20

Integrating structural geological data into the inverse modellingframework of iTOUGH2

J. Florian Wellmann a,n, Stefan Finsterle b, Adrian Croucher c

a CSIRO Earth Science and Resource Engineering, 26 Dick Perry Ave., Kensington, 6151 WA, Australiab Earth Sciences Division, Lawrence Berkeley National Laboratory, University of California, Berkeley, USAc Department of Engineering Science, University of Auckland, Private Bag 92019, Auckland, New Zealand

a r t i c l e i n f o

Article history:Received 11 March 2013Received in revised form13 September 2013Accepted 22 October 2013Available online 31 October 2013

Keywords:UncertaintyImplicit geological modellingMultiphase ow simulationSensitivity analysisParameter estimationMonte Carlo

a b s t r a c t

The validity of subsurface ow simulations strongly depends on the accuracy of relevant rock property valuesand their distribution in space. In realistic simulations, this spatial distribution is based on two geologicalconsiderations: (1) the subsurface structural setting, and (2) smaller-scale heterogeneity within a hydrostrati-graphic unit. Both aspects are subject to uncertainty, whereas techniques to address heterogeneity are wellestablished, no general method exists to evaluate the inuence of structural uncertainties. We present amethod to include structural geological data (e.g. observations of geological contacts and faults) directly into aninversion framework, with the aim of enabling the inversion routine to adapt a full 3-D geological model with aset of geological parameters. In order to achieve this aim, we use a set of Python modules to combine severalpre-existing codes into one workow, to facilitate the consideration of a structural model in the typical modelevaluation steps of sensitivity analysis, parameter estimation, and uncertainty propagation analysis. In asynthetic study, we then test the application of these three steps to analyse CO2 injection into an anticlinalstructure with the potential of leakage through a fault zone. We consider several parts of the structural settingas uncertain, most importantly the position of the fault zone. We then evaluate (1) how sensitive CO2 arrivingin several observation wells would be with respect to the geological parameters, (2) if it would be possible todetermine the leak location from observations in shallow wells, and (3) how parametric uncertainty affects theexpected CO2 leakage amount. In all these cases, our main focus is to consider the inuence of the primarygeological data on model outputs. We demonstrate that the integration of structural data into the iTOUGH2framework enables the inversion routines to adapt the geological model, i.e. to re-generate the entire structuralmodel based on changes in several sensitive geological parameters. Our workow is a step towards a combinedanalysis of uncertainties not only in local heterogeneities but in the structural setting as well, for a morecomplete integration of geological knowledge into conceptual and numerical models.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Structural geological models are commonly used to incorporateinformation about major geological units and their rock properties intoow simulations. It is well known that these geological models containuncertainties (e.g. Mann, 1993; Brdossy and Fodor, 2001; Thore et al.,2002; Turner, 2006; Suzuki et al., 2008; Caumon, 2010; Wellmannet al., 2010; Caers, 2011; Cherpeau et al., 2012; Lindsay et al., 2012) andit is reasonable to assume that simulated ow elds are sensitive tochanges in the structural geological model.

We propose a framework to test sensitivities of simulated owelds with respect to structural parameters derived from geologi-cal data, and to use observed ow eld responses to invert forthese structural parameters. We establish an automated link

between structural geological modelling (using an implicit geolo-gical modelling method) and multi-phase ow simulations (usingthe general-purpose ow simulator TOUGH2). TOUGH2 is used fora wide range of applications, from hydrogeological studies andcontaminant transport, to carbon sequestration, geothermal reser-voir engineering and nuclear waste disposal (Pruess et al., 2011).The link to TOUGH2 is computationally enabled via PyTOUGH, aset of Python modules offering pre- and postprocessing routinesfor TOUGH2 simulations (Wellmann et al., 2011). Our forwardworkow from structural data to ow simulations is then inte-grated into an inverse modelling framework, iTOUGH2 (Finsterle,1999), to use these data as parameters in inversions as well assensitivity and uncertainty analyses.

The evaluation of sensitivities of simulation results to inputparameters is often performed using a manual procedure, forexample by testing the inuence of minimal and maximal parametervalues. Although this procedure can provide insights into the modelbehaviour, the overall informational value of the analysis is restricted(e.g. Carrera et al., 2005). A systematic analysis of sensitivities based

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Computers & Geosciences 65 (2014) 95109

on mathematical principles delivers (in addition to quantitativesensitivity measures) a detailed error evaluation, including informa-tion on parameter covariances and correlations (Refsgaard, 1997; Sunand Sun, 2006). For ow simulations with TOUGH2, this functionalityis implemented in iTOUGH2. In addition to sensitivity analysis,iTOUGH2 provides methods for parameter estimation (or inversion)from observed data and for uncertainty propagation analyses (e.g.Finsterle, 1999, 2004). With our work, we enable the application ofthese iTOUGH2 functionalities to the analysis of geological data andstructural parameters used to develop and automatically update theunderlying geological model.

With structural data, we consider direct measurements orinferred estimates of geological surface contact points and orien-tations, for example a point dening the position of a stratigraphicinterface at depth identied from a well log, or the strike and dipof a fault observed in an outcrop. Integrating structural informa-tion into an inverse framework requires a method that automati-cally constructs a 3-D structural geological model from a relativelysmall set of parameters representing geological data. In addition, ithas to be possible to export the continuous geological modeldirectly into a discrete format, suitable for subsequent owsimulations, without any manual interaction.

These functionalities can be achieved with implicit volumetricmodelling methods (Caumon, 2010). Instead of constructing sur-faces between geological units, these methods interpolate a 3-Dscalar potential eld to structural geological data, directly honour-ing Geological constraints like stratigraphic relationships or faultinuence (Lajaunie et al., 1997; Calcagno et al., 2008; Caumon, 2010).GeoLogical contacts are dened as equipotential surfaces in thescalar eld. We apply a method that was specically developed tocreate reliable models for hypothesis testing, even for sparsestructural geological input data sets (Putz et al., 2006; Calcagnoet al., 2008). An additional important feature of these implicitvolumetric methods is that they enable a query of geological unitsanywhere in space, as they provide completely sealed rockvolumes (Caumon, 2010). We will use this feature to facilitateautomatic mesh generation for the ow simulation.

