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Journal of Natural Gas Science and Engineering 42 (2017) 69e84

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Journal of Natural Gas Science and Engineering

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Seismic assisted history matching using binary maps

Dennis Obidegwu, Romain Chassagne*, Colin MacBethInstitute of Petroleum Engineering, Heriot-Watt University, Edinburgh, EH14 4AS, UK

a r t i c l e i n f o

Article history:Received 11 October 2016Received in revised form26 January 2017Accepted 7 March 2017Available online 10 March 2017

Keywords:4D seismic interpretationHistory matchingBinary mapsGas exsolutionGas dissolutionWater evolution

* Corresponding author.E-mail address: [email protected] (R. Chass

http://dx.doi.org/10.1016/j.jngse.2017.03.0011875-5100/© 2017 Elsevier B.V. All rights reserved.

a b s t r a c t

This paper addresses the challenge of integrating 4D seismic data with production data in a quantitativemanner in order to improve the forecasting ability of a reservoir model and reduce the associated un-certainty. It presents a history matching workflow that has been applied to production data and timelapse seismic data. In this procedure, the production data objective function is calculated by the con-ventional least squares misfit between the historical data and simulation predictions, while the seismicobjective function uses the Current measurement metric between a binary image of saturation change.This approach is implemented on a real field data from the United Kingdom Continental Shelf (UKCS),where uncertain reservoir parameters which consist of global and local parameters are initially assessed.These parameters include flow based multipliers (permeability, transmissibility), volume based multi-pliers (net-to-gross, pore volume), as well as the end points of the relative permeability curves (criticalsaturation points). After the initial screening, sensitive parameters are selected based on the sensitivityanalysis. An initial ensemble of fluid flow simulation models is created where the full range of uncertainparameters are acknowledged using experimental design methods, and an evolutionary algorithm isused for optimization in the history matching process. It is found that the primary control parameters forthe binary seismic gas match are the permeability and critical gas saturation, while the volumetric pa-rameters are important for the binary seismic water match in this particular reservoir. This approach iscompared to seismic history matching using full seismic modelling, preserving all amplitudes. The re-sults demonstrate that the binary approach gives a good match to gas saturation distribution and watersaturation distribution, and the reservoir parameters converge towards a solution. The conventionalapproach does not capture some signals of hardening and softening in the seismic data, and hence insummary, the binary approach seems more suitable as a quick-look reservoir management tool. A uniquefeature of this study is the application of the binary approach using Current measurement metric forseismic data history matching analysis, as this circumvents the use of the uncertain petroelastic model.This approach is easy to implement, and also helps achieve an effective global history match.

© 2017 Elsevier B.V. All rights reserved.

1. Introduction

Reservoir engineers desire the ability to predict the perfor-mance of an oil field in an efficient and timely manner; this iscoveted as it expedites efficient reservoirmonitoring, management,planning and economic evaluation (Obidegwu et al., 2014). In orderto accomplish this objective, different procedures and mechanismsare employed to acquire, coordinate and interpret data obtainedfrom the reservoir as input to the reservoir simulation model. Thismodel has to confidently replicate the historical data for it to beconsidered worthy of realistic predictions, and this process of

agne).

updating the reservoir model to satisfy the historical data is knownas history matching. Over the past years, production data (oil rates,water rates, gas rates, pressure) have been the main historical dataavailable, however, time-lapse (4D) seismic data is now considereda major dynamic input for history matching. That a model ismatched to production data is not a sufficient condition for it tomake improved predictions (Sahni and Horne, 2006), the modelneeds to integrate all available data as well as the geologistsinterpretation of the reservoir in order to provide the most repre-sentative reservoir model or models (Landa, 1997; Wang andKovscek, 2002). The need to monitor fluid displacement is a greatchallenge that has been successfully overcome with the use of 4Dseismic technology (Hatchell et al., 2002; Vasco et al., 2004;Portella and Emerick, 2005; Huang and Lin, 2006; Kazemi et al.,2011), which is the process of repeating 3D seismic surveys over

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D. Obidegwu et al. / Journal of Natural Gas Science and Engineering 42 (2017) 69e8470

a producing reservoir in time-lapse mode (Avansi and Schiozer,2011). Quantitative use of 4D seismic data in history matching isan active research topic that has been explored extensively (Arenaset al., 2001; Aanonsen et al., 2003; Gosselin et al., 2003; MacBethet al., 2004; Staples et al., 2005; Stephen and MacBeth, 2006;Kazemi et al., 2011; Jin et al., 2012), the main challenge beingquantitatively incorporating the 4D seismic into the reservoirmodel (Landa, 1997; Walker et al., 2006).

