Coupled Geological Modeling and History Matching ofFine-scale Curvilinear Flow Barriers

Lisa StrightJef Caers

Hongmei Li

Stanford Center for Reservoir Forecasting

May 2006

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Abstract

An accurate modeling of flow path connectivity is critical to reservoir flowperformance prediction. Flow path connectivity is controlled by the complexshape, extent and spatial relationships between pay intervals, their intersec-tion with wells, and the existence of flow barriers between wells. Thesefeatures can be represented in three different scales of reservoir modelingvariables: the large scale facies object, the mid-scale effective property atthe cell-center (porosity and permeability), and the extremely fine-scale con-sisting of thin flow barriers that cannot be accurately represented in currenthigh-resolution pixel-based models.

To preserve these important fine-scale geological features at the flow sim-ulation block scale, we propose introducing an additional modeling variableas the edge of a model cell. This cell edge is a continuous or categoricalvalue associated with the cell face and is defined in conjunction with thecell centered property which is often reserved for facies types and/or petro-physical properties. The edge property is modeled in conjunction with thepixel-based facies to preserve the correct spatial associations with the largescale facies objects during upscaling and history-matching. For the flow sim-ulation model, the edge properties are easily translated into transmissibilitymultipliers.

Using the example of 3D shale-drapes attached to channel-sand bodiesin a turbidite environment, we show how such shale drapes can be accu-rately upscaled and history matched to production data while maintainingthe geological concept that describes the drape geometry. The perturba-tion parameter in history matching is the continuity of the shales as theedge property. More generally, we show how this coupled modeling of cell-center and cell-edge allows for more flexible reservoir modeling, opening upthe potential for modeling and history matching complex geological featureseffectively at the scale that they are relevant, without additional computa-tional cost of flow simulation.

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1 Introduction

1.1 The Need to Model Thin, Irregularly-Shaped Surfaces

Reservoir stratigraphy is dominated by multi-scale structures that may im-pact the flow and recovery of reservoir fluids. One of the major challengesin reservoir modeling and simulation lies in our ability to capture the infor-mation at these various scales when it impacts the recovery prediction of areservoir model.

An example of a depositional environment where these multi-scale struc-tures are likely to occur is shown in the Figure 1. The figure shows a de-tailed turbidite system with amalgamated channel bodies. (Data courtesyof Shell). At the base of each channel is a shale drape (shown in yellow).These shale drapes are flow barriers that potentially compartmentalizes thereservoir depending on their continuity as a surface. The surface that rep-resent the shale drapes are irregularly-shaped and are at a significantly dif-ferent scale than the channel bodies. If these potential flow barriers are notincluded in the simulation model, predictions would severely misrepresentconnectivity and subsequent recovery. Therefore, it is not only the presenceof this fine scale feature that is important but the continuity as a flow barrierthat is critical to describing the reservoir flow.

Figure 1: Detailed geologic model containing fine scale heterogeneities,Model courtesy of Shell

These type of features exist in many different depositional settings. Forexample in the shales that exists between clinoforms or as mud drapes alongamalgamation surfaces in a meandering stream system. The methodologyset forth within this paper is general and could be applied to modeling anyfine-scale irregularly-shaped feature.

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1.2 Data Resolution

The process of modeling these shale drapes is complicated by the fact thattheir thicknesses may be on the order of centimeters and that they arecomplex curvilinear 3-dimensional surfaces. Figure 2 illustrates the largedisparity of scale at which core, well-log, seismic, and production data informthe reservoir. A well-log or core provide a point measurement that delineatesthe presence or absence of a shale drape. However, these data do not samplethe reservoir at a fine enough scale to deterministically describe the complex3-dimensional geometry of these curvilinear surfaces and whether they arecontinuous flow barriers. At the other end of the spectrum, seismic data ismuch too coarse to detect the shale drape.

Figure 2: The Missing Scale Problem

Even if we were able to deterministically describe these thin, irregularly-shaped surfaces from available data, their scale is orders of magnitude smallerthan the model gridblock of meters or 10s of meters in scale, hence a prob-lem presents itself. Ascribing this thin surface property to the entire gridcell will destroy its continuity as a surface and its role as a flow barrier.This implicit assumption, whereby the heterogeneity within that grid cell isignored and an explicit upscaling is performed, is often termed the missingscale problem.