As we directly consider structural parameters, such as geologi-cal surface contact points and fault dip measurements, ourapproach is fundamentally different from methods that considerrock property variations on a smaller scale. It is common practicein geological modelling to rst generate a structural geologicalmodel with a separation of domains with similar geological orpetrophysical properties (usually referred to as zonation approach,see Carrera et al., 2005; Oliver and Chen, 2011), and then topopulate these zones with rock properties, often with statisticalmethods to reect heterogeneities within these zones. The grid-based simulation of multiple realisations for local heterogeneitiesis computationally straight-forward, widely performed, and imple-mented in multiple software packages, for example the geostatis-tical software package GSLIB (Caers, 2011; Deutsch and Journel,1998). Excellent overviews of the available methods are given inChils and Delner (1999), Deutsch (2002) and (Caers, 2011).

By contrast, the generation of multiple structural geologicalmodels that are consistent with initial structural data and geologicalconstraints is not a trivial task, and no general method is available todate (see chapter 8 of Caers, 2011). The main difculty lies in thecomplete automation of the entire modelling procedure from initialstructural data for reasonably complex and full 3-D geological modelsto discretise numerical models used for process simulation. Currentlyavailable methods focus on modifying a stratigraphic surface after ithas been modelled (Lecour et al., 2001; Thore et al., 2002; Samsonet al., 1996; Caers, 2011). An interesting approach has been proposedby Suzuki et al. (2008) where several different initial structuralmodels are rst constructed in a manual step, and the simulatedstratigraphic surfaces are subsequently adapted using a dynamic data

integration procedure. An important aspect of the work by Suzukiet al. (2008) is that they combine the evaluation of differentstructural starting models with an adaptation of stratigraphic hor-izons in the simulated models. However, the authors state that theydo not attempt to parameterise the entire complex reservoir geo-metry as it would be, in their words, extremely difcult. In a recentpublication, Cherpeau et al. (2012) address this issue and describe atechnique, based on an implicit structural geological modellingmethod, for inverting dynamic ow data to determine parametersdescribing the geometry of a fault network. Our work is conceptuallysimilar to this novel approach, but we attempt a complete para-meterisation of the model using initial structural data (surface andfault contact points and orientation measurements), whereasCherpeau et al. (2012) concentrate on the parameterisation of faultnetworks. With our work, we aim to add the aspect of directlyconsidering structural data of complex 3-D geological models asparameters in a general multi-physics joint inversion framework.

We focus in the following on the computational implementationof our method for ow simulations with TOUGH2. We will rstdescribe the underlying structural geological modelling and owsimulation methods and our approach to combine both techniques,and nally their integration into the iTOUGH2 framework. We willthen apply the workow to a CO2 injection scenario to evaluate thepotential risk of CO2 leakage through a fault. We systematicallyexplore the use of structural geological parameters in three typicalmodel evaluation procedures: (1) sensitivity study, (2) parameterestimation, and (3) analysis of uncertainty propagation.

2. Materials and methods

The aim of this work is to enable the control of structuralparameters, and therefore the geometry of the geological model,from an inverse ow simulation framework, iTOUGH2. To achievethis aim, two aspects have to be addressed:

1. A workow is required that completely automates all stepsfrom geological model construction to input le generation forthe ow simulator.

2. This workow then has to be integrated into the inverseframework of iTOUGH2.

We attempt to resolve both aspects with a combination of existingsoftware and simulation codes using a set of Python and Cprograms. An overview of our approach is presented in Fig. 1, and wedescribe the relevant aspects below. In addition, we briey outlinerelevant features of the functionality of iTOUGH2 for sensitivityanalysis, parameter estimation, and uncertainty propagation analysis.

2.1. Combining geological modelling and multi-phase owsimulations

The integration of structural geological data into ow simula-tions is commonly performed in several steps (e.g. Carrera et al.,2005; Bundschuh and Arriaga, 2010). Starting from the availablegeological data (for example derived from borehole information,outcrop observations, or interpreted seismic data), a continuousgeological model is constructed. This model is then discretised forthe subsequent ow simulation, for example in a cartesian ortetrahedral grid. A typical method is to create a mesh that issuitable for the applied simulation procedure, and then to mapgeological units to each cell in the model (also referred to as modelzonation). In the next step, grid cells are populated with propertiesaccording to the geological units they represent; these propertiesmay be a stochastic realisation drawn from parameter distribu-tions. With the addition of boundary conditions, sources and sinks,

J.F. Wellmann et al. / Computers & Geosciences 65 (2014) 9510996

and other simulation settings, this procedure provides the basis forthe ow simulation.

The technical difculty in automating the entire procedure liesin the rst part: the generation of a discrete geological modeldirectly from geological data or structural parameters. We addressthis by combining an implicit structural geological modellingmethod with existing pre- and postprocessing tools through aset of Python and C programs. The pre-existing software thatwe integrate is partly commercial, but all our novel developmentsare open-source and freely available (see Appendix B).

2.1.1. From discrete structural data to a geological modelAwide range of methods exists to create structural representations

of the subsurface setting, commonly called a geological frameworkmodel, from geological data (e.g. Mallet, 1992; Galera et al., 2003;Calcagno et al., 2008; Caumon et al., 2009). The essential part ofcreating a meaningful geological model is to combine all availablestructural data (such as surface contacts between stratigraphic units,points dening the location of faults, and orientation measurements ofsurfaces) with reasonable geological rules (topological, orientation,and age constraints) to derive a consistent interpretation of the spatialdistribution of geological units (e.g. Caumon et al., 2009). Implicitgeological modelling methods simplify this process with an automaticinterpolation of the best model that honours both the geologicalconstraints and all available data (Mallet, 2004; Calcagno et al., 2008;Caumon, 2010). We apply here an implicit geological modellingapproach based on potential-eld interpolation (Lajaunie et al., 1997).