Fig. 1 shows the different domains in which seismic data couldbe incorporated into the reservoir model as has been describedpreviously (Stephen and MacBeth, 2006; Landa and Kumar, 2011,Alerini et al., 2014). The three main domains are: (1) The simula-tion model domain, where the observed seismic data is inverted tochanges in pressure and saturation, and are then compared withthe simulation output (Landrø, 2001); (2) The impedance domain,where the observed seismic data is inverted to changes in imped-ance, and the simulation model is forward modelled to derive im-pedances, and both impedances are then compared (Ayzenberget al., 2013), or (3) The seismic domain, where the impedancesderived from the simulation model are convolved with a wavelet togenerate a synthetic seismic, and this is then compared with theobserved seismic (Landa and Kumar, 2011). The aforementioneddomains use seismic modelling, rock physics modelling or petro-elastic modelling to address this challenge, however these model-ling processes are complex, time consuming, use laboratory stresssensitivity coefficients, as well as Gassmann's equation assump-tions (Landrø, 2001; Gosselin et al., 2003; Stephen et al., 2005;Floricich, 2006; Amini, 2014). There have been other methodsthat circumvent the complex seismic modelling process (Landa andHorne, 1997; Kretz et al., 2004; Wen et al., 2006; Jin et al., 2012;Rukavishnikov and Kurelenkov, 2012; Le Ravalec et al., 2012;Tillier et al., 2013) which employed the use of image analysistools, binary processing, or dynamic clusters to integrate theseismic data into the reservoir model. In this paper, a method isproposed where seismic data and simulation data are converted tobinary seismic gas maps and binary simulation gas maps respec-tively, such that a comparison of the observed seismic data directlywith the simulation output in the binary inversion domain ispossible (Fig. 1). The objective function for calculating the misfit ofthe production data will be the popular least squares misfit, whilethe seismic objective function will be the Current measurementmetric (Glaun�es et al., 2008; Chassagne et al., 2016). This approach

Fig. 1. The different domains at which seismic history matching can be explored e the siminversion domain is proposed as a quick-look reservoir management tool.

is contrasted with the conventional seismic modelling approxi-mation scheme, and the context of the study is set by a UKCS fielddataset.

2. Field data set

The binary seismic assisted history matching concepts in thispaper will be applied to a real field data located at the UnitedKingdom Continental Shelf (Martin andMacdonald, 2010), with theaim of history matching the observed data, as well as forecastingthe future production profiles and saturation distributions as ameans of validating the new improved models. The main featuresof the data are that the reservoir pressure is close to its bubble pointpressure, such that the commencement of production activities willlead to depressurization and gas exsolution; and that there is asubsequent pressure maintenance scheme in place by the use ofwater injector wells, so there will be water sweep distributionsexpected in the reservoir. The reservoir permeability is in the rangeof 200 mD to 2000 mD, with a reservoir porosity ranging from 25%to 30%. The pore compressibility is 7� 10�6 psi�1, oil viscosity is 3.5cp at reservoir temperature, water viscosity is 0.5 cp at reservoirtemperature, and the oil formation volume factor is 1.16 rb/stb.Fig. 2 shows an outline of the reservoir, the position of the waterinjectors and oil producers, and the timeline of activity of the wellsrelative to the multiple seismic data surveys. There are 10 years ofproduction activity from 1998 to 2008, and it should be noted thatthe history match will be implemented for the first 7 years, whilethe remaining 3 years will be used to validate the history matchingprocess and forecasting ability. It should be also noted that the 3years used for the forecasting analysis is not really forecast per se,but observed historical data which is held back to validate thehistory matching exercise. The simulation model was provided bythe field operator, and its dynamic properties will be discussed inthe next section.

3. Methodology

3.1. Simulation model conditioning

The simulation model used in this study has dimensions ofapproximately 9600 m by 4900 m by 700 m, and has 128 cells by53 cells by 35 cells in the X, Y and Z direction respectively. The

ulation model domain, the impedance domain, and the seismic domain. The binary

Fig. 2. Outline of the reservoir and the position of the producers and injectors. The solid stars and circles correspond to the well TD for the injector wells and producer wellsrespectively. (b) Timelines of activity for the wells in the chosen sector relative to the monitor seismic data (M1 to M6) surveys (Obidegwu et al., 2014).

D. Obidegwu et al. / Journal of Natural Gas Science and Engineering 42 (2017) 69e84 71

simulation model runtime on a standard computer workstation(Intel CPU E5-1650 @ 3.20 GHz) with 6 processors is approximately5 h. This computer specification will be used all through thisanalysis. In order to efficiently generate multiple runs of the modelwhich is required in a history matching process, the runtime has tobe reduced to an appreciable level; however this has to be achievedwithout distorting the output results, as the simulation model maygive non-physical results if too coarse a grid is used (Carlson, 2003).The initial model is modified and upscaled to different levels ofcoarseness shown in Table 1 and Fig. 3, and the output results arevalidated against the initial model output. The upscaling processinvolves rebuilding the grid structure to a coarser mesh, and usingpore volume weighted averaging for the volumetric parameters,and flow based upscaling for the transmissibility parameters.

Table 1 shows the different models (model 1 to 7) that werecreated, their cell dimensions, their simulation runtime, and theirleast squares error misfits relative to the initial model. The totalspatial misfit was calculated for pressure distribution, water satu-ration distribution and gas saturation distribution in the field, whilethe total well data misfit was calculated for oil production, gasproduction, water production and field pressure (Fig. 3 (a)). Allthese outputs were combined equally to generate the combined

misfit. Fig. 3 (b) shows the total spatial misfit, total well data misfitand the combined misfit for the model outputs plotted againstsimulation model runtime.

