Analysis and modelling of the hydraulic conductivity in aquitards: application to the Galilee Basin and the Great Artesian Basin, Australia Zhenjiao JIANG Bachelor of Science (Jilin University, China), 2008 Master of Science (Jilin University, China), 2011 Thesis submitted in accordance with the regulations for the Degree of Doctor of Philosophy School of Earth, Environmental and Biological Sciences Science and Engineering Faculty Queensland University of Technology 2014 Key Words Aquifer, aquitard, Bayesian inference, coal seam gas, coherence analysis, cokriging interpolation, Eromanga Basin, fluvial processes, Galilee Basin, geological process based model, Great Artesian Basin, harmonic analysis, hydraulic conductivity, kriging interpolation, numerical simulation, perturbation method, accumulation, spectral analysis sediment transport, sediment Abstract The hydraulic conductivity (K) of an aquitard is of critical importance in controlling groundwater flow and solute transport in a multilayered aquifer-aquitard system Direct measurement of K is commonly based on the Darcy’s law, which expresses a linear relationship between K and pressure/water-level differences As aquitards are of low permeability, measurement of K in a realistic timeframe requires a large pressure difference within the testing interval As a consequence, direct K measurement for an aquitard is mostly limited to the laboratory tests, where the larger pressure difference can be controlled But due to the scale effect induced by the heterogeneity of the aquitard, the resultant K from laboratory tests can be several orders different with K at the practical scale (such as the sizes of discretized cells in the regional-scale numerical simulation for groundwater flow) The focus of this dissertation is the development of alternative methods to enable estimation of K in the aquitard at a regional scale, mainly including an analytical approach and a geological process-based method The analytical approach, which combines the harmonic and coherence analysis, is developed to calculate the vertical hydraulic conductivity (Kv) in the aquitard, based on the long-term water-level measurements in the aquifers overlying and underlying the target aquitard The harmonic analysis derives Kv as a function of leakage-induced water-level fluctuations in the aquifers The coherence analysis rules out the noise which interrupts the leakage-induced water-level fluctuations The method is validated by synthetic case studies, and then is applied to calculate Kv for both the Westbourne and Birkhead aquitards within the Eromanga Basin, Australia From this, Kv for the Westbourne aquitard is estimated to be 2.17×10-5 m/d and for the Birkhead aquitard is 4.31×10-5 m/d Combining harmonic and coherence analysis above can result in a regional-scale Kv, which is, however, averaged over heterogeneity of the aquitard As an alternative, another methodology which can infer the heterogeneous K distribution in the aquitard is proposed The method is based on the fluvial processes simulation, assuming that the target aquitard is formed by a river system Steps in this methodology are: -1- (1) 1D stochastic fluvial process-based model is developed on the basis of the Exner equation, by revisiting the flow velocity in the model as the stochastic description (mean and perturbation) of velocity As a consequence, the riverbed and channel evolution, and the variation of river discharge can be accounted in the model Two-phases of sediment transport (sand and silt) are modelled to reproduce a sandstone/siltstone architecture (with respect to high/low permeable rock structure), which result in 2D profiles of the sandstone proportion (2) The sill, nugget and correlation length of sandstone proportion is then extracted, and is used in the kriging procedure to infer a 3D representation of sandstone proportion (3) The sandstone proportion is converted to K values based on the classical averaging method that vertical K is the harmonic average of original K in sandstone and siltstone, whilst the horizontal K is the arithmetic average of K in sandstone and siltstone The methodology is applied in the Betts Creek Beds (BCB), which is an aquitard separating a key coalbed from several major aquifers in the Galilee Basin, Australia BCB was deposited by a river system in the Permian over a period of 20 million years, and is composed by sandstone, siltstone, claystone and shale K for the siltstone, claystone and shale were tested by centrifuge permeameter core analysis K for sandstones are tested by the drill stem test, and also inferred from the downhole logs of the electrical resistivity and sonic velocity using cokriging-Bayesian approach Herein, the fine-grained sediments (siltstone, claystone and shale) which have similar K values are uniformly referred to as “siltstone” The lithological architecture (sandstone/siltstone) of BCB is simulated by combining the stochastic fluvial process model and the kriging method Finally, 3D spatial distribution of K can be inferred by substituting K of sandstone and siltstone in the lithology architecture K measured by laboratory testing, field drill stem test and the cokriging method represent the values on a small scale, but averaging methods, which convert the lithological architecture to the heterogeneous K distribution, result in upscaled K values -2- Contents Abstract……… Contents…… List of Figures I Acknowledgements III Statement of Original Authorship V Statement of Contribution of Co-Authors