The fundamental concept in this approach is that a set ofgeological structures can be represented as isosurfaces in one ormultiple interacting scalar potential elds (Lajaunie et al., 1997;Calcagno et al., 2008). The scalar eld is dened at any pointp x; y; z in space as a function T(p). An interface is one isosur-face of this eld with an (unknown) value tk so that Tp tk. Twogeological observations of the same geological surface thereforehave the same potential eld value, and an orientation measure-ment anywhere in space corresponds to the gradient T of theeld. The potential eld itself is estimated as a co-kriging functionwith a polynomial drift and a stationary covariance (see Calcagnoet al., 2008, for details of the method).

In the context of our work, the important advantages of thisimplicit geological modelling approach are that (1) the formula-tion of geological surfaces and volumes in a potential eld directlyhonours geological constraints, (2) the interpolation can beupdated when data are changed, and (3) the potential eld Tp)is dened anywhere in 3-D space. The method has been appliedsuccessfully to complex geological settings, including multiplydeformed mountain ranges (Maxelon et al., 2009) and fault net-works (Calcagno et al., 2012). The most important aspect of themethod is that a realistic geological model can be dened with alimited number of structural parameters (Putz et al., 2006;Calcagno et al., 2008). This enables us to include the initialgeological data as structural parameters in an inverse framework.

The described implicit modelling method is implemented in acommercial software package (GeoModeller, www.geomodeller.com)and its functionality can be assessed through an application pro-gramming interface (API). The entire input data set for a geologicalmodel, together with geological constraints, is stored in an XML le.

We developed a Python package (pygeomod, see Appendix Bfor availability) to access the data in the input le and the essentialmethods in the API required to compute the geological model.Using this package, it is possible, for example, to change theposition of a single structural geological observation, such as asurface contact point, using only a few lines of Python code.An example is given in A.3.

2.1.2. From continuous to discrete geological modelThe second part of the workow addresses the generation of a

discrete version of the geological model. Discretisation is arequirement of the numerical solver implemented in the owsimulator. A rectilinear cartesian mesh is generated. Once themesh is dened, an identier is assigned to each cell according tothe geological unit at the position of the cell center in thecontinuous geological model.

The automation of this step is possible because the geologicalmodel, constructed in the rst step, is a continuous function that isdened everywhere in space. Once the potential eld T(p) and thecorresponding isosurface values tk of the geological surfaces aredened, the geological unit can be determined from the value ofthe potential function. This functionality can be accessed throughthe API of the geomodelling software. The API can be accesseddirectly via Python, but for computational efciency, we pro-grammed this part in C and wrapped it with a Python modulefor high-level access (see A.1 for an example).

2.1.3. Generation of the simulation input leThe next step involves the population of grid cells with relevant

rock properties and the generation of an input le for the owsimulator. The majority of the methods required for this step arealready implemented in PyTOUGH (Croucher, 2011; Wellmannet al., 2011), a set of Python modules for pre- and postprocessingof TOUGH2 simulations. We extended the functionality ofPyTOUGH with several additional methods, implemented in thePython package geopytough (see Appendix B).

The spatial structure of a TOUGH2 mesh is completely speciedby blocks with dened volumes and properties, and the connec-tions between pairs of blocks. PyTOUGH contains methods forworking with layered grids. We use these methods to automati-cally generate a rectangular grid over the extent of the geologicalmodel. Relevant rock properties (permeability, porosity, etc.) are thendened on the basis of the discrete geological model (see previousstep) and a dened list of rock properties for each geological unit.In addition, it is possible to dene boundary conditions, an atmo-sphere block, and sources and sinks. The results of this step are

Geomodeller PyTOUGH

iTOUGH2PEST interface

Template file

Instruction file

TOUGH2Simulation

Output observations (iTOUGH2)

Dummysimulation

Structuralgeological

data

Geologicalmodelling

parameters Geologicalmodel

(continuousin 3-D)

Mesh definition

Discretegeological

modelTOUGH2input file

Externalsimulation

Input Parameters (iTOUGH2)

Fig. 1. Integration of structural geological data into the inverse framework ifiTOUGH2 through the PEST interface: the methods combining structural geologicaldata, geological model construction with GeoModeller, and input le generationwith PyTOUGH are controlled by iTOUGH2 through the PEST interface.

J.F. Wellmann et al. / Computers & Geosciences 65 (2014) 95109 97

stored in the mesh and input les for the TOUGH2 simulator. Foran example, see A.1.

2.1.4. Flow simulation and analysis of resultsThe multiphase ow simulation is performed with TOUGH2,

using any of the available equation of state (EOS) modules (Pruesset al., 2011; Pruess and Spycher, 2007a). As the simulation itself isexecuted with a system call, no further automation is required atthis step. Once the simulation is performed, the output le isanalysed, again with PyTOUGH. With the grid methods describedin the previous step, it is possible to automatically visualize thesimulation results, including plots of thermodynamic variables atone block over time, slice plots through the model, or full 3-Dvisualisations with the Visualization Tool Kit (www.vtk.org).

The ow simulation itself and the analysis of the resultscomplete the workow from geological data to ow simulation.As all steps are integrated into Python modules, the completeautomation of the workow is straight-forward. It is, for example,possible to move a geological surface contact point vertically,which triggers an update of the geological and ow models, theow simulation and analysis or results to observe what effect thischange has on the simulated ow eld. A practical example of thispossibility is described in Section 3.1.

2.2. Integration into the inverse framework of iTOUGH2

The second part of the methodological development is theintegration of the workow described above into iTOUGH2, whichis a general inverse modelling framework to perform sensitivityanalysis, parameter estimation, and uncertainty propagation.(Finsterle, 1999, 2004; Finsterle and Zhang, 2011a). It has beenused to study inverse problems in a wide range of multiphase owproblems, including geothermal reservoir engineering, carbonsequestration, nuclear waste isolation, and environmental studies(e.g. Finsterle, 2004; Kiryukhin et al., 2008; Zhang et al., 2011;Finsterle and Zhang, 2011b).

The capabilities of iTOUGH2 are accessible to externally providedmodels, including pre- and postprocessors, through the use oftemplate and instruction les dened by the PEST protocol(Doherty, 1994). Template les are used to control input parametersadjusted by iTOUGH2; instruction les parse output les and extractthe values of interest, passing them to iTOUGH2. A brief example of atemplate le denition is given in A.4. For more details on theinterface and its possibilities, see Finsterle and Zhang (2011b).