Model 5 was selected as the most suitable model for the historymatching exercise in terms of runtime efficiency and simulationaccuracy. It was upscaled laterally by a factor of 4, such that itsvertical heterogeneity is preserved and the material balance in themodel is conserved so as to maintain the characteristics of the fieldgeology and reservoir quality (King, 2007). Model 5 does not havethe lowest misfit or the fastest runtime, but its selection makes thepoint that there is often a need to trade-off between simulationmodel output accuracy and simulation model runtime in everyupscaling exercise as highlighted by Maschio and Schiozer (2003).They state that the loss of information is inevitable using anyupscaling technique, and that the two key aspects that must betaken into account are the agreement of the results obtained fromthe upscaled model when compared to the initial model, and theupscaling computational performance. Having conditioned thesimulation model to an acceptable runtime for history matching,the 4D seismic data is now conditioned to be an input into thehistory matching process.

Table 1The parameters of the different upscaledmodels as compared to the initial model. Model 5was selected as themost suitablemodel for the historymatching exercise in terms ofrun time efficiency and simulation accuracy (see Fig. 3).

Cell Dimensions Runtime (Mins) Spatial Misfit Well Data Misfit Combined Misfit

Base case 128 � 53 � 35 295.24 0 0 0Model 1 32 � 53 � 07 1.03 0.5066 0.5539 0.3073Model 2 64 � 27 � 17 7.01 0.4372 0.6084 0.2978Model 3 32 � 53 � 35 8.27 0.4942 0.6484 0.3268Model 4 128 � 53 � 07 9.21 0.4150 0.6234 0.2942Model 5 64 � 27 � 35 9.45 0.3919 0.5239 0.2616Model 6 64 � 53 � 35 28.34 0.3597 0.4995 0.2448Model 7 128 � 27 � 35 40.94 0.3953 0.5424 0.2674

Fig. 3. (a) shows the cumulative field oil production, cumulative field gas production, cumulative field water production and field average pressure for the initial base case model,the chosen model (model 5), and the worst case model after upscaling (b) shows the total spatial misfit, total well data misfit, and the combined misfit versus simulation runtime forall the upscaled models highlighting the chosen model 5 in a light green square. FOPR; Field Oil Production Rate, FGPT: Field Gas Production Rate, FWPT: Field Water ProductionRate, FOPR; Field Production Rate. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)


3.2. 4D seismic data conditioning

The concept of 4D seismic data integration is to complementproduction data. 4D seismic data has broad spatial and low tem-poral frequency while production data has low spatial and broadtemporal frequency (Jin et al., 2012). The corresponding charac-teristics of these data aid in obtaining realistic models of thereservoir through a seismic assisted history matching scheme.History matching is an inverse problem, it is a process of simulta-neously perturbing reservoir parameters such that it can be rep-resented as a minimization problem with the aim of reducing themisfit between the observed data and model predicted data

through an objective function where observed dynamic data areused to condition the reservoir model. The use of the conventionalleast squares formulation for computing production data misfit hasbeen shown to be suitable and efficient (Oliver and Chen, 2011),such that it can be significantly reduced during the historymatching process, and properly characterizes the error between thesimulated data and the real data. However, applying the leastsquares formulation to compute the seismic objective function andmismatch has been shown to be unsuitable because of the nature ofseismic data (Aanonsen et al., 2003; Roggero et al., 2012; Le Ravalecet al., 2012; Tillier et al., 2013), hence the need to search for asuitable alternative.


The proposed approach is such that the observed 4D seismicdata is converted to binary seismic gas and water maps. Theobserved 4D seismic data is initially clustered and separated into‘softening’ and ‘hardening’ signals; historical production data arethen superimposed on the maps to aid the interpretation anddeciphering of potential gas and water signals due to the injector/producer positioning, as well as the volumes produced which arerepresented by the size of the bubble in the bubble chart. Appli-cation of these processes leads to the final binary seismic gas andwater maps as shown in Fig. 4. The softening and hardening signalson seismic are represented by red and blue colours respectively.The softening signal is as a consequence of pressure increase or gassaturation increase. A drainage process will give rise to a softeningsignal due to the different elastic properties of the fluids, as a non-wetting phase fluid displaces a wetting phase fluid, i.e. gas dis-placing oil or water, or oil displacing water. Conversely, a hardeningsignal is as a consequence of pressure decrease or an imbibitionprocess, where awetting phase fluid displaces a non-wetting phasefluid, i.e. water displacing oil or gas, or oil displacing gas. Fig. 4highlights an example of generating the binary maps from 4Dseismic data, by clustering the 4D seismic data into “hardening” and“softening” signals using k-means clustering, and then interpretingthe binary gas and water signals with a validation against waterinjection and oil production at wells. The inter-mixing betweenwater saturation, gas saturation and pressure signals in the 4Dseismic data will likely be characterised in the “ambiguous signal”region (shown on the colour bar in Fig. 4), and will therefore not becaptured by the binary approach.

