Accepted Manuscript

Using predictive uncertainty analysis to optimise tracer test design and dataacquisition

Ilka Wallis, Catherine Moore, Vincent Post, Leif Wolf, Evelien Martens,Henning Prommer

PII: S0022-1694(14)00335-7DOI: http://dx.doi.org/10.1016/j.jhydrol.2014.04.061Reference: HYDROL 19592

To appear in: Journal of Hydrology

Received Date: 26 November 2013Revised Date: 18 March 2014Accepted Date: 24 April 2014

Please cite this article as: Wallis, I., Moore, C., Post, V., Wolf, L., Martens, E., Prommer, H., Using predictiveuncertainty analysis to optimise tracer test design and data acquisition, Journal of Hydrology (2014), doi: http://dx.doi.org/10.1016/j.jhydrol.2014.04.061

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Using predictive uncertainty analysis to optimise tracer 1

test design and data acquisition 2

3

Ilka Wallis* 1,2

, Catherine Moore3,4

, Vincent Post1,2

,Leif Wolf5, Evelien Martens

6 and Henning 4

Prommer2,6,7

5

6

1School of the Environment, Flinders University, Adelaide, GPO Box 2100, SA 5001, 7

Australia 8

2National Centre for Groundwater Research and Training, Flinders University, Adelaide, GPO 9

Box 2100, SA 5001, Australia 10

3CSIRO Land and Water, Dutton Park QLD 4102, Australia 11

4Institute of Environmental Science and Research Ltd, Porirua 5240, New Zealand

12

5 Karlsruhe Institute of Technology, Kaiserstr. 12, 76131 Karlsruhe, Germany 13

6CSIRO Land and Water, Private Bag No. 5, Wembley WA 6913, Australia 14

7School of Earth and Environment, University of Western Australia, Crawley, 6009 15

16

*corresponding author; email: ilka.wallis@flinders.edu.au; Tel: +61 8 8201 2020; Fax +61 8 17

8201 3567 18

Submitted to Journal of Hydrology 19

20

21

22

ABSTRACT 23

Tracer injection tests are regularly-used tools to identify and characterise flow and transport 24

mechanisms in aquifers. Examples of practical applications are manifold and include, among 25

others, managed aquifer recharge schemes, aquifer thermal energy storage systems and, 26

increasingly important, the disposal of produced water from oil and shale gas wells. The 27

hydrogeological and geochemical data collected during the injection tests are often employed to 28

assess the potential impacts of injection on receptors such as drinking water wells and regularly 29

serve as a basis for the development of conceptual and numerical models that underpin the 30

prediction of potential impacts. 31

As all field tracer injection tests impose substantial logistical and financial efforts, it is crucial to 32

develop a solid a-priori understanding of the value of the various monitoring data to select 33

monitoring strategies which provide the greatest return on investment. 34

In this study, we demonstrate the ability of linear predictive uncertainty analysis (i.e. “data 35

worth analysis”) to quantify the usefulness of different tracer types (bromide, temperature, 36

methane and chloride as examples) and head measurements in the context of a field-scale aquifer 37

injection trial of coal seam gas (CSG) co-produced water. Data worth was evaluated in terms of 38

tracer type, in terms of tracer test design (e.g., injection rate, duration of test and the applied 39

measurement frequency) and monitoring disposition to increase the reliability of injection impact 40

assessments. This was followed by an uncertainty targeted Pareto analysis, which allowed the 41

interdependencies of cost and predictive reliability for alternative monitoring campaigns to be 42

compared directly. 43

For the evaluated injection test, the data worth analysis assessed bromide as superior to head 44

data and all other tracers during early sampling times. However, with time, chloride became a 45

more suitable tracer to constrain simulations of physical transport processes, followed by 46

methane. Temperature data was assessed as the least informative of the solute tracers. However, 47

taking costs of data acquisition into account, it could be shown that temperature data when used 48

in conjunction with other tracers was a valuable and cost-effective marker species due to 49

temperatures low cost to worth ratio. In contrast, the high costs of acquisition of methane data 50

compared to its muted worth, highlighted methanes unfavourable return on investment. Areas of 51

optimal monitoring bore position as well as optimal numbers of bores for the investigated 52

injection site were also established. 53

The proposed tracer test optimisation is done through the application of common use 54

groundwater flow and transport models in conjunction with publicly available tools for 55

predictive uncertainty analysis to provide modelers and practitioners with a powerful yet 56

efficient and cost effective tool which is generally applicable and easily transferrable from the 57

present study to many applications beyond the case study of injection of treated CSG produced 58

water. 59

Keywords: experimental design, tracer tests, coal seam gas, data worth, linear predictive 60

uncertainty analysis, optimisation, Pareto analysis 61

1. Introduction 62

63

Tracer injection tests are regularly-used tools to identify and characterise flow and transport 64

mechanisms in aquifers. Such tests can be used to derive subsurface hydraulic properties, and to 65

investigate the transport behaviour of both non-reactive and reactive solutes in groundwater. 66

Examples of practical applications are manifold and include, among others, managed aquifer 67

recharge schemes (e.g. Culkin et al., 2008, Descourvieres et al., 2010, Wallis et al., 2011), 68

aquifer thermal energy storage systems (e.g., Zuurbier et al. 2013), the storage of CO2 emissions 69

in deep aquifers (e.g. Michael et al., 2010) and, increasingly important, the disposal of treated 70

coals seam gas (CSG) production water or produced water from oil and shale gas wells into deep 71

aquifers (NWC, 2011; U.S. Dep. of the Interior, 2011). The hydrogeological and geochemical 72

data collected during the injection tests often serve as a basis for the development and 73

parameterisation of conceptual and numerical models that are subsequently used to predict the 74

larger-scale and longer-term hydraulic and water quality impacts of operational injection, storage 75

and abstraction schemes. 76

77

All field tracer injection tests impose substantial logistical and financial efforts. This is 78

particularly so within the context of injection of CSG-produced water, given the often 79

considerable depth of the targeted aquifers, in many cases exceeding 1 km. A significant number 80

of sampling events is often not only required during injection, especially under dynamically 81

changing flow conditions, but also in the post-injection monitoring phase, to capture long-term 82

geochemical changes. Monitoring may include continuous recording of various data types using 83

cost-effective down-hole sensors, for example for temperature, pressure or electrical conductivity 84

data (Ma et al., 2012). However, data acquisition for most chemical constituents to date still 85

relies on more costly laboratory analysis of water samples. To minimise efforts and costs, 86

sampling strategies that can most efficiently identify and characterise the transport mechanisms 87

and geochemical processes in the targeted aquifers within the given budget and access 88

constraints need to be chosen. A robust a priori understanding of the costs and the value (i.e., 89

data worth) of the available data types will allow (i) optimisation of the trial design (e.g., types of 90

tracers amended, concentrations of amended tracers, duration of amendment); (ii) optimisation of 91

monitoring strategies (e.g., type and frequency of the collected data); and (iii) reduction of the 92

uncertainty of model predictions, and thus maximise the predictive power of models simulating 93

long-term impacts during and after operational injection. The proposed methodology requires to 94

set up a numerical groundwater model already ahead of the trial. 95

96

Within the context of water resources modelling, the assessment of “data worth” involves 97

quantification of the utility of observation data in reducing the uncertainty of model predictions 98

of future environmental behaviour (e.g., first or mean contaminant arrival time, magnitude of 99

plume spreading) which underpin management decisions. The value of a data type or an 100

observation location is greater, the more it enhances the certainty with which the model is able to 101

predict such environmental behaviour. By comparing the difference in predictive uncertainty 102

with or without such data, the value of potential observations is assessed. Predictive uncertainty 103

is typically computed using global optimisation methods, such as Monte Carlo simulations (e.g.. 104