In this work, we take advantage of the PEST interface implemen-ted in iTOUGH2 to combine geological modelling and TOUGH2 owsimulations, described in Section 2.1. The essential parts are visua-lised in Fig. 1. iTOUGH2 is the central part: input parameters andoutput observations are dened, and the ow simulation withTOUGH2 is performed. In addition, iTOUGH2 controls the input legeneration through template les in the PEST interface and a pre-processing script that invokes the workow from structural geologi-cal data, through the geological model, to grid and input legeneration. Awide range of aspects can be controlled with iTOUGH2:the structural geological data themselves (position and orientation ofstructural elements), the network of faults, geological modellingparameters, the mesh denition (discretisation) and renement,the assignment of boundary conditions, geostatistical parameters,and formation properties.

As some of the algorithms implemented in iTOUGH2 requireevaluation of derivatives of the model output with respect toselected input parameters, the following issue arises as a result ofthe proposed workow. When a continuous geological model ismapped onto the discrete grid used by the ow simulator (see2.1.2), the objective function is likely discontinuous, i.e., a gradual

change in a structural geological parameter may lead to a discreteresponse. Derivative-based methods are of limited use for para-meter estimation in this case. Several derivative-free parameterestimation methods for discontinuous objective functions areavailable in iTOUGH2 (Finsterle, 1999). In the simulation study inSection 3.2.2, we apply the downhill simplex method.

3. Application: impact of structural uncertainties on CO2injection

As a test of the integration of implicit geological modelling intothe iTOUGH2 framework, we apply the developed methods to astudy of CO2-injection into a reservoir in an anticlinal structure.We focus on the (low-dimensional) parameterisation of the entiregeological model and the consideration of uncertainties in thesestructural geological parameters.

The simulations are arranged according to the description inthe materials and methods section above. In the rst example, wewill show how structural parameters can be changed, and howthis change is automatically passed through to the ow simulationusing a short Python script. In the second example, we demon-strate how this automated workow enables iTOUGH2 to usestructural geological data for sensitivity analyses, parameter esti-mation and uncertainty propagation analysis.

3.1. Forward simulation and change of the geological model

The example model represents a carbon sequestration scenariowhere CO2 is injected into a reservoir in an anticlinal structure below alow permeability sealing layer. The anticlinal structure is offset by afault, where the fault damage zone can be a potential leakage pathwayfor CO2 (Fig. 2). The problem is simulated as a 2-D vertical slice with alateral extent of 5 km, a depth of 2 km, and a thickness of 200 m.

The geological model can be adjusted with only six freestructural geological parameters, presented in Fig. 2: three points(RW, RT, and RE) dene position and shape of the anticlinalstructure, and an additional point (S), representing the positionof the top of the seal, which has uniform thickness. The position ofthe fault zone is parameterised by two points (FT and FB) near thetop and bottom of the fault. The error bars shown in Fig. 2 indicateuncertainties in these parameters: depth and shape of reservoirand seal are uncertain, and so is the lateral position of the faultzone. The following additional geological constraints are consid-ered known and are thus xed for the base model and all derived

z =

2 km

E-W = 5 km

Shallow observation wells

CO2 injection well

Seal

Reservoir

RW RT

S

REFT

FBFault zoneStructural geol.

parameters

Fig. 2. Conceptual model for CO2 injection study: 2-D vertical model showing anticlinalstructure, potential leakage through fault zone, and position of shallow observationwells. The geological model is parameterised with six structural geological parameters:three points (RW, RT, and RE) for the shape and position of the anticline, one point (S) forthe top position of the seal, and two points (FT and FB) for the position of the fault zone.Error bars indicate uncertainties in these parameters: reservoir top and seal haveuncertain depths, and the fault zone has uncertain lateral position.


models: thickness of fault zone, position of the reservoir top at thewest side of the fault, age constraints between reservoir, seal andcover rock, and the inuence of the fault zone on the differentgeological units. For further details, see the geological modelavailable online (see Appendix B).

The injection simulation is performed with TOUGH2's ECO2Nequation-of-state module (Pruess and Spycher, 2007b). This prop-erty module describes mixtures of water, NaCl, and CO2 and heat,enabling the simulation of CO2 injection into deep aquifers, withconsideration of salinity. The implemented thermodynamic equa-tions are valid for temperatures of up to approximately 110 1C andpressures of 600 bar.

Rock properties are assigned similarly to those in the CO2injection example studies described in the ECO2N manual (Pruess,2005). The two main lithologies are adapted to the CO2 injectionscenario dened here: a sand-rich lithology and a low-permeability

shale. The reservoir cap rock (i.e. the seal) is simulated as a shale,while all other rocks are simulated as sand-rich lithologies. Relativepermeability and capillary pressure functions are dened using thevan Genuchten model (Van Genuchten, 1980).

The simulation is performed in two steps. To determine initialpressure and temperature conditions, a steady-state conductivetemperature eld is simulated for a basal heat ux of 0.06 W/m2

and an atmospheric temperature of 15 1C, resulting in a tempera-ture gradient of approximately 30 1C per kilometer. Pressure at thesurface is set to 1 atmosphere. In the next step, we simulate theinjection of 25 kg/s of CO2 into the anticlinal structure for 30 years.Initial salt mass fraction in the entire model domain is 1%, and noCO2 is present before injection. The simulation of CO2 injectionitself is performed in isothermal mode.

The combination of geological modelling and TOUGH2 simula-tion is an example of the rst part of the workow presented in

Fig. 3. Discrete geological model, spatial distribution of CO2 after 30 years of injection, and CO2 at observation wells for (a) the base case and (b) the modied versiongenerated by adding 300 m to the lateral position of the fault (parameters FT and FB in Fig. 2). Note that geological model construction, discretisation, TOUGH2 input legeneration and simulation, and visualisation of results are automatically updated without any further manual interaction (see Appendix A for code). (a) Base case.(b) Modied model.


Fig. 1. It involves combining Geomodeller with PyTOUGH togenerate a TOUGH2 input le. For the relevant Python code, seeA.1, and for the visualisation to generate Fig. 3, see A.2.