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1.3 The Limitation of the Pixel

Current property modeling approaches focus on modeling the large-scale fa-cies bodies and the mid-scale effective properties. Boolean techniques orpixel–based techniques, such as 2–point sequential indicator simulation ormultiple–point geostatistics, can be used to generate channel locations andlarge-scale internal channel heterogeneity; however, they prove insufficientwhen attempting to model the fine-scale thin shale barrier as shown in Fig-ure 3. These classical geostatistical approaches work well with calibratedor effective properties, but they do not provide enough modeling flexibilityto capture the missing scale. Instead, the fine scale surface-based featureis enveloped into a much larger grid block as an effective property. Theproblem, therefore, of modeling thin, irregularly-shaped shales lies not withthe modeling techniques but, instead, is an inherent problem with the modeldiscretization and single point representation of geologic features with thepixel.

Figure 3 illustrates the loss of the missing scale through upscaling. Thefluid flow between the two base channels (red and gray) is inhibited by thecontinuous channel drape (black) separating the two channels. At this veryhigh resolution, the pixels are able to resolve and represent the shale surfaceas a barrier between the channels because the surface sufficiently inhibitsflow from one channel to another in a traditional 5-point (2D) or 9-point(3D) scheme in a flow simulator. However, the final goal of most reservoirmodeling is flow prediction and high resolution models require upscalingfor flow simulation to be feasible. Using standard upscaling techniques,the integrity of the shale barrier is compromised because it no longer acontinuous surface that separates the two channels.

Another option would be to use a conformable grid to explicitly modelthe location and the thickness of the channel and the channel drape. Withthis modeling approach, the thin shale layer could be represented with sur-faces and the cells contained between the two surfaces as flow barriers eitherwith transmissibility modifiers or zero vertical permeability values. Themain problem with this approach is that as the number of channels andchannel barriers increase the conformable grid becomes increasingly com-plex with variable cell sizes and shapes which may lead to convergence is-sues during simulation. Finally, geostatisical methods are most efficient ona Cartesian grid and are not adapted to accurately handle variable blockdistance and volume differences. While Cartesian grids may be over sim-plistic, they are robust, a feature that is useful when applying geostatisticaltechniques and automating history matching.

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Figure 3: Shales drape the bases of each channel and create separate flowunits in the reservoir. If this model is represented with pixels, upscalingdestroys the shale drape continuity.

Finally, when modeling approaches fail to capture important flow detail,the model is altered during the history matching process to match the mea-sured reservoir production and pressure data at the well over time. Thisapproach generally consists of modifying relative permeability, Kv/Kh ra-tios, and/or utilizing pore volume and transmissibility multipliers in thevicinity of the wells. These properties are perturbed manually until a matchis reached and the resulting model often lacks geologic consistency with theoriginal concept of the reservoir, and even geologic reality.

This paper presents a methodology to address these issues of modelingthin, irregularly-shaped features, such as shale drapes, with a new modelingvariable. This new modeling variable is the edge of a model cell that is acontinuous or categorical value associated with the cell face and is defined inconjunction with the cell centered property. The cell edge and cell-centeredproperty jointly define an edge model to capture the behavior of the flowbarriers in flow simulation through a simple translation into transmissibilitymultipliers. Because the extent and continuity of the cell edge is unknown,it is then perturbed until a history match is reached.

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2 Proposed Approach – Thinking Beyond Pixels

In order to solve this issue of modeling thin shales, we must start to thinkbeyond pixels, Boolean methods, conformable gridding and post-geologicmodeling history matching fixes. This paper presents a proposal for using“edge” properties in combination with multiple-point geostatistics to rep-resent the continuity of fine scale flow barriers. This is a general approachthat can be extended to many other geological phenomena. This approachutilizes the fact that flow barriers can be represented by zero transmissibilityvalues in a reservoir simulator to stop the flow between grid cells.

An example of such thinking is presented in Voelker (2005) who modeledthin, highly conductive fracture networks that behaved like flow conduits,also called super-k permeability, and spanned large portions of the reservoir.Voelker proposed using a well model to include the dominating effects ofthe fracture networks, shown in Equation (1). The well model is a set ofconnections in hydrostatic equilibrium connected via transmissibilities. Theconventional well model is represented simply as a set, Sw, of connectiontransmissibilities, Tw

j , in hydrostatic equilibrium,

Sw = {Tw1 , Tw

2 , . . . , Twj : ρfluid} (1)

where w is a fracture name, and j is the block being connected.The condition that the connections are in hydrostatic equilibrium is rep-

resented by ρfluid, the density of the well fluid. Voelker found that modelingthe fracture networks in this manner, as a set Sw of transmissibilities, de-coupled the simulation grid from the geologic description, allowed greaterflexibility in description of large-scale fracture networks and improved theability to model the impact of the fine scale, connected nature of the frac-tures all within the framework of the general implementation in conventionalflow simulators.