For the seismic binary representation, a detectable change insaturation is assigned a value of one, while no change is assignedzero. The pore volume weighted gas and pore volume weightedwater saturation difference maps (monitor year minus baselineyear) are also generated from the simulation model and then

Fig. 4. The process of generating the binary (gas and water) maps from the 4D seismic data. Tsignals; historical production data are then introduced to aid the interpretation and decipheas the volumes produced which are represented by the size of the bubble in the bubble chaInset shows the 4D seismic colour bar in amplitudes and the associated physical interpreta

converted to binary simulation gas and water maps, where a valueof one also represents presence of gas or water respectively, andzero represents an absence of gas and water respectively. The bi-nary seismic maps (gas and water) are then compared to thosepredicted from the simulation maps using a binary seismic objec-tive function. The objective function is calculated on the simulationmodel scale, so the 4D seismic data is arithmetically upscaled to thesimulation model scale before converting to binary maps.

In order to convert to binary maps, cut-off values representingthresholds need to be obtained. These can be derived from a cali-bration exercise using seismic forward modelling, or by interactiveinterpretation which requires a clear understanding of the 4Dseismic response in terms of the dynamic behaviour of the reservoir(Jin et al., 2012). A combination of both methods is utilised, whereseismic forward modelling is used to determine the initialthreshold values in collaboration with k-means clustering; thenintegration of reservoir engineering knowledge, injector and pro-ducer well activities, reservoir geology and structural contour, aswell as 4D seismic concepts are applied to generate the binaryseismic maps.

The procedure for interpreting a suitable threshold is shownbelow:

a. To interpret as exsolved gas, the reservoir pressure should bebelow bubble point pressure, or at least should have previouslybeen below bubble point pressure, so that there will be gas(exsolved gas) present in the reservoir.b. The presence of gas signal around a producer well is validatedfrom gas production profile of the well.c. The gas may be present at expected locations, for example atlocal structural highs.d. The presence of water is expected around water injector wells

he 4D seismic data are initially clustered and separated into ‘hardening’ and ‘softening’ring of potential gas and water signals due to the injector/producer positioning, as wellrt. Application of these processes leads to the final seismic binary gas and water maps.tion of the 3 subset regions.

Fig.procomreas


e. Being aware that amplitude decrease (softening) in the 4Dseismic data is as a consequence of gas, as well as pressure in-crease (Calvert et al., 2014), the amplitude decrease caused by anincrease in pressure around a water injection well is removedfrom the analysis; however in the case of a gas injector well(where an increase in pressure and the presence of gas cause thesame softening effect on seismic data), the magnitude of thepressure and gas saturation will need to be determined in orderto ascertain which has a more dominant effect on the seismicdata. It should be noted that there are no gas injector wells inthe data provided for this reservoir of interest.f. The same as above applies to an amplitude increase (hard-ening) in the 4D seismic data, which can be as a consequence ofwater saturation or pressure decrease, as it is unlikely forinjected water to coincide with a pressure decrease; hence anyhardening signal that is not around an injector well is ignored.

3.3. Binary objective function

The Current measurement metric (Glaun�es et al., 2008) is usedas the binary seismic objective function to quantify the similarity/dissimilarity between the binary simulated pore-volume weightedsaturation difference map and the binary 4D seismic data differ-ence map. Some of the advantages of this binary approach are thatit eliminates the magnitude of the difference in values of thesimulator output and the seismic data and simplifies the compar-ison, as opposed to a normalisation exercise which will only enablethe data have the same range (i.e. the gas saturation differencemaximum range value is 100, while that of the 4D seismic differ-ence amplitudes can be more than 10 000), it bypasses the complex

5. Binary Seismic Assisted History Matching Workflow - combining the production dataduction history match loop; the continuous black arrows (lower part) highlight the seismbined path; while the green arrows (circular arrows) shows the direction of the loop. Ton. (For interpretation of the references to colour in this figure legend, the reader is re

petro-elastic model procedure, it provides a means of comparingthe observed seismic data to the simulation model output, and thatit is a fast and effective method of extracting useful informationfrom the data. It should also be noted that the selection of appro-priate weight coefficient values for obtaining the objective functionis usually driven by reservoir engineering experience and can becase-dependent (Tillier et al., 2012). For the production data, thepractice of boosting the effects of the ill-fitted production data isadopted, and this is done by selecting the weights as being pro-portional to the square of the difference between the datacomputed for the base case model and the observed data (Kretzet al., 2004); while the different time steps of the binary seismicdata are equally weighted. The combined production data and 4Dseismic data objective function is normalized (Kretz et al., 2004)such that at the initial iteration of the history match, the combinedmisfit is a value of one, and this is shown in equation (1) below:

O:F: ¼ 12

XNp

i¼1

fhi � sig2 þ12½HCMM � (1)

where Np represents the production data analysed, h is the his-torical observed data while s is the simulated output. The HCMM isthe Current measurement metric (Glaun�es et al., 2008) we havechosen to compare the misfit between the seismic and simulatedbinary images and it is represented by equation (2)).