The discretised geological model and corresponding simulationresults for the base-case injection scenario are visualised in Fig. 3(a).The continuous geological model is discretised into a regular meshwith 80 cells in E-W, and 50 cells in z-direction. The spatialdistribution of CO2 in the model domain after a simulation time of30 years (Fig. 3(a), middle gure) shows the leakage through thefault and the main distribution around observation wells O3O6,visible also in the plots of CO2 mass fraction in the aqueous phaseat the observation wells as a function of time (bottom Fig. 3(a)).

Next, we use the same part of the workow with the additionalstep of changing the geological model with modications in thestructural parameters. With only a few lines of code (see A.3),the parameters dening the top and bottom positions of the fault(FT and FB) are increased by 300 m, resulting in a lateral shift of thefault zone towards the west (Fig. 3(b) top).

Re-running the code for model generation with these updatedstructural parameters results in a new TOUGH2 input le. Theupdated distribution of rocktypes, simulation results, and CO2histories at the observation wells are shown in Fig. 3(b). Thedifference in geological model, spatial distribution of CO2, and theCO2 mass fraction in the observation wells is evident.

This simple example shows that our approach enables thecombination of implicit structural geological modelling with inputle generation for TOUGH2 simulations. The steps from changingthe initial points of the structural model, recomputing the geolo-gical potential eld, discretising and exporting the geologicalmodel, and running the simulation of CO2 injection are allintegrated into one script (see Appendix A). In the next step, wemake use of this automation within the iTOUGH2 framework, i.e.,iTOUGH2 controlling and updating the geological parameters, andanalysing their impact on TOUGH2 simulation results.

3.2. Control of geological model construction with iTOUGH2

We will now apply the entire workow presented in Fig. 1,including the integration into iTOUGH2, for three commonlyperformed analysis steps with respect to simulation and modelevaluation (Carrera et al., 2005): sensitivity analysis, parameterestimation, and uncertainty propagation analysis.

In this modelling study, we evaluate the inuence of the sixstructural parameters dening the geological model (Fig. 2), aswell as six material properties (the permeability and porosity ofthe fault, reservoir, and seal). The initial values and assignedstandard deviations are summarised in Table 1. Note that we

consider changes relative to the initial value for the structuralparameters. A positive change to the points dening the faultposition (FT and FB) represent a shift towards the east, and for theother parameters a shift downwards.

In order to use iTOUGH2 as a wrapper for the workow fromgeological data to ow simulation for the CO2 injection study, thePython script developed in the previous section has to be modiedto a template le according to the PEST protocol (Finsterle, 2011).This is easily done by replacing each value dening the relativechange of a structural geological parameter (see A.3 for anexample) by a PEST-style variable name that can be interpretedby iTOUGH2. The modied Python script and the correspondingiTOUGH2 inversion input les are available from the onlinerepository (see Appendix B).

3.2.1. Sensitivity studyWe rst evaluate the local sensitivities of the simulated CO2

values at the observation wells with respect to structural andhydrological input parameters. For increased accuracy, we use acentral nite difference scheme for the approximation of theJacobian, requiring a total of 2n1 25 forward simulations,where n is the number of adjustable parameters.

Results from the sensitivity analysis provide insights intodata sensitivity, parameter inuence, and correlations betweenparameters. The parameter sensitivities are presented in Table 2.In addition to composite sensitivities, a measure of overall para-meter correlation 0or1 is obtained, where higher valuesindicate that the corresponding parameter is relatively independent.

Table 1Initial values, standard deviations and ranges of geological parameters and rock properties.

Type Parameter Parameter value

Id (unit) Name Initial Stdev From To

Structure (relative changes) RW (m) Reservoir left (0) 50 100 100RE (m) Reservoir right (0) 50 100 100RT (m) Reservoir top (0) 50 100 100S (m) Seal (0) 50 100 100FT (m) Fault position (0) 500 1000 1000FB (m) Fault position (0) 500 1000 1000

Property log(kR) (m2) Reservoir perm. 12.1 0.3 13 11log(kS) (m2) Seal perm. 16 1.0 17 15log(kF) (m2) Fault perm. 11.5 1.5 15 11R (%) Reservoir por. 15 2.5 5 30S (%) Seal por. 10.3 5 2 15F (%) Fault por. 15 10 5 35

Table 2Sensitivity analysis for the parameters dening the geological structure and rockproperties. The ratio between conditional and marginal standard deviation is ameasure of overall parameter correlation (higher values are less correlated).

Type Id Standard deviation Sensitivity

A Priori Marginal Output

Structure RW 50 10.600 0.621 53.4RE 50 40.100 0.419 12.0RT 50 17.700 0.412 43.8S 50 23.500 0.657 5.2FT 500 41.600 0.871 152.3FB 500 163.000 0.585 27.1

Property log(kR) 0.3 0.057 0.410 60.4log(kS) 1.0 5.350 0.047 10.6log(kF) 1.5 0.848 0.756 7.0R 2.5 0.8 0.502 48.1S 5 75.5 0.337 0.0F 10 58.0 0.048 10.1


For more details and an interpretation of the additional measures,see Finsterle (1999).

The parameters dening the geological structure have a stronginuence on simulated CO2 concentrations at the observationwells. The most inuential parameters are the structural pointsdening the top position of the fault (FT), and the west and top ofthe anticlinal structure (RW and RT). From the parameters of therock properties, only the reservoir porosityR and permeability kRare of comparable sensitivity. The values of indicate that thestructural point dening the top position of the fault, and the faultpermeability, are the least correlated parameters.

In addition to the sensitivities of the parameters, we also obtain acovariance analysis, which reects correlations between the differentparameters. The matrix of the direct, pairwise parameter correlationsis visualised in Fig. 4. As already evaluated with in Table 2, it isevident that the structural parameter dening the top of the fault FTand the permeability of the fault kF are the least correlatedparameters (with corresponding rows and columns showing neutralcolours). The top and east points dening the structure of theanticline (RT and RE) are highly correlated with almost all of the rockproperties, and the rock properties have strong correlations amongeach other. It is interesting to note that the correlations between thestructural parameters, i.e., the points dening the eastern (RE) andwestern (RW) ank of the anticline, are positively correlated. On theother hand, the point dening the top of the reservoir (RT) ispositively correlated with the western ank, but negatively withthe eastern ank. These correlations follow from the fact that thosepoints dene the shape of the anticline, and therefore the overallvolume of CO2 that can be stored before breakthrough through thefault occurs. The correlations between these parameters and thereservoir porosity R can be interpreted similarly.

