222222224

5.4.1. Optimization parameters55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555C++

5.4.2. Performance analysis of the first sequential calibration method55555555555555555555555555555555555555555555555555555555C+G

5.4.3. Performance analysis of gradual deformation followed by petrophysical inversion555555555555555555555555CD,

5.4.4. Performance analysis of combined (global) gradual deformation and petrophysical inversion5555CD,

5.4.5. Sensitivity of the objective function to calibration parameters555555555555555555555555555555555555555555555555555555555555CDD

5.5. Testing other flow models to better capture flow paths 2222222222222222222222222222222222222222222222222222222222222224 5

5.5.1. Testing a dual-porosity representation555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555CDG

5.5.2. Refined model55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555CD)

5.6. Conclusion222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222459

CHAPTER 6. CONCLUSION AND PERSPECTIVES ...143

6.1. Summary of results 22222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222455 6.2. Perspectives of future developments and research.222222222222222222222222222222222222222222222222222222222222222222222456

APPENDIX 1 ...155 APPENDIX 2 ...201

0

:

" ;

Figure 1.1: Components of a karst aquifer (Manda et al., 2006)55555555555555555555555555555555555555555555CC

Figure 1.2: Main Paleogeographic domains with location of the studied area (EHS).555555555CH

Figure 1.3: Experimental Hydrogeological Site – Location of wells

5555555555555555555555555555555555555555C-Figure 1.4: S tratigraphic chart for the jurassic555555555555555555555555555555555555555555555555555555555555555555555555555CE

Figure 1.5. Simplified geological cross section at the EHS location555555555555555555555555555555555555555CE

Figure 1.6: Transversal geological cross-section crossing the Poitou threshold(modified

after Gabilly et al., 1997) A means anticline, S means syncline. Note the change in

subsidence of paleohigh margins with time (NE margin during Liassic, SW margin during Upper Jurassic).55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555+C

Figure 1.7: EHS analogue outcrops study - Passelourdin site: (left) the rose diagram of fracture azimuths and poles shows three main clusters, with the corresponding poles shown in red, blue and green colors; (right) cyclographic traces of the mean

orientations of th5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555++

Figure 1.8: Cores from C2 well at about 97m depth: clay material is filling the upper "damaged" zone (karst residue) ; a vertical fracture is observed between two marly (dark) layers in the lower core.5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555+D

Figure 1.9: Bore-hole images as evidences of the paleo-karstic origin of the EHS

heterogeneities (Bourbiaux et al., 2007).55555555555555555555555555555555555555555555555555555555555555555555555555555+H

Figure 1.10: Wells set up in nested five-spots in the experimental site in Poitiers. Solid dots: wells tested in 2004, empty dots: wells tested in 2005.5555555555555555555555555555555555555555555+F

Figure 1.11: Representation of 3 typical shapes of drawdown curves from the pumping test of 2004 campaign (from Bernard, 2005).55555555555555555555555555555555555555555555555555555555555555555555555555DC

Figure 2.1: Truncated plurigaussian simulations (Chilès and Delfiner, 1999).5555555555555555555555G,

Figure 2.2: The Powell method and the trust region technique (Fornel, 2006)555555555555555555555G)

Figure 2.3: Iterative search process involving the gradual deformation of two realizations (one parameter of gradual deformation)555555555555555555555555555555555555555555555555555555555555555555555555555555H+

Figure 2.4: Iterative search process involving the gradual deformation of N+1 realizations

(Fornel, 2006)555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555HD

Figure 2.5: Vertical proportion curve computed from the well data (Doligez et al, 2007).