HCMM ¼XNs

i;j¼1

Kij

��cAij � cBij��2

(2)

where Ns represents the seismic time steps, A and B are the seismic

with the time-lapse seismic data. The continuous blue arrows (upper part) highlight theic history match loop; the orange arrows (middle part) showcases their individual or

he dotted blue arrows highlights the potential of updating the geological model withinferred to the web version of this article.)


and simulation binarymaps respectively, cAij and cBij denote the (i,j)-th Fourier coefficients of A and B, and K is the smoothing kernel. Thesmoothing kernel is mathematically represented by equation (3):

Kij ¼�i2 þ j2

�2�1þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffii2 þ j2

q ��p

(3)

where p is the smoothing parameter. When p is small the normbecomes more local, which means that small details are wellmeasured but large translations are not captured; however as pbecomes large, the norm becomes large and small details are

Fig. 6. The sensitivity analysis of the initial 104 parameters to the production data (oil, gassensitivity parameters are shown (top seven). From these parameters, 35 are selected forgeobodies after the sensitivity analysis.

Table 2Model Parameterization for history matching the reservoir. The global parameters are paare parameters that are perturbed over selected regions/geobodies.

Parameters Number Lo

Global NTG Multiplier 1 0Global Perm. Multiplier 3 0Global Poro. Multiplier 1 0Global Pore Vol. Multiplier 1 0Transmissibility Multiplier 3 0Regional NTG Multiplier 7 0Regional Perm. Multiplier 14 0Regional Pore Vol. Multiplier 3 0Critical Water Saturation 1 0Critical Gas Saturation 1 0Total Number of Parameters 35

missed while the larger displacements are well measured. Moredetails on the Current measurement metric and the smoothingkernel can be found in Chesseboeuf et al. (2015), applications andtests using this metric can be found in Chassagne et al., 2016.

3.4. Setting the scene

To perform the history match, an initial ensemble of models iscreated using the Latin Hypercube Experimental Design (LHED)method as implemented in Roggero et al. (2007), as multiplemodels have extensive coverage of the search space and deliver

and water) of wells P1 and P2, and also to the binary gas and water maps. The mostthe history matching exercise. Also shown are the initial geobodies, and the selected

rameters that are perturbed over the entire reservoir, while the regional parameters

wer Limit Start Value Upper Limit

.35 1 2

.35 1 5

.35 1 2

.35 1 21 3

.35 1 2

.35 1 5

.35 1 2

.4 0.428 0.50.001 0.05


robust results. The initial input parameter sampling is important,and is usually carried out using experimental design methods, suchas Plackett-Burman, LHED or Factorial Design (Schulze-Riegert andGhedan, 2007; Zubarev, 2009). The LHED is a statistical method forgenerating a sample of plausible collections of parameter valuesfrom a multidimensional distribution, and it is useful for exploringthe uncertainty range (Schulze-Riegert and Ghedan, 2007; Rissoet al., 2011; Maschio and Schiozer, 2014). An optimization algo-rithm is required for the optimization process in order to calibrateuncertain values in the reservoir. The optimization algorithm

Fig. 7. Normalized production profiles for wells P1 (left column) and P2 (right column) hiproduction data and binary seismic (gas and water), using Current measurement metric. (Forthe web version of this article.)

should be robust with suitable performance, deliver reproducibleresults and solutions within the uncertainty framework, and besimple to understand and implement (Schulze-Riegert and Ghedan,2007). The evolutionary algorithm satisfies these conditions, andcovers a broad application area, and has been used extensively forreservoir history matching (Schulze-Riegert and Ghedan, 2007;Maschio et al., 2008; Aranha et al., 2015). It is a derivative-freeoptimization method, as it does not require the computation ofthe gradient in the optimization problem (which will require accessto the simulator source code), and utilises only the objective

ghlighting the improved model responses (dark blue lines), after history matching tointerpretation of the references to colour in this figure legend, the reader is referred to


function value to determine new search steps. The basic outline ofthe evolutionary algorithm is based on the notion of Darwinianevolution where natural selection inspires “survival of the fittest”which leads to an increase in population fitness. The selection ofnew search steps are generated by applying recombination andmutation operators which generate new set of outputs. Based ontheir fitness, some of the outputs from the previous generation areconsidered for the next generation, and this process continues untiloutputs with sufficient fitness are found (Schulze-Riegert andGhedan, 2007).

In history matching, the termination criteria which signifies thecompletion of the exercise is usually until the objective function issmall enough, convergence is obtained, or the number of iterationsexceeds a maximum value (Tillier et al., 2012). The terminationcriteria used in this work is the convergence criteria. Whenconvergence of the objective function is achieved, an improved setof models and their accompanying uncertainty is generated. Theuncertainty is generated as a function of the variation in theresponse parameters. The probability redistribution of the a prioriuncertain parameters reduces the spread of the a posteriori dis-tribution, and as a direct consequence, reduces the dispersion of thereservoir response parameters, hence mitigating risk and uncer-tainty (Maschio and Schiozer, 2014). One of the advantages of usingthis approach is that multiple initial realizations can be updated tomatch the same dynamic data to assess uncertainty reduction inthe reservoir characterisation due to the integration of dynamicdata, and this is similar to the randomized maximum likelihoodmethod (Liu et al., 2001; Wen et al., 2006).

Fig. 8. The seismic binary (gas and water) maps compared to the simulation binary (gas andi.e. first 7 years will be used for the history matching exercise, while the last 2 monitors (t

As has been mentioned, the history matching exercise will beapplied using production data alone, binary seismic data (gas andwater independently) alone, and the combination of productiondata and binary seismic data (gas and water). Fig. 5 shows theworkflow for the binary seismic assisted history matching whichhas been developed using Python programming language andMEPO software.