This is one of the great advantages of modeling with edges; their directlink with transmissibility in conventional flow simulators, hence their ap-peal in addressing the missing scale. As a matter of fact, any geostatisticalmodel of permeability is converted to a transmissibility, essentially an edgemodel, before flow simulation. This is not a new idea, since the option to settranmissibility values already exists in all commercial flow simulators. Thecontribution of this research is in creating an ”‘edge”’ model of tranmissi-bility values prior to simulation by only changing the edge property of eachcell. The advantage of this approach is that each simulation cell can carryinformation about block or rock matrix permeability, which contributes to

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the flow between two cells, along with a full edge model to create an addi-tional dimension that captures the fine scale flow barriers or baffles betweentwo cells.

Using this approach, it is possible to surpass the limitations of the pixel,and not only model the effect of fine scale flow barriers but also gain theflexibility to utilize more powerful history matching techniques such as theProbability Perturbation Method (Caers, 2002). This idea potentially opensa new world of modeling complex geological features efficiently at the scalethat they are relevant.

2.1 Transmissibilities — An Application of Edges

Fine-scale features can be captured in simulation with transmissibility barri-ers. A transmissibility is a value that defines the magnitude of flow betweentwo grid nodes and is defined at the cell face between two nodes. For exam-ple, review the simple 2–dimensional simulation model discretization schemeshown in Figure 4.

Equation (2) describes the magnitude of flow,

Figure 4: Represent-ing shale drapes withtransmissibility multi-pliers

q, of a given fluid, f , across the cell face from nodei − 1 to node i. The flow, q, is a function of thetransmissibility at the face between the two cellsand the pressure difference between the two cells:

qf = γi− 12(pi − pi−1) (2)

The transmissibility at the face between thetwo nodes, Equation (3), is defined as:

γi− 12

=

(Aλf

Bf∆x

)i− 1

2

kxi− 1

2

γmultiplier (3)

Where A is the cross sectional area across which the flow, qf , occurs, λf

is the fluid mobility, Bf is the fluid formation volume factor, and ∆x thedistance between node i to node i − 1.

The block effective permeabilities, kxi− 1

2

, are transferred to a transmissi-

bility value, γ, along the face i− 12 as a harmonic average of the two effective

block permeabilities:

kxi− 1

2

=∆xi + ∆xi−1

∆xiki

+ ∆xi−1

ki−1

(4)

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γmultiplier in Equation (4) is a transmissibility multiplier that can bealtered during simulation to control flow between blocks, thereby overrid-ing transmissibilities calculated from block permeabilities generated duringmodeling and subsequent upscaling. By default, γmultiplier is equal to 1.This allows the magnitude of the flow between the two nodes to be definedby the effective rock properties of nodes i and i− 1, ki and ki−1, not recog-nizing the missing scale rock property; the flow barrier between the twonodes.

However, the multiplier can be set a priori and can either be a categoricalvariable, 0 or 1, or a continuous variable from 0 to 1 to capture the effectsof fine scale flow barriers between nodes. In the case of the categoricaledge variable, when γmultiplier is equal to 0, then a continuous, fine scaleflow barrier is effectively represented between the two nodes. A barrier thatinhibits flow, but does not completely prohibit it, can be captured with acontinuous variable.

The challenge lies in defining a method to capture this edge informationwithin a grid cell as a numeric value. Additionally, this edge informationmust be coupled with the block property to remain geologically consistentand meaningful.

2.2 Defining a Coupled Edge Property and Block Property

Figure 5 outlines a scheme that defines edges as vectors of binary values ata cell, where each binary value represents the presence or absence of an edgeproperty on each side of the cell. This binary number can be converted toa numeric number for a single value representation.

The attractiveness of defining the edge property in this manner lies in thefact that each cell is coupled with its neighbors; 4 neighbors in 2-dimensionsand 6 neighbors in 3-dimensions. For example, a cell that is defined with aleft edge (1000 or 8) shares the same edge as the cell to its left as a rightedge (0001 or 1). Therefore, the vector or single numeric value defined ateach cell carries details about the edge properties of the cell and the neigh-boring cells. Additionally, each cell carries the categorical or continuousproperty information at the cell center. This property should be explicitlycoupled with the edge property in a vector to ensure that the edge defini-tion is consistent with the controlling geologic geometry in the subsequentgeostatistical simulations.