VII Thesis Outline Chapter 1: Introduction 1.1 STUDY AREA 1.1.1 Regional geology 1.1.2 Stratigraphy 1.1.3 Hydrogeological features .9 1.2 RESEARCH AIM 10 Chapter 2: Methods review 13 2.1 ANALYTICAL METHOD 13 2.2 NUMERICAL INVERSION .14 2.3 GEOSTATISTICAL INTERPOLATION 15 2.4 GEOLOGICAL PROCESS-BASED MODEL 17 2.5 HYBRID METHOD 20 Chapter 3: Vertical hydraulic conductivity in the aquitards 21 Abstract 21 Keywords 21 3.0 INTRODUCTION .21 3.1 METHODS 23 3.1.1 Harmonic analysis of water-level signals 23 3.1.2 Calculation of phases 31 3.1.3 Selection of frequencies .32 3.1.4 Estimation of Kv 33 3.1.5 Procedures 34 3.2 SYNTHETIC CASE STUDY 35 3.2.1 Influence of aquifer thickness on Kv estimation 36 3.2.2 Influence of observation-well distances 38 3.2.3 Causal relationship .41 3.3 Hydraulic conductivity for the aquitards in the Great Artesian Basin 44 3.3.1 Materials 44 3.3.2 Estimates of hydraulic conductivity 46 3.4 SUMMARY AND CONCLUSION 49 Acknowledgements 50 Chapter 4: Stochastic fluvial process model 51 Introductory comments 51 Abstract 51 -1- Key words 52 4.0 INTRODUCTION 53 4.1 GOVERNING EQUATION 55 4.2 VELOCITY REVISITED 56 4.2.1 Manning velocity 56 4.2.2 Velocity perturbation induced by turbulence 57 4.2.3 Define channel evolution in the ensemble statistics of velocity 57 4.3 MASS BALANCE EQUATION REVISITED 60 4.4 SEMI-ANALYTICAL SOLUTIONS 63 4.4.1 Solution for the variance of sediment load 63 4.4.2 Solution for the mean sediment load 65 4.4.3 Solution for the mean and variance of sedimentation thickness 66 4.5 ALGORITHM 67 4.6 SYNTHETIC CASES STUDY 68 4.6.1 Synthetic example-1 69 4.6.2 Synthetic example-2 72 4.7 CONCLUSION 73 Acknowledgment 74 Chapter 5: Local-scale hydraulic conductivity determination 75 Introductory comment 75 Abstract 75 Key Words 76 5.0 INTRODUCTION 76 5.1 Study area and data description 78 5.1.1 General geological setting 78 5.1.2 Data analysis and pre-processing 80 5.2 METHODOLOGY 82 5.2.1 Bayesian framework 82 5.2.2 Cokriging model 83 5.2.3 Normal linear regression model 84 5.2.4 Theoretical differences between CK and NLR-based Bayesian method 85 5.3 HYDRAULIC CONDUCTIVITY ESTIMATION 87 5.3.1 Prior estimation 87 5.3.2 Updating by Bayesian statistics 88 5.3.3 Discussion 91 5.4 CONCLUSION 94 Acknowledgements 94 Chapter 6: Heterogeneity of the Betts Creek Beds 95 Introductory comment 95 Abstract 95 Keyword 96 6.0 INTRODUCTION 96 6.1 DEPOSITIONAL ENVIRONMENT OF BCB 99 6.2 METHOD 100 6.2.1 Two facies sediment accumulation simulated by SFPM 101 6.2.2 Selection of kriging method 101 6.3 WORKFLOW 102 6.4 RESULTS AND DISCUSSIONS 105 6.4.1 Sensitivity analysis 105 -2- 6.4.2 Model validation 106 6.4.3 3D heterogeneous hydraulic conductivity 111 6.4.4 Uncertainty 113 6.5 SUMMARY .118 Acknowledgements 120 Chapter 7: Summary and conclusions 121 7.1 ANALYTICAL APPROACH 121 7.2 COKRIGING AND BAYES INTERPOLATION .122 7.3 STOCHASTIC FLUVIAL PROCESS-BASED APPROACH 123 7.4 COMPARISION OF THREE METHODS 124 7.4.1 Analytical approach 124 7.4.2 Coupled cokriging and Bayes method .124 7.4.3 Process-based modelling 125 7.5 CONCLUSION 125 Appendix A: Drill Stem Test 127 Appendix B: Centrifuge permeameter core analysis 129 Appendix C: Erosion and deposition rate 131 C.1 EROSION RATE 131 C.2 DEPOSITION RATE 132 Appendix D: Conference abstracts 133 Bibliography 135 -3- Appendix C: Erosion and deposition rate The river water flow velocity is a key parameter which affects the sediment transport and accumulation via altering the erosion and deposition rates This section incorporates ensemble velocity in the expressions of erosion and deposition rates C.1 EROSION RATE A widely used expression for the erosion rate is given as (e.g Tucker, 2004; Lague et al., 2005): E  ke ( /   c3 / ) ,    c , (C1) where ke is the erosion efficiency (L2.5∙T2/M1.5),  is the shear stress (M/ L∙T2) and  c is the critical shear stress above which the erosion starts (M/ L∙T2)  c depends on river bed lithology which is calculated as (Cornelis et al., 2004):  c  kt (  s   f ) gd , (C2) where kt is shear parameter,  s is the dry density of sediments (M/L3), and  f is the density of water (M/L3) , d is the diameter of sediments (L) As this study derives the stochastic fluvial process-based model by introducing the statistics of velocity, Eq (C1) is converted to a function of velocity The shear stress and stream velocity satisfy (Dade and Friend, 1998):   cd  f v , (C3) where cd is the dimensionless drag coefficient Substituting Eq (C3) in Eq (C1) and making use of perturbation theory (Eq 4.21), the erosion rate is separated as a mean: E  ke [(cd  f )1.5 (v  3 v2 )v   c1.5 ] , (C4) and a perturbation: E  we v , (C5) where we  ke (cd  f )1.5 (3v   v2 ) Appendix C: Erosion and deposition rate 131 C.2 DEPOSITION RATE Assume that erosion and deposition can occur simultaneously, the deposition rate can be simply written as (e.g Winterwerp and Van Kesteren, 2004; Davy and Lague, 2009): D  , Hc where  is sediment load (L3/L2), (C6) H c is the stream depth (m) and  is the deposition coefficient, relating to the settling velocity (  s ), vertical sediment concentration distribution ( k d ) and in this study also relating to the probability of channel occurrence (p):   kd  s p , (C7) In this current study, the vertical sediment concentration distribution is not simulated, its influence on D are represent by a concentration coefficient k d  S is the settling velocity of the particles (L/T), which relates to the fluid and sediments properties (Dade and Friend, 1998): gd  s   f S  for d