3.5. Model parameterization

In order to proceed in a history matching exercise, pertinentreservoir parameters have to be perturbed. Over the years of pro-duction in this reservoir, it has been observed that the major chal-lenges to the field development and management plan are the fieldconnectivity and the representation of its numerous geobodies.These geobodies were derived from the 3D seismic interpretationand used for geologicalmodel construction. An experimental designsensitivity study starting with 104 parameters was implemented todetermine which parameters and geobodies were most significantto the seismic assisted history matching objective function.

Fig. 6 shows the top 7 most significant parameters of thesensitivity analysis for gas production, oil production and waterproduction for wells P1 and P2 which would be used for the historymatching study, as well as the binary gas and water maps.Combining the geobody regions and global parameters, 35 pa-rameters were identified for the history matching exercise. Theseinclude the permeability multipliers, porosity multipliers, net-to-gross multipliers, pore volume multipliers, geobody

water) maps highlighting areas of mismatch. The first 4 monitors (the first four rows),he last 2 rows) i.e. last 3 years will be used for the forecasting analysis.


transmissibility multipliers, connate water saturation and criticalgas saturation. Table 2 shows all the parameters and the rangesused. The starting values of the parameters are the initial values,while the ranges are selected generally based on engineeringjudgement to cover possibilities, and such that the perturbedmodel remains physically and geologically meaningful andconsistent with the initial understanding of the field.

The upper limit of the volumetric parameter multipliers (NTG,porosity, pore volume) is twice their initial value, which exploresmost possibilities, while the lower limit is 0.35, such that thereservoir cells are not de-activated. The upper limit of the trans-missibility multiplier is three times the initial value, while thelower limit is zero, thus preventing any flow or communicationacross the transmissible boundary. The upper limit of the perme-ability multiplier is 5, while the lower limit is 0.35. The upper limitof the critical water saturation, which is the saturation at which thewater would gain mobility is 0.5, while the lower limit is 0.4. Theupper limit of the critical gas saturation, which is the saturation atwhich the gas would gainmobility is 0.05, while the lower limit is 0,which implies that at the point of gas exsolution, the gas becomesmobile immediately. These range of values have been identified inorder to characterize the reservoir in a realistic manner, however itis noted that the end values which are the limits might not be verypractical, but are useful to use as limits.

4. Application of binary seismic history matching

The initial state of the reservoir, base case conditions andimproved models of the history matching process are shown in

Fig. 9. The updated binary simulation maps compared to the binary seismic maps highlight(gas and water), using Current measurement metric.

Figs. 7e9. Fig. 7 shows the observed data, the base case model, theinitial ensemble and the improved models of the response pa-rameters (oil production rate, gas production rate and water pro-duction rate) of wells P1 and P2 which have been selected for thishistory matching exercise due to their location and availability ofhistorical data. The observed data represents data measured at thewells, the base case represents the initial model's production pro-file, while the initial ensemble represents profiles for the modelsgenerated using the Latin Hypercube Experimental Design whichencompasses the effects of the defined uncertain parameters.

The observed oil production rate and gas production rate ofproducer well P1 drops continuously for the first 3 years until animproved oil recovery plan is put in place by introducing injectorwell I5 to provide pressure support as well as water to sweep theoil. This action stabilizes the production rate for the subsequentyears. The same trend is observed for producer well P2, howeverthe oil production rate drops continuously for the first 4 years untilan inefficient injector well is replaced. The introduction of the newinjector well boosts and maintains the oil production rate for thesubsequent years until it gently declines.

The gas production rate of producer well P2 is high for the first 4years as there is gas exsolution in the reservoir due to poor pressuremaintenance, when this is curbed by introducing an injector well,the gas production rate drops and declines in the subsequent years.There is also uncertainty on some sporadic high values of gasproduction rate on producer well P2 which can potentially beattributed to noise errors (e.g. faulty gauge or just inaccuratereadings). The water production in wells P1 and P2 occurs signifi-cantly in the later years due to a rise in water cut from the water

ing areas of improvement after history matching to production data and binary seismic

Fig. 10. Normalized production profiles for wells P1 (left column) and P2 (right column) highlighting the improved model responses (dark blue lines), after history matching toproduction data and seismic data proxy. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)


swept from the injector wells.Fig. 8 shows the comparison of the seismic binary gas maps

versus the simulation binary gas maps, and the seismic binarywater maps versus the simulation binary watermaps. The gasmapsshow evidence of exsolved gas in the early years, and declining gasvolumes in the later years; while the water maps show littleamount of water in the early years but the water comes into fulleffect in the later years. The first 4 monitor surveys correspondingto the first 7 years will be used for the history match, while the last2 monitor surveys corresponding to the remaining 3 years will be

used to analyse the forecast. The areas of mismatch are highlightedwith question marks on the simulation binary gas and water mapsas compared to the seismic binary gas and water maps respectively,and getting the maps to match is the aim of the seismic assistedhistory matching exercise.