James and Gorelick, 1994, Parker et al., 2010), Fu and Gómez-Hernández, 2008). Monte Carlo 105

techniques often pose a considerable computational burden, as they consist of performing a large 106

number of forward model runs based on a random selection from model parameter distributions. 107

Their application therefore remains restricted mostly to groundwater models of limited run-time. 108

In order to assess data worth within the context of field-scale, multi-species non-reactive as well 109

as reactive transport problems, where model run times and the number of adjustable parameters 110

can be high, a computationally more efficient approach is desirable. A methodology which is 111

applicable to field-scale problems was initially presented by Moore and Doherty (2005) and later 112

extended by Christensen and Doherty (2008). This analysis is based on linear predictive 113

uncertainty analysis formulated for distributed parameter models and is incorporated as the 114

freely-available prediction uncertainty tools PREDUNC and PREDVAR into the PEST suite 115

(Doherty, 2010a, b) (Figure 1). The approach derives estimates of simulated prediction 116

uncertainty based on direct propagation of uncertainties originating from incomplete knowledge 117

of model parameters. Computational efficiency is gained by assuming that the system response is 118

sufficiently linear over the range of evaluated parameters to establish relative contributions to 119

uncertainty. This allows the calculation of predictive uncertainty to be made rapidly, so that it 120

can be repeated for many alternative monitoring strategies (potential monitoring sites, potential 121

observation data types and sampling times). 122

123

The methodology has been successfully applied to several synthetic numerical groundwater 124

model problems. Moore (2005), for example, investigated the worth of spatially distributed head 125

and hydraulic conductivity measurements with respect to the reliability of contaminant transport 126

predictions. Dausman et al (2010) investigated the relative worth of salinity and temperature 127

observations for predictions of the location of a theoretical salt water–fresh water interface, while 128

Fienen et. al (2010) used prediction uncertainty analysis to explore its use in a hypothetical 129

water-level monitoring network design by analysing the worth of head measurements for 130

drawdown and flux predictions. A recent example of the practical application of data worth to a 131

field-scale problem was presented by Engelhardt et al. (2013), where the suitability of the 132

artificial sweetener acesulfame as conservative tracer for sewage related fluxes and its value in 133

constraining simulated water and mass-fluxes was investigated. Nevertheless, a wider range of 134

studies which demonstrate the robustness of this methodology to field-scale problems in 135

hydrogeologically and geochemically heterogeneous porous media is still lacking, and moreover, 136

its use in conjunction with minimising the actual cost of data acquisition has also not been 137

demonstrated. This allows for the evaluation of a monitoring strategy subject to both cost and 138

rigour constraints and is of particular importance in the water resources context, where 139

monitoring is typically a significant effort and often under public scrutiny. 140

141

In this study, we demonstrate the ability of linear predictive uncertainty analysis (hereafter 142

simply referred to as “data worth analysis”) to quantify the usefulness of different tracer types 143

and head measurements in the context of a field-scale aquifer injection trial of CSG co-produced 144

water. Data worth is evaluated in terms of the degree to which chemical concentrations, 145

temperature and head data increase the reliability of injection impact assessments, employing the 146

metrics of dilution and time of travel. The relative merits of different tracer test designs are 147

explored. These differ in terms of where and when tracer concentrations are collected, the 148

injection rate and duration of the test, the tracer concentration to ambient concentration ratios 149

(signal to noise ratios) and the applied measurement frequency. We then formulate the trade-off 150

between the established relative value of tracer data on the one hand and the costs of its 151

acquisition on the other hand (Figure 1) to select monitoring strategies which provide the greatest 152

return for investment. 153

154

2. Data worth methodology 155

The uncertainty analysis theory underpinning the methodology of data worth is briefly 156

summarised here to provide the theoretical background for this work. Various particular aspects 157

are presented in more detail elsewhere (Moore and Doherty, 2005, Christensen and Doherty, 158

2008, Dausman et al., 2010, Fienen et al., 2010, Moore et al. 2011, Engelhardt et al., 2013). 159

160

A vector p can be partitioned into two subvectors p1 and p2. In the hydrogeological context 161

considered in this paper such a vector could comprise hydraulic parameters such as porosity and 162

hydraulic conductivity for distributed points in space. If p is comprised of multi-Gaussian 163

random variables with a covariance matrix C(p), then C(p) be partitioned on the same p1, p2 164

basis, e.g., (C(p1p1) or C11, C(p1p2) or C12, C(p2p1) or C21, and C(p2p2) or C22) . If elements of 165

p2 become known (e.g. field tests of hydraulic conductivity or porosity are undertaken), then 166

C’11, the covariance matrix of p1 conditional on knowing p2 is calculated as (Koch, 1987): 167

C’11 = C11-C21C-1

22C21 (1) 168

This formula can be used to characterise the reduction in uncertainty of model parameters, and 169

the predictions which depend on them, that is achieved by adding data that contains information 170

pertinent to model parameters, including the special case where a parameter value becomes 171

perfectly known, and its covariance becomes zero. 172

173

Now let a (m×1) vector p contain the values of parameters used by a model. Let the action of a 174

(linear) model on these parameters p be represented by the matrix X. Unless the parameter 175

values encapsulated in the vector p are accurately known at all places within a model domain, 176

they must be described in probabilistic terms. Therefore, let the covariance matrix of p be 177

denoted as C(p). Further, let the vector h represent observations of system state comprising the 178

model calibration set and allow for these observations to be contaminated by measurement noise 179

ɛ, such that: 180

h = Xp+ɛ (2) 181

Let s (a scalar) designate a prediction made by the model; let the sensitivities of this prediction to 182

model parameters be represented by the vector y. Then s is calculable using the relationship: 183

s = ytp (3) 184

Combining (2) with (3) leads to: 185

���� = ��� 0

� ���� (4) 186

From the propagation of error formula we can calculate: 187

C ���� = �y� 0

� ��(�) 00 �(�)� �� �

0 � = ����(�)� ���(�)��(�)� �(�)� + �(�)� (5) 188

Where C(p) is the covariance of innate parameter variability, and I is the identity matrix. In 189

Christensen and Doherty (2008) equation (1) and (5) are combined. This is shown to be a 190

Bayesean formulation of linear predictive uncertainty in Fienen et al (2010) and Dausman et al. 191

(2010). The Bayesean approach abandons the notion of a calibrated model, and instead a suite of 192

model outputs are used to describe the possible predictions, as encapsulated by equation (6): 193

ơ2

s= ytC(p)y - y

tC(p)X

t[XC(p)X

t + C(ε)]

-1 XC(p)y (6) 194

In this work this formulation is used to evaluate the worth of different tracer test designs. It is 195

important to note the assumption of model linearity encapsulated in equation 6. The implication 196

of this being that calculated predictive errors should be considered in a relative rather than 197

absolute magnitude sense where models exhibit non-linear behavior. However because data 198

worth analysis is explicitly a relative comparison between alternatives, rather than a calculation 199

that obtains absolute values, the use of equation 6 in this context is considered appropriate. In 200

addition, where compared quantities may be affected by an erroneous assumption of model 201

linearity, relativity of the compared alternatives may nevertheless be preserved (Doherty et. al. 202

2010). Equation 6 also assumes independence between parameter and error covariance terms, but 203

correlation between these terms can exist when the model is under determined. However, given 204

the relative rather than absolute nature of this assessment, the omission of these correlation terms 205

is considered acceptable. 206

207

The cost effectiveness of different tracer test design options were explored within a Pareto 208

optimisation framework (Pareto, 1906; Stadler, 1979). The Pareto front is the locus of points 209

along which it is not possible to lower one objective function without increasing another, and 210

was first demonstrated in a predictive uncertainty context by Moore et al. (2010). The framework 211

was applied in two dimensions whereby one objective function was defined in terms of the 212

uncertainty of a prediction as calculated using equation (6), and the second objective function 213

was defined in terms of the cost of the tracer test analyses. The Pareto optimisation framework is 214

available through the PEST software suite (Doherty, 2010a,b) and the major components of this 215

optimisation methodology are summarised in the flow chart depicted below (Figure 1). 216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