In addition to the relevance of sensitivity and correlationanalyses for experimental and observational design, the analysisof these measures is important for subsequent parameter estima-tion. In general, the more sensitive a parameter is, and the lesscorrelated it is with other parameters, the better we will be able toestimate its value from the available observations.

The formal analysis of sensitivities with iTOUGH2 com-bined with our workow therefore provides direct insight into

sensitivities and correlations for the initial structural geologicalparameters. In the next step, we will use parameter estimationmethods to determine if the structural parameters can be identi-ed from a given set of observations.

3.2.2. Parameter estimationIn our example model, we simulate the observation of CO2 in

several shallow observation wells above an area where a leakagezone (in our case parameterised as a fault) would be expected. In arealistic case, it could be of interest to determine the position ofthis leakage zone, given the measurements of CO2 concentrations.In the sensitivity study, it was determined that the parameter FTdening the top position of the fault has a signicant inuence onthe objective function (Table 2), and that we should be able todetermine the value of this structural parameter by inversemodelling.

We apply a parameter estimation algorithm to see if it ispossible to determine several structural parameters that denethe main features of the structural geological model, using CO2data from observation wells. As this is a synthetic example, themain interest is to see whether the parameter estimation proce-dure, in combination with our method of re-creating the structuralmodel directly from a small set of geological parameters, is capableof generating a sufciently wide range of different structuralmodels, and of identifying models close to that used to generatethe synthetic data (Fig. 3(a)).

As pointed out in Section 2.2, derivative-based parameterestimation methods are not suitable for the problem consideredhere; we therefore use the derivative-free downhill simplexminimisation algorithm. As structural parameters, we considerthe parameters dening the western side and the top of thereservoir anticline (RW and RT) in addition to the fault top to allowfor wider variability in the structural geological model. In additionto the three structural parameters, we consider the rock propertiesof the fault zone to be uncertain and assign initial values that areoffset from the values used for the forward simulation (FT500,RW and RT25, log kF 12:5, F 0:1, for comparison withinitial values, see Table 1).

Results for the evolution of the structural parameters duringsuccessive downhill simplex iterations are presented in Fig. 5. Thealgorithm explores initially a wide range of different struc-tural models, based on the three structural parameters. After

Fig. 4. Matrix visualisation of estimated direct parameter correlations. The struc-tural parameter dening the top position of the fault (FT) and the permeability ofthe fault kF show the lowest correlations with other parameters.

Fig. 5. Convergence of the structural parameters during parameter estimation withthe downhill simplex method. The y-scale is set to twice the parameter standarddeviation (Table 1).


approximately 15 iterations, the position of the fault is relativelywell established. Parameters for the structural points dening thetop and west side of the reservoir anticline are reasonably welldetermined within the accuracy of the model discretisation.

Two of the structural models that were explored duringparameter estimation are shown in Fig. 6. The difference in thestructural models is clearly visible in the position of the fault.The nal structural model obtained as a result of the analysis issimilar to the initial model in Fig. 3(a), with an anticlinal structurethat is less pronounced than in the two models shown here.

3.2.3. Uncertainty propagationFinally, we evaluate how uncertainties in the structural geolo-

gical model propagate through the predictive model of CO2leakage. Building on the results from the inversion, we wish toevaluate the total amount of CO2 leaked through the fault, togetherwith estimated upper and lower bounds, given the uncertainties in

the parameters. Instead of simply using the initial, uncorrelatedparameter standard deviations described in Table 1, we propagatethe full covariance matrix as determined by the inversion throughthe prediction model.

In iTOUGH2, two uncertainty propagation methods are imple-mented: the Monte Carlo method and linear propagation analysis(FOSM). We use here the Monte Carlo method, as the linearityassumptions in the linear propagation analysis are too limiting inour example. We can expect a complex response due to theinherent non-linearity of two-phase ow and the discrete impactof geological structures on leakage.

The analysis of the sensitivity matrix showed that some of themodel parameters are strongly correlated (Fig. 4). Consequently,instead of independently sampling from each parameter distribu-tion, we account for parameter correlations using a Latin Hyper-cube sampling design (Zhang and Pinder, 2003). We generate 100realisations, using as the means the best estimates of the threestructural parameters (FT, RW and RT) and the rock properties of

Fig. 6. Examples of structural models explored during parameter estimation with the downhill simplex method, requiring only an adjustment of three structural parameters.

Fig. 7. Results of uncertainty propagation analysis for total mass of CO2 in the different geological units as a function of time. The green line shows the median value, dashedblue lines 5% and 95% quantiles and the gray dots lower and upper bounds. The numbers indicate the number of the parameter set leading to this result. (For interpretationof the references to color in this gure caption, the reader is referred to the web version of this article.)


the reservoir (kR andR), and the full covariance matrix (see TableC1) as determined at the minimum of the objective function.

Results of the analysis are shown in Fig. 7. The green lines inthe four subgures represent the median for the mass of CO2 inthe respective geologic units, the dashed blue lines the 5% and 95%quantiles, and the grey dots are the minimal and maximal valueswith numbers indicating the parameter set leading to this result.The uncertainty in structural parameters and reservoir propertiesconsiderably affect the predictions of interest. For example, theCO2 arrival time at the fault ranges from 3 to 8 years, and theestimated total amount of CO2 stored in the reservoir after aninjection period of 30 years varies from 4109 to 1.2110 kg.Note that the amount of CO2 leaking through the fault to theatmosphere is very large in this synthetic reservoir. This unfavour-able outcome may be a result of the 2-D nature of the model alongwith the chosen location and properties of the fault, whichestablish an escape pathway for the injected CO2 that cannot bebypassed, leading to the high leakage amount once the cumulativeamount injected has reached the limited storage volume beneaththe anticlinal structure.