To history match to both production data and binary seismicdata (gas andwater), their combined objective function is weightedequally as previously stated, as per Kretz et al. (2004). After historymatching to both production data and 4D binary seismic data, theupdated production profile and saturation distribution are shown

Fig. 11. The base case 4D seismic maps, observed 4D seismic maps, and history matched (to production data and seismic data) 4D seismic maps for all the relevant time-steps. Thefirst 4 monitors (the first four rows) are used for the history matching exercise, while the last 2 monitors (the last 2 rows) are used for the forecasting analysis.


in Figs. 7 and 9. Fig. 7 shows the production profiles of the updatedmodels (in dark blue colour) and there is an improvement, whileFig. 9 shows the updated simulation binary maps compared to theseismic binary maps highlighting areas of significant improvementon both the updated gas maps and updated water maps. Fig. 12ashows the histograms of selected converging parameters, wherethe horizontal permeability multiplier is about 2.0, the critical gassaturation value tends towards a value of 3.5%, and the pore volumemultiplier is approximately 1.1.

The history matching exercise is also conducted when matchingto production data alone, binary seismic gas data alone, and binaryseismic water data alone (Obidegwu, 2015), and their forecastability will be discussed.

5. Application of seismic modelling approximation

In order to implement a seismic assisted history matchingscheme, the 4D seismic data has to be integrated into the historymatching loop. A procedure previously proposed and used by

MacBeth et al. (2004), Floricich (2006), Fursov (2015) and MacBethet al. (2016a) which enables quantitative estimation of the simi-larity between the seismic data and the simulation model outputwill be adopted as the conventional method. A relationship be-tween the seismic data and the average maps of the reservoirsimulation output dynamic properties (pressure distribution, watersaturation and gas saturation) is proposed and analysed. Co-efficients are derived which determine the impact of the individualdynamic properties on the generated seismic data, and a scalar map(ideally the baseline seismic) is applied to the dynamic propertiesso as to capture the effects of the reservoir geology, porosity, net-to-gross and general static properties. These relationships will be usedto generate the seismic response, thus avoiding a full physicsseismic modelling which is time consuming.

For the history match to both production data and seismicmodelling, their combined objective function has weights of equalproportion as stated previously. After history matching to bothproduction data and seismic modelling, the updated productionprofile and 4D seismic data proxy are shown in Figs. 10 and 11.


Fig. 10 shows the production profiles of the updated models (indark blue colour), and there is an improvement. The third columnon Fig. 11 shows the history matching to production data and 4Dseismic data proxy maps compared to the observed 4D seismicmaps (second column). There are some areas of hardening andsoftening signals match. Fig. 12b shows the histograms of selectedconverging parameters, where the horizontal permeability multi-plier is about 2.5, the critical gas saturation value tends towards avalue of 2.5%, and the pore volume multiplier is approximately 1.2.The history matching exercise is also conducted when matching tothe 4D seismic data proxy alone (Obidegwu, 2015), and the forecastability will be discussed.

6. Discussion

It has been shown that constraining the reservoir simulationmodel to a variety of data (4D seismic data, production data, both)

Fig. 12. (a) Histogram of selected parameters for HM to production data and binary seismicproxy. (c) Objective function and uncertainty plots for history matching using binary appro

affect the updated parameters differently, ideally more constraintsmean a better history matching solution (Wang and Kovscek, 2002;Katterbauer et al., 2015). When matching to binary seismic gas, thepermeability multipliers and critical gas saturation converged to areasonable degree, while the volumetric parameters (porosity, netto gross) remained relatively unconstrained. However, whenmatching to binary seismic water, volumetric parameters appear tohave a strong effect. Also the seismic modelling approximationanalysis seemed to improve the seismic match but the parametersdid not converge fully. In order to have a better grasp on thisanalysis, the objective function and uncertainty for the scenariosare plotted as shown in Fig. 12c. These have been normalized to avalue of 100 and 1 respectively for ease of comparison. It isobserved that combining the production data and binary seismic(gas and water) reduces the uncertainty and gives a reduced misfitvalue (Huang et al., 1998; Walker and Lane, 2007; Jin et al., 2011).The objective function and uncertainty of the proxy seismic

data. (b) Histogram of selected parameters for HM to production data and seismic dataach and proxy approach.

Table 3Forecast misfit for the average of the improved models. The well data misfit iscalculated using the least squares error, and the seismic misfit (gas and water) iscalculated using the Current measurement metric.

Well Data Seismic (Gas) Seismic (Water)

Basecase 14 285 4792 9254Seismic Gas alone 10 225 2901 8361Seismic Water alone 11 251 4125 5595Well & Seismic (G &W) 6054 2835 5711

Table 4Percentage improvement to the initial base case model using the Current mea-surement metric as the binary seismic objective function.

Well Data Seismic (Gas) Seismic (Water) Combined

Seismic Gas alone 28.40% 39.50% 9.60% 25.80%Seismic Water alone 21.20% 13.90% 39.50% 24.90%Well & Seismic (G &W) 57.60% 40.80% 38.30% 45.60%

Table 6Percentage improvement to the initial base case model.