* Predictions are predictions of interest for the problem at hand. The optimisation goal for this study is the reduction of 241

uncertainty of (i) transport time predictions and (ii) concentration dilution predictions. Both are key characteristics for assessing 242

the impact of the re-injection of treated CSG operational water on aquifer geochemistry. 243

Figure 1: Flow chart of employed optimisation methodology. 244

245

3. Application of data worth methodology 246

3.1 Case study 247

Analysis of trade-off in

costs vs. reliability

Numerical Model relating

prediction* to parameter inputs

Measurement data types and

disposition to explore Calculated sensitivities of

prediction to parameters

Parameter probability

distribution

Observation data worth: Calculated reduction in

prediction uncertainty with additional

observation data

Parameter worth: Calculated reduction in

prediction uncertainty with increased

parameter knowledge

PEST SUITE

PREDUNC / PREDVAR

PARETO ANALYIS

The case study that provided the motivation for the present data worth analysis is a deepwell 248

injection site located in northern Queensland, Australia, where a large-scale injection program 249

for treated CSG production water (permeate water) is proposed. Here, the operator of the site is 250

investigating the suitability of the local aquifer for re-injection of reverse osmosis (RO) treated 251

water. The target aquifer is the Precipice Sandstone aquifer of the Surat Basin (Elliott, 1989; 252

QWC, 2012), which, at the site, extends from approximately 420m below ground level (mbgl) to 253

515mbgl (Figure 2). The aquifer is comprised of fine- to coarse-grained sandstones with 254

interbedded siltstones and mudstones representing a generally upward-fining, fluvial sedimentary 255

sequence. The main injection horizon is the coarse-grained lower 60 m of the formation, termed 256

the Braided Stream Formation which is of high primary and secondary porosity, and which is 257

characterised by high permeability and rapid, preferential flow through fractures. The Precipice 258

Sandstone is separated from overlying and underlying aquifers by thick sequences of mainly silt- 259

and mudstones (QWC, 2012). 260

261

The groundwater in the target aquifer prior to the start of injection is anoxic, as indicated by high 262

methane and Fe2+ concentrations, and the absence of appreciable concentrations of oxygen, 263

nitrate or sulphate (Table 1). The injectate is reverse osmosis treated CSG water (RO permeate), 264

and further treated by membrane removal of dissolved gases and UV sterilisation. The resulting 265

water is oxic water with a low mineralisation. A summary of average RO permeate chemistry is 266

given in Table 1. 267

268

A range of potentially suitable tracers were considered that included, on one hand groundwater 269

constituents that already prevail in the ambient groundwater and, on the other hand, added or 270

‘amendment’ tracers. Potential monitoring of these proposed tracers aims to (i) document the 271

spreading of the RO permeate within the target aquifer and (ii) to subsequently use this 272

information to establish quantitative models (Table 1). The range of potentially suitable ambient 273

tracers included methane, which prevails at high concentration in the ambient groundwater but is 274

absent in the oxic injectant (Table 1), therefore acting as a “negative” tracer. Differences in 275

chloride concentration between the injectate and the groundwater are relatively low (Table 1) 276

and chloride was therefore regarded as a potentially less suitable tracer with respect to its value 277

for constraining physical transport processes. However, chloride is widely used in field tracer 278

tests elsewhere because of its conservative behaviour (i.e., non-reactive) and hence was included 279

in the current data worth analysis for comparison. Potassium bromide (KBr) was identified as 280

suitable amendment for the injectate. Under the conditions considered here, bromide has proven 281

to behave conservatively in the subsurface and not to react with the aquifer matrix or other 282

solutes (Davis et al., 1980). For the purposes of this study, KBr was assumed to be dosed into the 283

injectate at concentrations of 0.25 mg/l, i.e., several times that of the background (0.06 mg/l) for 284

7 days at the start of the injection trial before switching back to the original RO water 285

composition without KBr amendment (Table 1). Finally we also included temperature in the data 286

worth analysis. Temperature is increasingly recognised as a valuable, cost-effective 287

environmental tracer in groundwater studies (e.g. Anderson, 2005). Where the difference 288

between the injectate and the ambient groundwater temperature was sufficiently large, 289

temperature was also shown to be a suitable tracer in managed recharge applications (e.g., 290

Prommer and Stuyfzand, 2005, Greskowiak et al., 2006). At our study site, injectate 291

temperatures were expected to vary with surface temperatures. Besides solute and heat tracers, 292

hydraulic heads were assumed to be monitored on a continuous basis and therefore included in 293

this way for the data worth analysis. 294

295

Table 1 Ambient and injectate water chemistry (Source: Origin Energy Resources LTD) 296

Analyte Units RO Permeate Precipice Sandstone

water at Injection Site Min Max Median

Temperature °C Variable depending on ambient

temperature 37

Electrical Conductivity µS/cm 98 201 130 230

Redox potential mV - - - -220

pH

6.86 7.92 7.35 6.4

Total Dissolved Solids mg/L 44 88 58 113

Bromide mg/L 0.07 0.14 0.1 0.06

Carbonate Alkalinity mg/L BD* 0.4 BD* <1

Bicarbonate Alkalinity mg/L 15 21 19 <1

Total Alkalinity mg/L 12 18 16 <1

Sulphate mg/L BD* BD* BD* 4

Chloride mg/L 20 46 26 13

Calcium mg/L BD* 7.7 0.1 4

Magnesium mg/L BD* 1.9 BD* <1

Sodium mg/L 17 27 23 35.5

Potassium mg/L 0.1 0.6 0.3 2

Iron mg/L BD* 0.075 0.036 4.02

Methane µg/L BD* BD* BD* 11950

* BD: Below detection limit 297

298

3.2 Model description 299

3.2.1 Conceptual model and numerical model setup 300

As the natural groundwater flow velocities are with gradients of less than 0.01 very small at the 301

injection site compared to those induced by the re-injection operation, radial-symmetric flow and 302

transport conditions were assumed. Flow and solute transport were therefore simulated using a 303

2D quasi-radial flow and transport model that represents a radial-symmetric 3D domain, using a 304

previously developed and tested approach (Greskowiak et al., 2005, Wallis et al., 2012). This 305

allows for savings in model run times of one to two orders of magnitude (Wallis et al. 2012) and 306

allows the calculation of predictive uncertainty to be made rapidly. The finite-difference model 307

MODFLOW (Harbaugh, 2005) was used for the flow simulations while solute and heat transport 308

were simulated with the multi-species transport simulator MT3DMS (Zheng and Wang, 1999, 309

Langevin et al. 2009; Ma et al. 2012, Engelhardt et al. 2013). The model has a radial extent of 310

515m with grid cell-sizes increasing from 1 m near the injection well to 15m at the outer model 311

fringes, where a constant head boundary was implemented. The total simulation period was set to 312

100 days, whereby the amended RO permeate was injected during the first 7 days. The model 313

simulation period was divided into 5 stress periods, which varied in length between 2 and 78 314

days to represent the variability of injection rates and KBr amendment in the injection water. The 315

resulting flow and transport model represents the expected major flow and concentration pattern 316

created by the injection well and served as the base case scenario for the subsequent data worth 317

and network design analysis (Figure 3). 318

319

3.2.2 Model parameterisation 320

The geological sequence of the Precipice Sandstone Formation was separated into 9 model layers 321

with four distinct conductivity zones that were defined on the basis of the lithological profile 322

obtained from core logging as well as the geophysical down-the-hole surveys and the test pump 323

program conducted by the operator (Table 2 and Figure 2). The analysis of the collected core 324

material showed fracturing within the main injection horizon, i.e., the Braided Stream Formation 325