0

Figure 2.7: The optimization settings window. The optimizationalgorithm and important control parameters for the optimization are selected from this window55555555555555555555555555-C

Figure 2.8: Flow chart summing up the main steps of a gradual deformation-based

optimization including the main features depicted in this chapter55555555555555555555555555555555555-+

Figure 3.1: Schematic and general illustration of wells for the permeability estimations

55555--Figure 3.2: Permeability map of the EHS: a thick black line delimits the drilled zone of interest within the Site; wells are shown as white circles; well permeabilities range from around 100 millidarcys to nearly 11 Darcys555555555555555555555555555555555555555555555555555555555555555-)

Figure 3.3: Construction of reference grid in HERESIM Software555555555555555555555555555555555555555555)+

Figure 3.4: Vertical Proportion Curves (VPC) of lithotypes for all wells used for the

geostatistical model55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555)H

Figure 3.5: Qualitative distribution of facies in the present geostatistical model (left,

mono-Gaussian) and in the more advanced model (right, bi-Gaussian/not used here)

5555555555)-Figure 3.6: Experimental vertical variograms555555555555555555555555555555555555555555555555555555555555555555555555555555))

Figure 3.7: 3D geostatistical facies model of the Site (HERESIM software)5555555555555555555555555)F

Figure 3.8: West-East facies cross-section of the Site: a poor vertical connectivity of the conductive facies is expected555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555)E

Figure 3.9: North-South facies cross-section of the Site: the conductive lithotype looks here more areally-continuous than in the West-East direction, but no vertical connection is observed between the 50m and 85m productive levels within that

section555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555)E

Figure 3.10: West-East permeability cross-section of the Site55555555555555555555555555555555555555555555555F,

Figure 3.11: North-South permeability cross-section of the Site555555555555555555555555555555555555555555555F,

Figure 3.12: West-East connectivity section including 3 groups of connected water facies bodies5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555FC

Figure 3.13: North-South connectivity section including 3 groups of connected water facies bodies55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555FC

Figure 4.1: Left: Gridded model of the drilled Site area with well locations. Right: Gridded model with surrounding fluid-source cells5555555555555555555555555555555555555555555555555555555555555555555555555555EC

Figure 4.2: The 3D model generated by SIMVIEW IFP software, with the large volume source facies surrounding the Site555555555555555555555555555555555555555555555555555555555555555555555555555555555555555EC

Figure 4.3: Initial detailed facies model (left) converted to an equivalent lumped facies model (right)55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555ED

0

Figure 4.4: Preliminary flow inversion tests: the resulting calibrated lumped model is seemed to match measured pressure responses as accurately as the detailed model. Simulated pressures after petrophysical properties inversion are compared to

measured data at the Site: pressure drop (dP, bar) evolution with time (h) for pumped

well M7 and 3 selected observation wells during the first 24 hours.5555555555555555555555555555555ED

Figure 4.5: Selected data: location (Top) and pressure responses (Bottom) of the selected pumped well, M7, and of the observation wells showing significant pressure

interference with M75555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555EH

Figure 4.6: Simulated pressures after petrophysical properties inversion are compared to

measured data at the Site: pressure drop (dP, bar) evolution with time (h) for pumped

well M7 and 3 selected observation wells during the first 24 hours.5555555555555555555555555555555EF

Figurle 4.7: Top-left graph (on the top, right): Objective function evolution for the lumped facies model using the gradual deformation method: calibration is done on pumped well M7 and observation wells together. Other plots: Objective function evolution for wells M7, M5 and M9 pressure data. Note that the whole optimization process includes several steps, each step involving the deformation of a given set of

geostatistical realizations. A temporary abrupt rise in the objective function may occur during the iterative deformations of such a step. This is due to the highly non-linear relationship between fluid flow results and geostatistical deformation: in that case, the

iteration is re-started with a reduced variation of the deformation parameters.5555555555C,,

Figure 4.8: Comparison of simulated pressures after petrophysical inversion or gradual deformation of facies, with the field data: evolution of the pressure drop dP (bar) versus time (h) for the pumped well M7 and selected observation wells during the first 24 hours.555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555C,C