Well Data Seismic Data Combined

Seismic alone 26.32% 35.98% 31.15%Well & Seismic 44.38% 30.38% 37.38%


analysis give relatively higher values, and a possible cause is thatthe absolute magnitude of the signals, as well as their positioningare being matched, hence making it more challenging. Bycomparing the updated models prediction with the initial modelpredictions (Tables 3, 4, 5 and 6), the forecasting ability can beassessed. It is found that matching to binary seismic gas alone givesa 26% improvement, matching to binary seismic water alone gives a25% improvement, while matching to combined production dataand binary seismic (gas and water) gives a combined 46% percentimprovement, with 58% improvement on well data match. On theother hand, matching to proxy seismic alone gives a 31%improvement, while matching to combined production data andproxy seismic gives a combined 37% improvement, with 44%improvement onwell data match. It is observed that combining theproduction data and binary seismic (gas and water) produces amore effective forecasting result than using the proxy seismicanalysis. Matching of production data alone will produce modelsthat match the reservoir behaviour at the wells, but these will notbe consistent with the overall fluid-flow behaviour (Kretz et al.,2004), and this is why the introduction of 4D seismic data isnecessary (Oliver and Chen, 2011; Katterbauer et al., 2015; Stephenand Kazemi, 2014; Tolstukhin et al., 2012), so as to capture the areain-between the wells and hence obtain a more robust predictivemodel. It can be concluded that for this case study, combining theproduction data and binary seismic (gas and water) produces themost effective result and it is believed that this method should beapplicable to other case studies and produce similar positiveresults.

Overall, the seismic integration within the history matchingprocedure is still an open question. If the seismic domain approach(Landa and Kumar, 2011) is selected, seismic modelling and a petro-elastic model have to be designed, and this introduces a significantuncertainty into the model. If we decide to bring the seismic to thepressure/saturation domain, the petro-elastic modelling is still anecessity, as well as an inversion process which is non-unique (Jinet al., 2011; Landrø, 2001). Finally an intermediate domain can be

Table 5Forecast misfit for the average of the improved models. The well data misfit iscalculated using the least squares error, and the seismic misfit is from seismicmodelling.

Well Data Seismic Data

Basecase 14 285 271 108Seismic alone 10 525 173 548Well & Seismic 7945 188 745

used, the seismic impedance domain, this is the preferred approachin most literature (Gosselin et al., 2003; Reiso et al., 2005; Roggeroet al., 2007; Emerick et al., 2007; Ayzenberg et al., 2013). Never-theless this last option also exhibits the disadvantages of the pre-vious ones. These different approaches require a lot of time toestablish the appropriate rock physics model or seismic modelling,moreover the uncertainty within these methods are very signifi-cant, which does not help to establish a robust update of the model.Some attempts to circumvent these issues have been published(Landa and Horne, 1997; Kretz et al., 2004; Wen et al., 2006; Jinet al., 2012; Rukavishnikov and Kurelenkov, 2012; Le Ravalecet al., 2012; Tillier et al., 2013; MacBeth et al., 2016b) using imageanalysis tools, binary processing, dynamic clusters or a seismicproxy, they constructed a more or less direct relation between theseismic and the simulation domain. The comparison of the uncer-tainty on the updatedmodel across methods is not an easy task andrarely achieved, especially when it is applied to a real dataset. Inthis study we applied to a UKCS field dataset, a 4D seismic historymatching method, which circumvents the conventional seismicmodelling approach. Also we compared the binary methodology toa seismic history matching exercise using a seismic proxy, thesetting up of a conventional seismic history matching as show inFig. 1 would have been an ultimate comparison but extremelycostly in terms of computing time and choices for the wholeworkflow which is often a matter of debates. The quantification ofuncertainty/errors and strict comparison in between seismic his-tory matching methods should be a preoccupation when it comesto test a new methodology, even if needed, it is really not a trivialassessment.

7. Conclusion and future work

Field scenarios that this method can be applicable to are fieldsthat exhibit gas exsolution (Kretz et al., 2004), water flood patterns(Jin et al., 2012), and have identifiable seismic signals. This isrequired in order to implement the interpretation of the data aswell as conversion to binary maps. For scenarios where there isuncertainty on the threshold values, a ternary (�1, 0, þ1) repre-sentation of the signal might be suitable as this helps reduce theambiguous region in the binary representation, also this additionalinformation could serve as a quantification of the uncertainty in thebinary seismic history matching process.

In addition for thick reservoirs (i.e. reservoirs above tuningthickness), a binary volumetric approach may be more suitable, asopposed to an averaged binary map method, but then the questionof how to include the third dimension in the objective function hasto be thought carefully.

Apart from the fact that this method is circumventing thetraditional way, the binary mapping has the ability to characterizephysical features we are sure of and use only this information toupdate the model which is by itself a certain philosophy on seismichistory matching, instead of massive data integration, we carefullyselect what should be used to update the model.

Acknowledgements

We thank the sponsors of the Edinburgh Time-Lapse Projectphase V and phase VI (BG, BP, CGG, Chevron, ConocoPhillips, ENI,


ExxonMobil, Hess, Ikon Science, Landmark, Maersk, Nexen, Norsar,OMV, Petoro, Petrobras, RSI, Shell, Statoil, Suncor, Taqa, TGS andTotal) for supporting this research. Also, special thanks to BP forproviding the data set. We thank Schlumberger for the use of theirPetrel, Eclipse and Mepo software.

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