(BSF, model layer 8). Therefore a dual domain mass-transfer approach was implemented for this 326

layer (Feehley et al., 2000; Liu et al., 2007). This approach allows mimicking the characteristic 327

transport behavior that is created where highly permeable portions of the aquifer, including 328

fractures, exchange mass with stagnant or slow-flowing zones (Haggerty, 2001). Likely flow and 329

transport model parameter values and the lower and upper limits excepted for these parameters 330

were estimated based on published reports on the aquifers in this region (Radke, 2012) (Table 2). 331

In the case of the heat transport parameters, estimated values were based on literature data and 332

actual measured, site-specific, lab-determined thermal conductivity and heat capacity values by 333

the operator. Vertical and horizontal hydraulic conductivities and porosity were defined in the 334

model using the pilot points method (de Marsily et al., 1984, Doherty 2003) to introduce 335

parameter heterogeneity. Thereby, mean parameter values (Table 2) were uniformly assigned to 336

a total of 117 pilot points (one point placed into every 5th model cell) and then spatially 337

interpolated to all active model cells using kriging. The spatial variability was thereby assumed 338

to be log-normally distributed and characterized through a variogram with a range of 250m, sill 339

of 0.2 and a nugget of zero. The use of distributed pilot point parameters mitigates contamination 340

of the data worth analysis from the structural error associated with parameter lumping, as they 341

introduce minimal assumptions about the geometry and lumping of the hydraulic-conductivity 342

and porosity field (e.g. Moore 2005, and Doherty and Welter, 2010, and Fienen et al. 2010). In 343

total the model is comprised of 244 model parameters (Table 2). Figure 2 illustrates the 344

simulated tracer concentration and heat distribution patterns within the BSF created by the 345

injection well computed using the mean hydraulic properties as listed in Table 2. 346

347

Table 2: Model parameterization 348

Parameter

Model

layer Units

Distributio

n Mean

Lower

limit

Upper

limit

PEST

parameter

group

Storage coefficient L1-9 - uniform 1.00E-05 1.00E-06 1.00E-04 stor

Kh1) - varying log of kh by 3*sd0.22) L8 [m/d] pilot points 100 4.56 2196 kh

kh1) - varying log of kh by 3*sd0.22) L1, 3, 9 [m/d] pilot points 1.00E-04 4.56E-06 0.0022 kh

kh1) - varying log of kh by 3*sd0.22) L2, L5 [m/d] pilot points 0.1 0.0046 2.2 kh

kh1) - varying log of kh by 3*sd0.22) L4 [m/d] pilot points 10 0.46 219.6 kh

n1 - porosity – mobile domain L1-7, 9 - pilot points 0.1 0.05 0.3 por

n2 - porosity (BSF3)) – mobile domain L8 - pilot points 0.01 0.005 0.1 por

n3 - porosity (BSF3)) - immobile domain

L8 - Uniform 0.04 0.01 0.1 por

n3 - porosity - immobile domain

L1-7, 9 - Uniform 0.0001 not allowed to vary n.a.

m - mass transfer rate L8 [1/d] uniform 1.00E-04 1.00E-05 1.00E-03 mass

Dispersivity L1-9 [m] uniform 1 0.5 2 disp

Therm. Diffusivity L1-7, 9 [m2/d] uniform 0.0452 0.014 0.14 thermdif

Therm. diff. (BSF3)) L8 [m2/d] uniform 0.0941 0.028 0.28 thermdif

Thermal kd L1-9 [m3/kg] uniform 0.0002 0.00015 0.00022 thermkd

Bulk density (BSF3)) L8 [kg/m3] uniform 2660 1900 2900 thermbd

Bulk density L1-7, 9 [kg/m3] uniform 2520 1800 2800 thermbd

349 1) kh = kv 350 2) The parameter standard deviation descriptions for the hydraulic parameters are calculated in the log 351

domain, i.e. parameter standard deviation (sd) = 0.2( log domain) times 3 352 3) BSF = Braided Stream Formation 353

354

3.3 Optimisation of tracer test design and data acquisition 355

3.3.1 Optimisation goal 356

The data worth methodology is based on the premise that a measure of the worth of different 357

monitoring designs is its ability to reduce the uncertainty of key model predictions of future 358

environmental behaviour (Figure 1). The calculated uncertainty is thereby specific to the 359

required prediction type and is quantified by the standard deviation. The latter depends on the 360

uncertainty of the estimated hydrogeologic parameters (Table 2) and the ability of the selected 361

tracer data to constrain these parameters. The optimisation goal for this study is the reduction of 362

uncertainty of (i) transport time predictions and (ii) concentration dilution. Both are key 363

characteristics for assessing the impact of the re-injection of treated CSG operational water on 364

aquifer geochemistry. Our assessment of the predictions is composed of the time of solute 365

breakthrough within the BSF at 24m, 50m, 78m, 106m, 125m, 155m and 175m radial distance 366

from the injection well (Figure 2) and of the corresponding dilution. Unlimited observation 367

locations can be added as appropriate to reflect locations of actual risk receptors. The relative 368

worth of an observation location or tracer type is then ranked against others based on their ability 369

to reduce the uncertainty of these predictions at the selected locations depicted in Figure 2. 370

371

3.3.2 Monitoring network and data types 372

A base case observation network was established to explore optimal monitoring strategies. 373

Bromide, chloride and methane concentration as well as head and temperature data observations 374

were simulated at varying distances from the injection well (Figure 2). Tracer observations were 375

thereby placed in every 5th model cell into layers 1, 3, 5, 7, 8 and 9, providing a total of 78 376

potential observation locations for each tracer (Figure 2). This complete observation suite served 377

as the base case observation set (Table 3). 378

379

For all observation values a level of systematic uncertainty was assumed, which reflects the 380

measurement errors of the collected data as well as the level of observed background variability 381

in concentration, head and temperature data. It also includes model structural noise induced 382

through model artefacts e.g. discretisation, or alternatively the numerical dispersion or the 383

chosen advection scheme. The estimate of this measurement noise for each observation type was 384

based on the approximate accuracy expected for the respective laboratory methods (e.g., analysis 385

of bromide concentrations through ion-chromatography) in conjunction with the expected 386

magnitude of errors induced during field sampling. Background variability of each data type was 387

available from the injection site. The combination of measurement and structural noise of 388

observation data was considered in the data worth analysis by assigning weighting factors equal 389

to the inverse of the total observation uncertainty (which combines measurement and model 390

structural error). Based on the above, the observation values were assumed to have a systematic 391

uncertainty expressed as a standard deviation equal to 5% (temperature data), 10% (head 392

observations), 15% (chloride and bromide concentrations) and 20% (methane concentrations) of 393

measured values. 394

395

396

Figure 2 Cross-section through radial model grid, showing position of the 9 model layers and 65 model 397

cells in radial direction. Also shown are 78 potential observation locations (blue circle) and spreading 398

prediction locations (red square) and the lithological and natural gamma log profile of the injection bore. 399

400

3.3.3 Alternative monitoring configurations 401

A number of additional, alternative monitoring configurations where then defined and compared 402

with the base case network (see Table 3) and included: (i) different monitoring network designs 403

based on different numbers and locations of observation bores, and different monitoring 404

frequencies, and (ii) different injection test configuration based on changes to the ratio between 405

concentration of injectant to ambient solutes, and to the applied injection rate. These different 406

scenarios thereby target the optimum combination of the spatial disposition of monitoring wells, 407

the temporal disposition of measurements made at these wells, and the signal to noise disposition 408

of the tracer tests, where optimum is defined in terms of ability to reduce predictive uncertainty. 409

410

Table 3: Model scenarios 411

Scenario Tracer Sampling Injection Br [mg/l] Duration Scenario

frequenc

y

Rate Injectant Amendment type

Base case All tracers daily 500/1000 m3/d 0.25 1 week 78 observation bores

Scenario 1-4 All tracers daily 500/1000 m3/d 0.25 1 week Nr of obs. Bores

1): 1, 2, 3, 5

Scenario 5-9 All tracers2)

variable 500/1000 m3/d 0.25 1 week Sampling frequency

2): 2, 7, 14, 21, 30

Scenario 10-12 All tracers daily 500/1000 m3/d 0.25 1 week Timing of sampling: 1, 2, 3

3)

Scenario 13 Br daily 500/1000 m3/d 0.15 1 week Amendment of injectant conc.