The two structural models corresponding to the parameter setswhere CO2 reached the fault and atmosphere rst (parameter set 79)and last (parameter set 74) are shown in Fig. 8. Although thedifferences are not as pronounced as for the models exploredduring the parameter estimation routine (Fig. 6), the differences inthe structural models are clearly visible in the position of the faultand the shape of the anticline.

4. Discussion

The core of our method lies in the application of an implicitgeological modelling method that enables the construction ofrealistic and complex full 3-D structural models with a low-dimensional parameterisation (Calcagno et al., 2008). We exam-ined here a 2-D model for a relatively simple structural setting.However, numerous examples exist where the same implicitmodelling method has been applied to complex 3-D geologicalsettings (Martelet et al., 2004; Maxelon and Mancktelow, 2005;Joly et al., 2000; Calcagno et al., 2012). An important considera-tion is that the structural parameters are closely related totypical geological observations. In our synthetic simulationstudy, we considered observations of points dening the surfacecontact between main geological units (RW, RT, RE and S in Fig. 2)and the position of a fault (FT, FB). Orientation data, e.g., the dipof a fault, can be incorporated in an analogous manner (see theexample in A.3). Because orientation data are considered asgradients of the potential eld (Lajaunie et al., 1997), they arenot restricted to positions on an observed surface but can be

included anywhere in space, for example derived from mea-surements of sedimentary layering within one unit. The abilityto include both aspects, structural points as well as orientationmeasurements, provides great exibility in the construction ofthe structural models. However, special care should be taken inthe set-up of the initial model by limiting the number ofstructural parameters and by making sure they are only weaklycorrelated.

We described in detail in the introduction the difference betweenchanging the structural model, as we do here, and adjusting spatialdistributions of properties, as commonly performed with geostatisticalmethods. Both aspects usually contain uncertainties which, ideally,should be considered in a realistic evaluation where a ow simulationis based on an initial structural model. Geostatistical methods for thesimulation and estimation of property heterogeneity have alreadybeen implemented into iTOUGH2 (Finsterle and Kowalsky, 2008). Ourwork provides the methods to consider uncertainties in the initialstructural model. A systematic evaluation of both uncertainties in thestructural model and smaller-scale heterogeneities is possible withthis combination and the topic of further research.

Representing complex geology in a numerical model may leadto meshes with a very large number of elements and connections,making the simulation computationally demanding. This is espe-cially the case when thin layers or complex structural settings areconsidered. The methods that we apply for geological modellingand model discretisation are not restricted by the number ofelements. However, the computational demands of the TOUGH2simulation may be a limiting factor. Note that TOUGH2-MP (Zhanget al., 2008), a parallel version of the simulator, has been applied toproblems with several million grid blocks. TOUGH2-MP can beintegrated using PyTOUGH and executed as an external simulationthrough the PEST interface.

The fact that distinct geological units of the continuousgeological model are mapped onto a discrete mesh may lead toproblems when numerically evaluating derivatives with respect tostructural parameters, as a small change in a structural parametermight not change the discrete structural model at all. As men-tioned before, this may prevent or limit the use of derivative-basedparameter estimation methods, specically the LevenbergMar-quardt algorithm, which is generally very successful for non-linearinverse problems. We thus used the downhill simplex as aderivative-free parameter estimation algorithm in our demonstra-tion of the workow. Other derivative-free parameter estimationmethods that could be applied include grid search, simulatedannealing, harmony search, differential evolutionary algorithmand other global minimisation algorithms implemented iniTOUGH2. However, different strategies can also be envisaged onthe level of the geological discretisation by ensuring that smallchanges in geological parameters always lead to continuous,

Fig. 8. Single realisations of the structural geological model corresponding to the parameter set for shortest (model 79, left gure) and longest (model 74, right gure) timefor leakage into the fault zone and the atmosphere (Fig. 7).


differentiable changes in the simulation output. Such strategiesinclude adaptive meshing (in a sense of adapting a mesh to achanged geological model realisation), or the inclusion ofsmoothly varying property averages across stratigraphic unitinterfaces as a function of the position of this interface within acomputational element.

5. Summary and conclusions

We developed a workow that enables the adaptation of ageological model through structural parameters within a frameworkfor forward and inverse modelling of multiphase ow in fracturedporous media. We developed methods to automate the entireprocedure from geological modelling, to model discretisation, toinput le generation for ow simulations, to ow simulation andanalysis of model results. An important feature of our approach isthat we integrate the construction of the geological model through apowerful implicit geological modelling approach: the input mesh forthe ow simulation is directly reconstructed from primary structuralparameters, such as surface contact points, fault observations, ororientation measurements. The integration enables us to considerthis type of geological information directly in typical model evalua-tion procedures, like sensitivity analysis, parameter estimation, oruncertainty propagation analysis. Our workow provides a way toevaluate the inuence of structural data on ow simulation results,and to estimate primary structural geological parameters from avariety of observations.

We tested the proposed methodology for the three iTOUGH2application modes with a synthetic example of CO2 injection intoan anticlinal structure, with potential leakage through a fault zone. We

constructed a structural geological model consisting of four geo-logical units and dened six geological parameters (contact pointsbetween the different units) that enabled us to modify the mainfeatures of the model that are considered uncertain in our case: thedepth and shape of the anticlinal structure, the thickness of the seal,and the lateral position of the fault. We showed that, with only a fewlines of code, it is possible to change the parameters dening theposition of the fault, and to update the input mesh for the owsimulation given the new geological model. We showed that iTOUGH2is able to examine the structural model in sensitivity, inverse model-ling, and uncertainty propagation analyses. Given the often dominanteffect that the geological structure has on ow simulation results, theproposed parameterisation of geological features and the integrationinto the iTOUGH2 framework adds an important new capability, as itallows the modeller to formally analyse aspects of the conceptualmodel, estimate the geometry of geological structures, and evaluatethe impact of related uncertainties on the simulate system response.

Acknowledgments

We would like to thank the three anonymous reviewers fortheir constructive comments. The rst author is funded by a CSIROOfce of the Chief Executive Post-Doctoral Fellowship schemewithin the CSIRO Earth Science and Resource Engineering Division.The work of the second author was supported, in part, by the U.S.Dept. of Energy under Contract no. DE-AC02- 05CH11231. Specialthanks to Intrepid Geophysics Ltd. for providing an academicversion of the software GeoModeller.