Figure 4.9: Gradual deformation of the EHS model with pumped well M7 and some observation wells as calibration constraints: 2D section of model at the depth of 68 meter (from the initial realization on top on the left, to the optimal one on bottom the right).5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555C,+

Figure 4.10: Gradual deformation of the EHS model with pumped well M7 and some observation wells as calibration constraints: lateral vertical sections (from the initial realization on top on the left, to the optimal one on bottom the right)55555555555555555555555555C,+

Figure 4.11: Local gradual deformation of the EHS model in a region including wells M7 and M9: horizontal section at the depth of 68m. Only the region of interest is affected by the gradual deformation process (from the initial realization on top on the left, to the

0

optimal one on bottom the right). Note that the bottom images are quite close, because at that stage, the optimization process had nearly converged to the optimal facies distribution.555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555C,D

Figure 4.12: Comparison of simulated pressures after petrophysical inversion, global gradual deformation of facies and local gradual deformation of facies, with the field data: evolution of the pressure drop dP (bar) versus time (h) for the pumped well M7 and observation well M9 during the first 24 hours.555555555555555555555555555555555555555555555555555555555C,D

Figure 4.13: Forward/predictive simulation of pumped well M6 and its interferences.

Comparison with field data: evolution of well pressure drop dP (bar) with time (h) for

pumped well M6 and selected observation wells during the first 24 hours.55555555555555555C,H

Figure 5.1: Comparison of simulated pressures after petrophysical inversion or gradual deformation of facies, with field data: gradual deformation method has been

performed before petrophysical property inversion. Evolution of the pressure drop dP (bar) versus time (h) for the pumped well M7 and selected observation wells during the first 24 hours55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555CCD

Figure 5.2: Comparison of the second sequential calibration (GDM before Petrophysical inversion) to the previous sequential calibration (Petrophysical inversion before GDM). Wells showing the largest difference in calibration results between the two sequences have been selected here.55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555CCG

Figure 5.3: Comparison of simulated pressures after petrophysical inversion or gradual deformation of facies, with field data: gradual deformation method and petrophysical property inversion have been performed in a combined calibration process (single-phase calibration). Evolution of the pressure drop dP (bar) versus time (h) for the

pumped well M7 and selected observation wells during the first 24 hours555555555555555555CC)

Figure 5.4: Comparison of results of combined (single-phase) calibration (GDM and Petrophysical inversion in a single phase) to the results of firstly-designed calibration

method (dual step i.e, Petrophysical inversion and then GDM). Evolution of the

pressure drop dP (bar) versus time (h) for the pumped well M7 and selected

observation wells during the first 24 hours .5555555555555555555555555555555555555555555555555555555555555555555555CCF

Figure 5.5: Comparison of simulated pressures after petrophysical inversion or gradual deformation of facies, with field data: Global and local gradual deformation are performed with only one parameter. Evolution of the pressure drop dP (bar) versus time (h) for the pumped well M7 and selected observation wells during the first 24 hours.555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555C+,

0

Figure 5.6: Comparison between the results of global gradual deformation with one parameter and that with four parameters. Evolution of the pressure drop dP (bar) versus time (h) for the pumped well M7 and selected observation wells during the first 24 hours.555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555C+C

Figure 5.7: Comparison between the results of local gradual deformation with one parameter and that with four parameters. Evolution of the pressure drop dP (bar) versus time (h) for the pumped well M7 and observation well M9 during the first 24 hours.555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555C++

Figure 5.8: Optimization settings for WELGEM petrophysical inversion .5555555555555555555555555555C+D

Figure 5.9: Optimization settings for gradual deformation (CONDOR platform).5555555555555555C+D

Figure 5.10: Objective function evolution for petrophysical property inversions: Objective function for detailed facies model inversion to the left and objective function for

lumped facies model inversion to the right.55555555555555555555555555555555555555555555555555555555555555555555555C+G

Figure 5.11: Evolution of the objective function for the lumped-facies model during global gradual deformation. Comparison between optimizations with one and four 4

parameter(s) of gradual deformation. Evolution of the objective function with the iteration number for all wells together and for selected observation wells.555555555555555555C+)