Scenario 14 Br daily 500/1000 m3/d 0.20 1 week Amendment of injectant conc.

Scenario 15 Br daily 500/1000 m3/d 0.50 1 week Amendment of injectant conc.

Scenario 16-17 Br weekly 500/1000 m3/d 0.25 variable Duration of amendment: 2; 12 days

Scenario 18 All tracers daily 1000/2000 m3/d 0.25 1 week Injection rate doubled

Scenario 19 All tracers daily 250/500 m

3/d 0.25 1 week Injection rate halved

Scenario 20 Cl

daily 500/1000 m3/d 0.25 1 week

3)Cl permeate conc. = 11.5 mg/l

Scenario 21 Cl

daily 500/1000 m3/d 0.25 1 week

3)Cl permeate conc. = 15 mg/l

Scenario 22 Cl

daily 500/1000 m3/d 0.25 1 week

3)Cl permeate conc. = 20 mg/l

Scenario 23-24 Cl daily 500/1000 m3/d 0.25 1 week Cl noise = St. Dev. 10%, 20%, 40%

1) Nr. of observation bores - 1: 124m; 2: 98m and 195m; 3: 67.5m and 145m and 267.5m; 5: 67.5m and 98m and 412

145m and 195m and 267.5m radial distance in BSF 413

2) Sampling frequency: 2=every second day; 7 = weekly; 14 = 2-weekly; 21= three-weekly and 30=monthly 414

3) Timing of sampling: daily sampling during (1) first month of trial; (2) second month and (3) third month of trial 415

4) Chloride background conc. = 11 mg/l, i.e. signal to noise ratio = 11.5/11 (Scenario 17), 15/11 (Scenario 18), 416

20/11 (Scenario 19) and 28/11 (base case). 417

418

4. RESULTS 419

4.1 Base case solute migration 420

The solution migration behaviour of the base case flow and transport model is illustrated in the 421

breakthrough curves in Figure 3. Chloride and methane display conservative breakthrough 422

behaviour. Bromide concentrations peak in the base case during the first 7 days, i.e., the phase 423

during which tracer amendment at the start of the trial still persisted. In the following 424

concentrations dilute during aquifer passage until at the end of the trial the Br peak has 425

dissipated. Compared to the migration rate of the concentration fronts of bromide, chloride and 426

methane the temperature signal is retarded. 427

428

429

Figure 3 Simulated solute concentrations and temperatures with time within the Braided Stream Formation aquifer 430

(model layer 8). 431

432

4.2 Improved parameter knowledge to reduce predictive uncertainty 433

The first analysis performed on the base case was undertaken to provide insights into the relative 434

significance of direct hydrogeological parameter knowledge in terms of constraining the 435

uncertainty of the chosen solute spreading predictions. The goal of this analysis was to identify 436

those parameters for which increased knowledge would provide the largest reduction in 437

uncertainty of dilution and travel time predictions. The worth of increased parameter knowledge 438

was assessed in two stages. Firstly the uncertainty of a prediction was calculated, assuming all 439

model parameters were known to a level of certainty commensurate with that described in Table 440

2. Then, sequentially, parameters were assumed to be perfectly known at each pilot point 441

location (i.e. “freezing” a parameter to a value and assuming no uncertainty). The extent to 442

which a direct parameter measurement would be able to reduce the uncertainty of a prediction 443

was then quantified from equation 1, and then normalised by the sum of all parameter 444

contributions to uncertainty, to provide a range from 0 to 1. This relative worth of different 445

parameter types is summarised in Figure 4 for a travel time prediction in close proximity to the 446

injection well (24m), then at 78m, as well as at a distant prediction location (175m). 447

448

For both the dilution and travel time predictions, porosity was identified as the parameter of 449

greatest significance for making reliable predictions. This is a credible result and reflects the fact 450

that within the context of injection schemes, where background flow is often negligible, 451

groundwater flow velocities are injection rate driven, regardless of the hydraulic conductivity. 452

Aquifer porosities govern the conservative transport velocities and control how far a solute will 453

migrate. Thus, conductivity measurements obtained, e.g., through discharge tests, would be of 454

limited usefulness to reduce predictive uncertainties, while measurements of porosity would be 455

most informative. However, for injection schemes in which the background flow represents a 456

more important component of the overall groundwater flow hydraulic conductivities would 457

acquire greater significance. 458

459

Dilution predictions are similarly sensitive to porosity and to the mass exchange rate at locations 460

in close proximity to the injection well, where injection has resulted in concentration contrasts 461

between matrix and fracture networks. With distance the relative worth of hydraulic conductivity 462

data increases as the solute spreads out beyond the BSF into over- and underlying aquifer 463

formations and as the background flow field gains in importance but the worth of conductivity 464

data remains well below that of porosity. Other parameters make minimal contributions to 465

predictive uncertainty reduction. 466

467

468

469

470

471

Figure 4: Summary of relative reduction in dilution prediction uncertainty at 24m, 78m and 175 m radial distance 472

from the injection well through enhanced knowledge of various hydraulic parameters. 473

474

4.3 Regions of greatest data worth and ranking of different data types 475

The purpose of the second analysis that was undertaken for the base case was to identify optimal 476

tracer test measurement locations and assess the relative usefulness of different data types, when 477

making predictions of the spreading of CSG permeate. Starting from a baseline, which assumes 478

no observation data (i.e., no pre-existing monitoring network) individual observation data types 479

were sequentially added at the 78 potential observation locations and the subsequent reduction in 480

predictive uncertainty calculated. Thus, the worth of each individual potential observation 481

location and data type was established, independently of any other potential observations. 482

483

Data worth was thereby calculated as the normalised decrease in predictive uncertainty variance 484

according to: 485

������ = !"#$%#&'#( )*++!,-,&.( (7) 486

487

488

where ������ is the normalised decrease of prediction uncertainty variance for a given 489

observation; �/01�0230� is the decrease in prediction uncertainty variance incurred through 490

addition of a given observation to the calibration data set; and ����24� is the total predictive 491

uncertainty variance for a given data type. 492

493

494

495

496

497 Figure 5 The spatial distribution of data worth (equation 8) within the 2nd week and 8th week of injection, for all 498 tracer observations with respect to the solute dilution prediction at 106m from the injection well. 499 500 501

4.3.1 Regions of greatest data worth 502

In Figure 5, the contours of predictive uncertainty decrease achieved through addition of 503

individual observation types and locations are depicted for monitoring data at 2 and 8 weeks 504

after injection. These contours indicate that the general area where added observations will 505

provide maximum information are coincident with the high hydraulic conductivity region of the 506

model (Braided Stream Formation) where most of the injectant is moving, and where there is the 507

greatest concentration change (i.e., the greatest signal to noise ratio), thus most informative are 508

observations ahead of the plume, before full breakthrough of the injectant (Figure 3 and 5). 509