The previous description was for codes in 2D. Extending the codes to3D is a simple exercise in bookkeeping. The representation of the edgeproperties in 3D are shown in Figure 6.

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Figure 5: Representation of edge properties on a 2D grid

Figure 6: Representation of edge properties on a 3D grid

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2.3 Building an Edge Model

The process for generating an edge model can easily be demonstrated witha simple, 2–dimensional picture of multiple, stacked, meandering channels,Figure 7. Below is the workflow that describes a process for building anedge model.

Step 1. Construct a geologically-based model at any scale and in any for-mat. Define the large-scale and fine-scale facies relationships between,for example, channels and shale drapes. Index each large-scale faciesbody, from 1 to number of facies bodies. An example input couldbe a deterministic or unconditional Boolean model where each large-scale facies body is indexed individually and the edges separate theindividual facies bodies.

Step 2. Select a model grid size defined by number of cells in x- and z-directions, nx, nz and the cell size in the x- and z-directions, dx, dz.This grid is ultimately the simulation grid, so choose the size accord-ingly. Superimpose this grid over the image from Step 1 and place gridnodes at the center of each grid cell.

Step 3. Start a search in the x-direction of the grid stopping to check forthe presence of the barrier between grid nodes. If the pixel value of thetwo nodes differs, then the edge between the two nodes is flagged as ashale. The assumption is that if a barrier is a continuous surface and ifthe barrier is detected along the line between the two grid points thenthere is no flow between the two grid nodes. Repeat for z-direction(and y-direction if model is 3D).

Step 4. Finally search all grid nodes to get categorical block properties,for example channel or non-channel, or use an upscaling technique toobtain an effective continuous block property.

An example of this process is shown in Figure 7 where a fine-scalegeologic model is generated (Step 1, left side of Figure 7) and a coarsesimulation-scale grid is generated and overlain on the geologic model (Step2, right side of Figure 7). The edge property in this example is defined as thepresence or absence of a shale barrier (blue) between two nodes. This edgeis then directly transferable to the simulator as a transmissibility multiplier.At each node of the edge model is a numeric value describing the categori-cal edge configuration and a pixel-value describing channel or non-channelfacies.

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Figure 7: Simple 2D Edge Model. Initial geologic model (left) and finalcoupled edge and pixel model (right)

An important point to note about this edge model is that the multi-scale channel model is discretized into a significantly coarser regular Carte-sian grid through the edge model building process. Although the explicitdescription of the channel shape is compromised, the edge model shouldcapture the impact of the flow barriers and subsequent compartmentaliza-tion on the simulation model. Additionally, the coarse discretization makesit possible to transfer the simulated results directly to a simulation model,bypassing the upscaling process. This has significant implications for usingautomatic history matching techniques. However, there is an inherent up-scaling process between the original geologic model from Step 1 to the edgemodel. Section 3 outlines a process to define an appropriate choice for thelevel of coarsening to the upscaled grid. Therefore it is acceptable to usethis coarse discretization. This method is not limited to a Cartesian grid,however, and the Cartesian grid is chosen because of its robustness in com-mercial simulators. The same approach could be used with unstructuredgrids.

The previous example illustrated a process for building an edge modelwith a simple 2-dimensional case. In 3-dimensions, the edges become contin-uous surfaces that are directly associated with the location of the large-scalefacies bodies, Figure 8.

2.3.1 Visualization of Edges in 3-Dimensions

One of the challenges in building a model of edges in 3D is in visualizing theimage to check whether the edges are accurately representing the channelboundary and that the edges are connected completely to represent a com-

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Figure 8: Simple 3D Edge Model. Initial geologic model (left) and finalcoupled edge and pixel model (right)

plete surface. This issue was solved using visualization tools in MATLABthat allow the face of a cell to be plotted in 3D. The results of a 3D trainingimage example in the next section show the training image plotted in thisway. Additionally, xy-, xz- and yz-slices are also generated to check theconsistency of the edge property with the pixel property.

2.3.2 3-Dimensional Edge Model: The Shell Model

A fine scale, 100x100x209 cell, 3–dimensional model of multiple, stacked, me-andering channels was generated using SBEDTM (Geomodeling TechnologyCorporation, 2006), Figure 1. This model was then numbered sequentially,Figure 9 (top), and then the conformably gridded model was snapped toan edge model grid of 50x50x50 cells (Steps 1-3). The Cartesian griddedmodel of the channels was then searched in the x-, y- and z-directions todetect transition either from one channel to another, or from channel tobackground (Step 4). The result of this simple pixel-based search is thedetection of the channel edge. The final edge model, is shown in the bottomimage of Figure 9.