Figure 5.12: Relative contribution of well data series in the objective function evolution for global gradual deformation with 4 parameters.5555555555555555555555555555555555555555555555555555555555555555C+F

Figure 5.13: Relative contribution of well data series in the objective function evolution for local gradual deformation with 4 parameters.5555555555555555555555555555555555555555555555555555555555555555555C+F

Figure 5.14: Evolution of the objective function for the lumped-facies model during local gradual deformation. Comparison between optimizations with one and four 4 parameter(s) of gradual deformation. Evolution of the objective function with the

iteration number for all wells together and for the wells in the deformation area.5555555C+E

Figure 5.15: Evolution of the objective function when gradual deformation (with 4

parameters) is performed before petrophysical inversion. Evolution of the objective function with the iteration number for all wells together and for selected observation wells.5555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555CDC

Figure 5.16: Evolution of the objective function for the lumped facies model by using the

gradual deformation method and petrophysical inversion mixed together.555555555555555555CD+

Figure 5.17: Gradient of the objective function with respect to calibration parameters for different steps. The numbers 1 to 20 state for the different calibration parameters. The

6

related parameters are given on the bottom of each number. The p1 to p4 represent the 4 parameters of gradual deformation.5555555555555555555555555555555555555555555555555555555555555555555555555CDD

Figure 5.18: Comparison between the inversions of the dual-porosity and the

single-porosity models of the Site. Variation of pressure drop (∆!) versus time (hour) for

well M7 and some interference wells; model calibrated to pumped well M7 and some interference wells for short term period (24 hours).555555555555555555555555555555555555555555555555555555555CD)

Figure 5.19: Comparison of the simulated pressures from both coarse and refined grids with field data. The fine-grid model is derived from the previously-inversed-deformed coarse model. Evolution of the pressure drop dP (bar) versus time (h) for the pumped well M7 and selected observation wells.5555555555555555555555555555555555555555555555555555555555555555555555555555CDE

6

:

"

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Table 3.1: Determination of the permeability at different wells by using drawdowns of quasi-steady state radial flow around pumped wells.55555555555555555555555555555555555555555555555555555555-F

Table 3.2: Petrophysical parameters calculated from cored-well C1 using the Miniplug method555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555),

Table 3.3: Facies coding used in well data files in HERESIM55555555555555555555555555555555555555555555555555)D

Table 3.4: Classification of the facies into the different lithological groups (lithotypes).555555)G

Table 4.1: The initial petrophysical parameters assigned to the geostatistical model: porosity-permeability values derived from the core data of well C1; estimated pore compressibility values (from overall pre-calibration) consistently with other dynamic studies.55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555E+

Table 4.2: Detailed facies (left) converted to lumped facies (right).5555555555555555555555555555555555555555E+

Table 4.3: Inversion parameters, denoted "?". Porosity value (0.15) for tight facies No. 1 is derived from core data.55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555E)

Table 4.4: Inverted values of lumped facies 1 and 2 using the short-term (24 hours) flow data from pumped well M7 and its observation wells as constraints.55555555555555555555555555555E)

Table 5.1: Inverted petrophysical parameters, Top: Results of petrophysical property inversion performed after gradual deformation of facies, Bottom: Results of

petrophysical property inversion performed before gradual deformation of facies.55CCH

Table 5.2: Inverted petrophysical parameters, Top: Results of the single-step calibration of detailed-facies model, Bottom: Results of dual-step calibration with inversion of petrophysical properties inversion before gradual deformation

5555555555555555555555555555555555CC-Table 5.3: Summary of performance for all optimization techniques. "Petro. Inv." stands for petrophysical inversion and "GD" stands forgradual deformation555555555555555555555555CD+

Table 5.4: Initialization of the dual-porosity model parameters from the calibrated single-porosity model results.

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