Comparing data worth at three selected times (Figure 5) illustrates the transient nature of “best 510

monitoring location”, which is related to the changing signal to noise ratio between the plume 511

and surrounding groundwater that occurs as the plume migrates from the tracer injection point. 512

Therefore observations close to the injection point (<50m) are most informative at the start of the 513

trial, but lose information content soon thereafter as groundwater rapidly attains the 514

concentrations of the injectant. With time the region of greatest data worth moves outwards into 515

the aquifer. However, because groundwater velocities decrease rapidly away from the injection 516

point due to the radial expansion in aquifer volume, the outward movement of the plume slows 517

successively. This region of data worth can be related to the solute front position (here defined as 518

the location in the aquifer where C/Co = 0.5) which moves proportional to √6789 in a radial 519

velocity field. For example the simulated methane data shows solute breakthrough (C/Co=0.5) 520

to occur at a distance of about 200 metres 60 days into the injection trial (Figure 3), but if instead 521

an observation well is located at three times that distance (600m), the time to breakthrough is 522

extended to about 1.5 years. At the same time dilution reduces concentration contrasts and 523

diminishes predictive information contained in these more distant observations. This 524

combination creates the down gradient limits to the regions of data worth depicted in Figure 5. If 525

data worth is integrated at each location for all tracer types and over the entire duration of the 526

injection trial, i.e. over 100 days, the optimal observation locations lie within radial distances 527

between 50m and 250m from the injection bore. 528

4.3.2 Tracer data worth 529

Under base case conditions, bromide is the superior tracer at earlier times: bromide provides the 530

lowest predictive uncertainty standard deviation (up to +/- 5 days during the first month of the 531

trial, Figure 7) compared to other tracers and it does so over a larger area compared to other 532

tracers (Figure 5).. However as Br amendment ceases, the Br concentration diminishes as the 533

solute plume spreads throughout the aquifer, thus decreasing the information content of Br 534

measurements as the injection trial progresses (Figure 5 and 7). At later times after injection, 535

chloride emerges as the tracer of greatest data worth, ahead of bromide, methane and 536

temperature. This same trend applies to predictions being made at increasing distances from the 537

injection well: the further the distance for which predictions are made, the more favourable 538

chloride becomes compared to Br (Figure 7). 539

540

For predictive locations close to the injection point, temperature data are of similar worth as 541

solute tracers (Figure 5 and 7). The usefulness of temperature data however decreases the further 542

away predictions are required in relation to the injection point and predictive uncertainty 543

standard deviations increase rapidly (Figure 7). Temperatures diminished usefulness with 544

increasing distance from the injection well is due to the velocity of the thermal front being less 545

than the pore water velocity as heat is exchanged between the injectant and the aquifer (e.g. 546

Brookfield et al., 2009), i.e., the temperature signal is strongly retarded compared to the solute 547

tracer concentration fronts and the contrast in temperature between CSG permeate and ambient 548

water becomes increasingly attenuated with travel distance. 549

550

The monitoring of head data provides no significant improvement in the reliability of solute 551

spreading predictions: groundwater heads provide minimal information content for predicting 552

solute spreading, as head observations provide no information on porosities, the main parameter 553

controlling solute spreading (results not shown). This confirms the previous finding on the 554

superiority of porosity data in predicting solute spreading and is a distinguishing feature under 555

injection-driven flow conditions. In contrast, under natural flow conditions, or for injection tests 556

which do not override the background flow, head data can be expected to be of more 557

significance. 558

559

4.4 Alternative monitoring designs 560

561

A selection of alternative feasible monitoring network configurations were evaluated and 562

compared to the base case (Table 3) in terms of their ability to reduce the uncertainty of travel 563

time and dilution predictions. The alternatives included: (i) reduced numbers of available 564

observation bores (scenarios 1-4, Table 3); (ii) reduced sampling frequencies (scenario 5-9, 565

Table 3); (iii) modified injectate to ambient concentration ratios and amendment durations 566

(scenario 10-15; 18-24, Table 3) and (iv) altered injection rates (scenario 16-17, Table 3). 567

568

4.4.1 Number of observation locations and measurement frequency 569

The accuracy of solute spreading predictions depends on the number of available observation 570

bores and the frequency at which these bores are sampled. In order to compare various 571

monitoring strategies and quantify their ability to improve the predictions of the spreading of the 572

injected CSG produced water, it was first assumed that observation data was available for all 573

tracers, at a daily sampling frequency, for all potential observation locations (i.e., 78 bores) (base 574

case scenario, Table 3). This results in a very small post calibration uncertainty standard 575

variation, which was compared with the uncertainties calculated for progressively coarser 576

sampling frequencies, for each individual tracer (scenarios 5 to 9, Table 3). 577

578

The impact of measurement frequency is shown in Figure 6a and depicts the contours of the 579

standard deviation of travel time error for all tracers and combinations of measurement 580

frequency, versus the distance at which a prediction of travel time is sought. As expected, with a 581

coarsening sampling frequency, the uncertainty increases. If all monitoring observations are 582

available, e.g., at 78 observation locations, the calculated standard deviation of predictions of 583

travel time is less than 1 day within a radial distance of about 100 meters, assuming all tracers 584

are sampled at least every three days. When sampling frequency is reduced to once per week, 585

such accuracy can only be achieved up to a radial distance of about 40 metres, reduced further to 586

about 20 meters if a monthly sampling regime was adopted. 587

588

The analysis of the influence of the total number of available bores on predictive accuracies 589

(Figure 6b, scenarios 1-4) indicated that data from a single optimally located observation bore, 590

sampled daily for all tracers within the region of greatest data worth, achieves a reduction of 591

uncertainty of almost two orders of magnitude. This can be compared with two optimally located 592

observation wells, sampled daily for all tracers, which achieves a further halving of predictive 593

uncertainty compared to the case of a single bore. Thereafter, additional observation wells 594

provide diminishing returns in terms of the rate of decrease in predictive error. The addition of a 595

third, fourth and fifth bore within the area of greatest data worth, i.e., between 50m to 250m 596

radial distance, leads to only minor reductions in uncertainty. This analysis indicates that two 597

appropriately located observation bores provide the greatest reduction in uncertainty; with any 598

further addition of monitoring bores incurring disproportionally low reductions in uncertainty in 599

this relatively homogeneous radial flow case. 600

601

602

603

604 Figure 6 Predictive uncertainty standard deviation of peak solute breakthrough [days] as a function of a) frequency 605 of sampling events and radial distance from the injection well (based on 78 observation bores) and b) number of 606 available observation bores for a prediction at 106m. Location of observation bores and integrated data worth over 607 the duration of the injection trial (i.e. 100 days) is also shown. Sampling frequencies: (1) = daily, (2)= every second 608 day … (30)= monthly sampling. 609