During the generation of such an edge model on a coarse grid, an up-scaling from a high resolution geologic model to a coarser edge model isperformed. Figures 1 and 9 show a geologic model that captures the shaledrape locations and thicknesses with surfaces. The resulting edge modelwas built on a Cartesian grid at a much coarser scale than the geologic grid.Not only was the model upscaled from a conformably gridded system to aCartesian gridded system, it also was upscaled from 100x100x209 cells to

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Figure 9: Process for building a 3D Edge Model out the Shell SBED Model.Initial geologic model (top) and Cartesian model (bottom) both with chan-nels sequentially numbered

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50x50x50 cells.The next section discusses a methodology to validate the selection of the

upscaled grid and its ability to honor the flow properties of the fine scalegeologic grid using pressure connection data.

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3 Upscaling

Generating an edge model provides the flexibility to represent edges on acoarse Cartesian grid, however, there is an upscaling process inherent in themodel building process. The previous section presented the methodology forbuilding an edge model without regard for the model grid selection. This isa critical step in building the edge model because it is important to preservethe flow behavior and connectivity of the fine scale model to the upscaledmodel. When working with an edge model, this upscaling step becomes allthe more critical.

This section presents a methodology to determine an appropriate level ofcoarsening. The results reveal that it is possible to upscale the edge propertywithout compromising the large scale flow connectivity while maintainingthe true compartmentalization as represented in the original fine scale modelwith flow barrier surface.

3.1 Choosing an Appropriate Grid for Upscaling

To investigate the loss of accuracy when upscaling the edge model, 3 differentcartesian simulation grids were chosen and the geologic model from Figure 1was upscaled to each of these grids. The resulting cartesian grids withsequentially numbered channels are shown in Figure 10.

For each of the above three grids, a constant high pressure boundary wasplaced at one end of the grid, while a constant low pressure boundary wasplaced at the other end. Each channel was tested in each grid if pressurecommunication existed from one end to the other. The logic in this processis that if the geologic model reveals a pressure connection for each channelfrom one end of the model to the other, then at least the upscaled modelshould also include this connection keeping in mind that each channel isa completely separated reservoir body due to the inclusion of fully sealingedges.

There are 18 channels in the original model and 15 out of the 18 chan-nels are continuous reservoir bodies. For example, channel 1 is shown inFigure 11 and for each of the three upscaled grids a pressure connectionexists, revealing that the connectivity of this large, continuous channel isnot strongly dependent upon the size of the upscaled grid.

The other end member is seen in Channel 15, Figure 12, where none ofthe grids have a pressure connection from end of the channel to the otherdue to downcutting of newer channels into this channel. Note that red ishigh pressure near the injector, white is low pressure near the producer and

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Figure 10: Various degrees of coarsening. Top grid shows geologic grid withchannels sequentially numbered. The lower three grids shows upscaled gridsfor the simulation model.

Figure 11: Channel 1 has a pressure connection from one end of the channelto the other independent of grid size.

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blue is the original reservoir pressure. The sections of the channel that arecompartmentalized in the coarse models are also compartmentalized in thefine models.

Figure 12: Channel 15 has a pressure connection from one end of the channelto the other independent of grid size.

Channel 2, Figure 13, shows some evidence that the 15 layer model istoo coarse. This is shown by the compartmentalized channel body in the15 layer model that is in complete communication in the 50 and 200 layermodels.

The summary of all of these results with a few additional grids can beseen in the following table. Note that the best grid size for upscaling waschosen as 50x50x50 although channel 15 was not connected as it was in theSBED model.

In summary, this section presented a methodology to select a simulationgrid such that the inherent upscaling in building the edge model preservednot only the large scale channel body connectivity, but also the continuity.This process shows the flexibility and adaptability of the edge propertiessince, as shown in Figure 3, pixel-based methods are unable to preserveedge continuity during the upscaling process.

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Figure 13: Channel 2 has a pressure connection from one end of the channelto the other for 200 layers and 50 layers, but has clearly been upscaled toocoarsely with 15 layers.

Figure 14: Summary of all of the upscaled results.

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4 Discontinuities in Edge Surfaces

All of the edge models presented so far have been continuous surfaces thatcompletely separate each individual large scale facies body into independentflow units. The other extreme is the case of complete absence of edge barrierswhere all of the flow units are fully connected. Comparisons between thewater saturation flood front profiles of these two end members is shown inFigure 15.