Appendix A. Code for model setup and modication

This section contains Python code snippets that illustrate the usage and exibility of the method presented in this manuscript. The entirecode for all examples and the geological model is available on the online repository (see Appendix B).

Python is an open-source interpreted programming language that provides powerful numeric and scientic methods as well as datavisualisation techniques (e.g. Langtangen, 2008; Prez et al., 2011). Python is available for virtually all relevant operating systems. Due to theexibility of the language, it is ideally suited to combining pre- and postprocessing of other simulation codes into a single framework.

A.1. Export of geological model into mesh format for TOUGH2 simulation

The geological model is exported with a Python wrapper for an external C program that accesses the API of the geological modellingsoftware (Geomodeller). The geological model is re-computed and exported into a regular grid (rectilinear grids are also possible):

For the TOUGH2 simulation, a template TOUGH2 input le is adapted and a new mesh is generated from the exported model:


A.2. Visualisation of rocktypes and CO2 distribution

The visualisation of rocktypes and CO2 distribution, as, for example, presented in Fig. 3 is possible with standard PyTOUGH methods.The discretised geological model (i.e. the distribution of rocktypes) can be visualised with

A slice plot of distribution of CO2 after 30 years of injection (the last time step) is generated with

A.3. Modication of geological model

The geological model is adapted with methods of the Python module geopytough:


In a similar way, it would be possible to adjust orientation measurements, for example to add 10 degrees to the dip of a faultorientation measurement:

A.4. Adjusting the Python script for use with iTOUGH2 through the PEST interface

The Python script for geological model construction and export has to be converted into a PEST template le for use with iTOUGH2.Only some minimal changes are required, basically substituting the values dening the relative changes with a PEST-style variable that canbe interpreted by iTOUGH2. Following the example in A.3, an example would be

With the according parameter block in the iTOUGH2 input le:

Complete examples for PEST template and iTOUGH2 input les are available on the online repositories.


Appendix B. Details of online repositories for code and example simulations

The Python modules that were developed for this work are available on the github page of the rst author:

- https://www.github.com/ohorovicic/geopytoughand- https://www.github.com/ohorovicic/pygeomod

Python scripts, geological model, TOUGH2 template les, and iTOUGH2 inversion setup les are also available on

- https://www.github.com/ohorovicic/publication_scripts.

Note that all modules are provided without any warranty or liability and published under a Creative Commons share alike license withattribution to the original work. When used in any way, refer this publication.

In addition, the following programs are required:

A 2.x Python installation, including matplotlib, Numpy and Scipy (available on- http://www.python.org); PyTOUGH, freely available on - https://www.github.com/acroucher/PyTOUGH; iTOUGH2 with the ECO2N modules (see - http://esd.lbl.gov/ITOUGH2/ for software, source code, and licensing); The commercial geological modelling software Geomodeller (See- http://www.geomodeller.com).

Table C1Matrix with estimated parameter variances and covariances (diagonal and lower triangular matrix) and correlation coefcients (upper triangular matrix) used for LHSsampling.

RW RT FT kR R

RW 0.23102 0.21 0.53 0.40 0.16RT 0.17102 0.31103 0.886 0.12 0.10FT 0.15103 0.94103 0.36104 0.04 0.002kR 0.29 0.31 0.32 0.23101 0.89R 0.55102 0.12101 0.64103 0.96103 0.50104

Fig. C1. Estimated covariances for the parameters in the CO2 injection study, obtained as additional result from the sensitivity study (Section 3.2.1).


The Python modules are independent of the underlying operating system. iTOUGH2 can be compiled on a wide range of operatingsystems and Geomodeller is currently available for Windows and Linux. The simulations presented in this work were performed on a 64-bit PC running Ubuntu Linux. The workow has also been tested successfully on Windows PCs.

Appendix C. Additional material related to the simulation results

C.1. Covariance estimation

A gure of estimated covariances, determined for the sensitivity analysis in Section 3.2.1.The table with covariance and correlation values used for LHS sampling in the Monte Carlo uncertainty propagation analysis is given

in Table C1.

C.2. Grid search

In order to obtain a better overall picture of the shape of the objective function, we will rst perform a simple grid search. As describedabove (Section 2.2), a grid search provides a detailed picture of the objective function, albeit for a very high computational cost.We therefore limit it to the two most sensitive parameters (see Table 2): the top position of the fault, and the porosity of the reservoir (Fig. C1).

The objective function is visualised in Fig. C2 for 11 increments for both parameters in the ranges of 0.05 to 0.25 for R and 500 to500 for FT. The minimum of the objective function, around the values used to generate the synthetic dataset (FT0, R 0:15) is clearlyvisible. In addition, the positive correlation between both parameters can be detected, as identied before by the evaluation of directcorrelations (Fig. 4): a position of the fault closer to the injection (increasing values of FT) is balanced by a higher reservoir porosity. It canalso be seen that, in the range evaluated here, only one clear minimum exists. The grid search, although an expensive parameterestimation method, reveals the interplay between a structural parameter, the fault position, and a rock property, reservoir porosity.

Fig. C2. Visualisation of the objective function for the two most sensitive parameters: the position of the top of the fault (FT), and reservoir porosity R .


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Integrating structural geological data into the inverse modelling framework of iTOUGH2IntroductionMaterials and methodsCombining geological modelling and multi-phase flow simulationsFrom discrete structural data to a geological modelFrom continuous to discrete geological modelGeneration of the simulation input fileFlow simulation and analysis of results

Integration into the inverse framework of iTOUGH2

Application: impact of structural uncertainties on CO2 injectionForward simulation and change of the geological modelControl of geological model construction with iTOUGH2Sensitivity studyParameter estimationUncertainty propagation

DiscussionSummary and conclusionsAcknowledgmentsCode for model setup and modificationExport of geological model into mesh format for TOUGH2 simulationVisualisation of rocktypes and CO2 distributionModification of geological modelAdjusting the Python script for use with iTOUGH2 through the PEST interface

Details of online repositories for code and example simulationsAdditional material related to the simulation resultsCovariance estimationGrid search

References

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