610

611

4.4.2 Ratio of injection concentration to ambient concentration 612

A number of numerical experiments were undertaken where the signal (injection concentration) 613

to noise (ambient conditions) ratio of tracers was increased via increasing amendment 614

concentrations and duration and/or reducing the measurement error, for instance through more 615

accurate sampling techniques (noise term in eq. 2) (scenario 10-15; 18-24, Table 3). To allow 616

comparisons between different tracer types, the difference between injection and ambient tracer 617

concentration was normalised by the standard error of tracer measurement (assuming standard 618

contrast to noise normalisation formulae). 619

620

The impact of the different amplitudes of the four tracer signals on predictive uncertainty is 621

plotted in Figure 7 based on scenarios 10 to 15. Prediction uncertainty is described in terms of 622

the standard deviation of error of the solute breakthrough time (in units of days) as a function of 623

increasing distance to the injection well and time of sampling. The figure clearly demonstrates 624

that bromide, as the amended tracer, is of greatest use for shorter-term predictions in closer 625

proximity to the injection well. The bromide amendment of 0.25mg/l (base case) yields a signal-626

to-noise ratio that is twice that of chloride during amendment, which again is twice that of 627

methane and temperature. However, after amendment ceases and as time progresses, the 628

amplitude of the Br signal diminishes and chloride becomes the more suitable tracer to constrain 629

physical transport processes. In contrast to bromide, temperature data gains in utility as time 630

progresses as heat successively propagates into the aquifer. However, due to its strong 631

attenuation compared to solute tracers, and despite its very low measurement error, the ability of 632

temperature data to inform CSG permeate spreading remains well below that of the solute 633

tracers. 634

635

The superiority of bromide as a tracer in this context can be further enhanced by increasing the 636

amendment concentration and/or amendment duration (results not shown). The minimum 637

amendment concentration required for Br to remain superior to chloride and other tracers at early 638

times in the injection trial was found to be 0.15mg/l (as depicted in Figure 7). Methane and 639

chloride maintain a constant signal to noise ratio at the injection site with the normalised ratio for 640

methane thereby being half that of chloride. This, together with a higher measurement error 641

makes methane the least reliable of the three solute tracers to predict solute spreading in this case 642

study. 643

644

645 Figure 7: Contoured predictive uncertainty standard deviation of peak solute breakthrough [days] as a function of 646 radial distance from the injection well and time of sampling. Contours are based on a potential observation network 647 consisting of 5 bores located within the area of greatest data worth (50 – 250m in BSF). (Time of sampling: daily 648 sampling during first month (1), second month (2) and during last month (3) of trial). 649 650

651

4.4.3 Injection rate 652

Under injection-driven groundwater flow schemes, the injection rate affects the tracer signal to 653

noise ratio, and hence the accuracy of dilution predictions. This relationship is depicted in Figure 654

8, where the injection rate is progressively increased. Within distances up to about 50 m from the 655

injection well, predictive accuracy is high, irrespective of the selected injection rate. However, 656

with increasing distance, larger injection rates reduce uncertainty. The result can be explained by 657

the increased number of observation bores with significant concentration increases that occur 658

with larger injection rates and the greater injected mass under higher injection rates, which in 659

turn, reduces the predictive uncertainty variance of the model (Figure 8). 660

661

Increasing injection rates also impact the relative worth of temperature data. At low injection 662

rates, there is a reduction in induced flow velocities, which increases the time available for 663

thermal energy uptake by the aquifer as the plume spreads into the BSF and over- and underlying 664

aquifer layers, resulting in a lowered signal to noise ratio and diminished usefulness of 665

temperature data relative to solute tracers. 666

667

Figure 8: Contoured predictive uncertainty standard deviation of peak solute breakthrough [days] as a function of 668 radial distance from the injection well and injection rate. Contours are based on the potential observation network of 669 78 bores under a daily sampling regime monitoring all tracers. 670 671 672

5. Cost analysis 673

Given the vast differences in costs of acquisition of different tracer and marker species, there is a 674

need to establish which monitoring strategy potentially provides the greatest return for 675

investment for implementation at the injection site. To incorporate cost into our analysis we 676

employ a methodology where cost effectiveness is defined in terms of both the reduction in the 677

uncertainty of a prediction achieved by various analyses, and their cost. This allows for the 678

evaluation of an optimal monitoring strategy subject to both cost and predictive accuracy. Costs 679

of sampling was based on representative laboratory charges, which are $44AUD /sample for 680

bromide; $82.5AUD/sample for methane and $10.5AUD/sample for chloride, while temperature 681

data is gathered using a temperature sensor with an integrated datalogger. One-off costs for these 682

dataloggers were distributed over the duration of the injection trial leading to approximate costs 683

for temperature data of approximately $1AUD$/sample. Sampling frequencies of bores were 684

altered repeatedly (range: daily to monthly monitoring), and independently for all tracers. The 685

resulting costs of each sampling strategy, and its ability to predict spreading behaviour was then 686

collated for each combination. 687

688

Pareto front based on all tracers 689

Figure 9a shows the Pareto fronts defined between two objective functions: (i) monitoring costs 690

and (ii) predictive accuracy for three solute breakthrough predictions (viz. travel time at 691

distances of 78m, 125m and 155m). The Pareto front characterises the front for which it is 692

impossible to further lower costs and improve accuracy simultaneously. One end of the Pareto 693

front establishes the most accurate, but also most expensive sampling campaign (daily sampling 694

of all tracers), while at the other end of the Pareto front the accuracy is minimised (monthly 695

sampling of all tracers), and the cost of the sampling campaign is low. Between these two 696

endpoints, neither costs nor predictive uncertainty can be lowered further, without raising the 697

other. Because the uncertainty is a function of the distance at which prediction of solute 698

spreading is sought, this analysis provides the Pareto front points for predictions of travel time at 699

three distances; at 78m, 125m and 155m from the injection well and on the basis of an 700

observation network consisting of 5 bores located within the area of greatest data worth (50 – 701

250m in BSF). (Figure 9a). 702

703

Tracer specific Pareto fronts 704

Based on this Pareto analysis, the outcomes of different monitoring designs can firstly be 705

compared separately and their merits in regards to predictive accuracy versus costs evaluated. 706

Figure 9b depicts the results for a single travel time prediction at a distance of 125m from the 707

injection well. The strongly diverging returns for investment of the different tracers are clearly 708

visible (Figure 9b). If analysing chloride only, the monitoring costs would be relatively low 709

overall with moderate predictive accuracy (i.e., standard deviation (sd) of 6 days or +/- 25% of 710

predicted peak solute arrival time under a daily monitoring regime). If instead only methane was 711

being analysed daily the predictive accuracy decreases, while monitoring costs would rise 8-fold. 712

This highlights the unfavourable return for investment of the methane tracer in this case study, 713

due to methanes' very high cost of acquisition but muted worth compared to other available 714

tracers. Temperature data measurements, when sampled in isolation, were also not adequate to 715

significantly constrain solute spreading predictions. While monitoring costs are low, the 716

reduction in uncertainty of predictions is the least of all tracers, confirming previous findings 717

(section 4). Monitoring Br data yields the most accurate predictions at the site (uncertainty sd= 718

2.4 days under daily monitoring). However, this decrease in uncertainty is penalised by a 4-fold 719

increase in monitoring costs compared to the “chloride-only” sample regime (Figure 9b). 720

721

Pareto analysis of combination of all tracers and all measurement frequencies 722

Closer examination of the Pareto analysis outputs revealed the influence of variable sampling 723

frequencies on predictive uncertainty and costs as the Pareto front is traversed (Figure 10a,b). 724

The analysis showed that it is possible to lower costs for very little increase in uncertainty, by 725

reducing the sampling frequency of methane, the most expensive tracer considered in this study 726

(Figure 10a). As lower costs are sought, it is most effective to reduce the frequency of methane 727

sampling, followed by bromide. In fact, removing methane altogether, while other tracers 728

continue to be monitored on a daily basis, increases predictive uncertainty only very marginally, 729

while costs decrease considerably. For instance, the predictive uncertainty standard deviation of 730

solute breakthrough at 125m increases only from 1.8 days (daily sampling of all tracers) to 1.9 731

days, if methane is omitted from the monitoring regime, however, overall monitoring costs 732

reduce by more than half. 733

734

In addition, Figure 10a and b indicate that when using a combination of tracers with variable 735

sampling frequencies it is possible to lower the predictive uncertainty for a very modest change 736

in costs. This is achieved through a combination of a high sampling frequency of temperature 737

data, the least costly tracer in this study, in conjunction with a solute tracer of greater information 738

content, such as chloride and or bromide. 739

740

A distinct point of diminishing returns can be established along the Pareto front, where lowering 741

the uncertainty incurs disproportional increases in costs. For a solute spreading prediction at 742

125m radial distance, predictive accuracies can be lowered over 15-fold from sd = 109 days 743

(monthly sampling of all tracers) to sd=7 days for an approximate two-fold increase in costs 744

(Figure 9b). However, a further halving of the uncertainty to 1.8 days (daily sampling of all 745

tracers) incurs a 10-fold rise in monitoring costs. This analysis suggest, that a sampling campaign 746

selected in proximity to the point of diminishing returns, such as daily sampling of temperature 747

data, weekly sampling of chloride and bromide data, while disregarding methane data entirely 748

would provide a monitoring strategy with a favourable return for investment at the injection site. 749

Such a sampling regime would result in costs of 56 AUS$/sample event or in total costs of 750

laboratory analysis charges of about 4500 AUS$ for a three month sampling campaign. 751

752 753 Figure 9 (a) Pareto front defining trade‐off between monitoring costs and accuracy for three peak breakthrough 754 predictions; (b): Pareto front defining trade‐off between monitoring costs and accuracy of peak breakthrough 755 prediction at 125m distance from injection well if single tracers are monitored. Each point on the Pareto front is 756 characterised by a unique combination of independent sampling frequencies (range: daily to monthly sampling 757 events) for Cl, Br, CH4 and temperature. Sampling frequencies: (1) = daily, (2)= every second day … (30)= monthly 758 sampling. 759 760 761 762

Figure 10 Changes in sampling frequency of Br, Cl, CH4 and temp. versus a) costs and b) predictive uncertainty as 763 the Pareto front for the peak prediction at 125m is traversed (Figure 9b) (only sub-set of points along the Pareto 764 front are shown for clarity). Frequencies: (1) = daily, (2)= every second day … (30)= monthly sampling. 765

766

6. Summary and Conclusions 767

This paper develops an approach for a model based tracer test optimisation methodology and 768

illustrates its practical application to an example where the factors that determine cost effective 769

test design and monitoring data acquisition were explored. The methodology employs a linear 770

predictive analysis theory from Moore and Doherty (2005) and Christensen and Doherty (2008), 771

with an uncertainty targeted Pareto methodology (Moore et al. 2010). 772

The constraints used by the optimisation method were the reduction in the uncertainty of 773

predictions of solute spreading as defined in terms of travel time and dilution. Based on the 774

numerical representation, we analysed different solute tracers, temperature and hydraulic heads 775

in terms of their utility to inform solute transport behaviour versus the cost of their acquisition. 776

The establishment of regions of greatest data worth and data worth ranking was followed by an 777

uncertainty targeted Pareto analysis, which was used to identify a monitoring regime, which 778

provided the best return on investment as defined in terms of cost and reliability. The Pareto 779

analysis allowed the interdependencies of cost, predictive reliability, and various monitoring 780

campaigns to be compared directly, thereby informing decisions of which monitoring regime 781

provides the greatest return for investment. 782

783

For the investigated injection scheme, porosity was identified as the parameter of greatest 784

significance for making reliable predictions above all other hydraulic parameters. This finding is 785

representative for injection schemes, which override ambient groundwater flow and were flow 786

velocities are injection rate driven, regardless of the hydraulic conductivity. Consequently, 787

conductivity data was found to make minimal contributions to predictive uncertainty reduction. 788

For the same reasons, monitoring of head data was found to provide no significant improvement 789

in the reliability of solute spreading predictions as hydraulic heads are not informing on 790

porosities, the main parameter controlling solute spreading under injection-driven radial flow 791

conditions. Under natural flow conditions, or for injection tests which do not override the 792

background flow, conductivity measurements and head data can be expected to be of more 793

significance. 794

Bromide was assessed as superior to head data and all other tracers during early sampling times 795

in the injection trial. However, once bromide amendment ceased, chloride became a more 796

suitable tracer to constrain simulations of physical transport processes, followed by methane. 797

Temperature data was assessed as the least informative of the solute tracers. With heat transport 798

being retarded due to the heat exchange between the injectant and the aquifer, the ability of 799

temperature records to describe solute spreading was diminished and decreased with growing 800

distance from the injection well. However, taking costs of data acquisition into account, it could 801

be shown that temperature data when used in conjunction with other tracers was a valuable and 802

cost-effective marker species due to temperatures low cost to worth ratio. In contrast, the high 803

costs of acquisition of methane data compared to its muted worth, highlighted methanes 804

unfavourable return on investment. The best return on investment at the injection site was shown 805

to be a combination of daily (high-frequency) temperature measurements, complimented by 806

weekly Br and Cl sampling, while omitting methane data entirely; these measurements being 807

obtained at two observation locations within the area of greatest data worth, i.e., at radial 808

distances between 50m and 250m from the injection bore. Any further addition of monitoring 809

bores achieved only small additional reductions in uncertainty in this relatively homogeneous 810

radial flow field. 811

812

This demonstration of tracer test design and monitoring disposition based on the extent to which 813

a data type reduces the predictive error variance provides modelers and practitioners with a 814

powerful yet efficient and cost effective decision making tool for field tracer test design. 815

Uncertainty of solute transport predictions can be estimated for a range of ‘what–if’ scenarios, 816

allowing efficient comparisons between different monitoring regimes: a given observation 817

location may be considered in the light of other observations; a specific tracer type can be 818

evaluated based on its utility in the light of other available tracers and marker species; sampling 819

frequencies can be selected based on the number of observation bores to be drilled and the 820

distance at which solute predictions are thought. Combining this with an analysis of data 821

acquisition costs allows rigorous comparisons to be made between different monitoring regimes 822

and the return on investment these provide. Efficiency is gained via a model linearity assumption 823

in the problem formulation, which allows the calculation to be made sufficiently rapidly, so that 824

it can be repeated at many alternative proposed monitoring sites, times and under different tracer 825

calibration constraints. The software for such analyses is in the public domain (Doherty, 2010a 826

and b). These are particularly important benefits in the context of tracer injection schemes in 827

deep aquifers, where monitoring reflects typically a significant financial burden. 828

829

Through the application of common use groundwater flow and transport models in conjunction 830

with publicly available tools for predictive uncertainty analysis the proposed tracer test 831

optimisation methodology is generally applicable and easily transferrable from the present study 832

to many applications beyond the case study of injection of treated CSG co-produced water. 833

Many practical water resources problems would benefit equally from a-priori knowledge of the 834

relative worth of different hydrogeological data types and monitoring locations to infer solute 835

transport behavior, especially in settings where target aquifers are deep and drilling and/or 836

monitoring costs high, as e.g. in the case of CO2 underground storage or disposal of produced 837

water from oil and shale gas wells. Potential other applications for such “data worth” analysis 838

include tracer injection experiments focusing on point source contamination, push-pull tests, in-839

situ iron removal operations aquifer storage and recovery (ASR) systems, aquifer thermal energy 840

storage (ATES) systems and in-situ bioremediation operations. 841

842

Acknowledgement 843

We gratefully acknowledge the contributions to this manuscript by Ryan Morris, Origin Energy 844

through provision of data, site information and hydrogeological expertise. We also thank 845

Sreekanth Janardhanan and Adam Siade from CSIRO for their reviews of earlier versions of the 846

manuscript. 847

848

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Highlights 992

-we investigate a field-scale injection trial of coal seam gas co-produced water 993

-we use numerical simulations to establish impact of injection 994

- we analyse the worth of field data to maximise reliability of impact assessment 995

-we use “data worth analysis” to optimise monitoring for the site 996

-we establish monitoring strategy which provides greatest return on investment 997

998

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