Figure 15: The two extremes of flow-unit connectivity. No shale drapesat the bases of channels results in plug flow and full shale drape coverageresults in completely separate flow units.

The top left image shows a piston-like oil displacement with water, whichis also demonstrated in a simple 2D layer model shown in the bottom leftimage. All of the water breaks through at one time at one pore volume ofmovable oil displaced as shown in the water production curve in the centerof the image. The top right image shows differential water advancement ineach of the separate flow units, also demonstrated with a simple 2D layermodel. The water production curve for this case is quite different than thepiston-like displacement case. At each timestep that water breaks through,there is a corresponding bump in the water production curve. Conceptually,the flow in the model with continuous shale drapes flows as if it were 18

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separate pipes from the injector to the producer and the flow in the modelwithout shale drapes flow as if there is one pipe from the injector to theproducer.

Outcrop data and production data from real fields have provided ampleevidence of the presence of ”‘holes”’ in the shale drapes. The amount ofcommunication between each of the separate flow units will be governedby the location, proportion, size and shape of these holes. The holes willhave a significant impact on the production profile and percentage of oilrecovery. The next section present a procedure for simulating holes in theshale drapes followed by a sensitivity analysis of the production data to thehole proportion and location.

4.1 Stochastically Generating Holes in the Shale Drapes

The process for generating holes in the continuous edge surfaces in 3D isoutlined in the steps below:

Step 1. Map the geologic model from depth coordinates to stratigraphiccoordinates. This is accomplished by taking the maximum lateral (i,j)extent of an individual facies body and collapsing the vertical extent(k) of the 3D facies structure into a 2D ”‘stratigraphic”’ representation.

Step 2. Each stratigraphic layer is now a region for hole simulation. Usinga geostatistical simulation method, holes are simulated in this strati-graphic space, where holes in each layer are simulated independentof one another. This is based on the assumption that the holes areonly associated with each large scale facies body and not across faciesbodies.

Step 3. For each stratigraphic layer, propagate the holes upward back intothe 3D edge model to generate the holes in the 3D model.

Step 4. If hole proportion is critical in 3D, check if the 3D hole propor-tion (surface area/total surface area) is preserved in this 2D to 3Dtransformation.

Section 4.1.1 demonstrates this process for a simple 2 channel modeland Section 4.1.2 demonstrates the process for the more complex 18 channelmodel.

Note that in Step 3, the holes are propagated vertically from 2D intothe 3D channel space, taking all of the cells that are intersected in the xy-,

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xz- and yz-planes. Depending on the size of the cells in the z-direction,this process may overestimate the proportion of holes in the 3D space asgenerated in the 2D space. The proportion preservation can be checked(Step 4) if this is a concern.

For the work in this paper, the proportion change from 2D to 3D isnot a critical parameter for two reasons. First, the models presented hereinhave significantly smaller cell sizes in the z-direction than in the x- and y-directions and are vertically exaggerated for display purposes only. For theShell model, the ratio of the vertical to lateral dimensions are approximately1:30 in the x-direction and 1:45 in the y-direction. Second, because the holesare a perturbation parameter in the history matching process and the exactproportions are not known, it is not as important to match exact proportionsfrom 2D to 3D.

4.1.1 Holes in Shale Drapes of a Simple 2 Channel Model

The process as outlined above is shown here for a simple 2 channel model.First, the channels in the depth grid (nx by ny by nz) are collapsed into astratigraphic grid (nx by ny by nchannels) (Step 1) Figure 16.

Figure 16: Transfer of depth grid to stratigraphic layer grid for a simple 2channel model.

Next, holes are stochastically simulated in each of the 2D regions. Fig-ure 17 shows the training image that was used to generate the holes, alongwith the resulting holes for each layer. The multiple-point algorithm snesimin SGEMS was used to generate these holes. A full 3D simulation wasperformed, using a template size that was only 2D. The resulting ”‘hole”’simulation is shown in the figure.

The location of holes is controlled by the simulation and that the propor-tion of holes is controlled by either, the proportion of holes in the training

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Figure 17: Stochastically simulate holes on a stratigraphic layer grid forthe simple 2 channel model with multiple point geostatistics and a trainingimage.

image or, if the servo system is used, a user specified proportion.Finally, once the holes are simulated, they are vertically propagated into

the 3D model as shown in Figure 18 (Step 3).

4.1.2 Holes in Shale Drapes of the Shell Model

The same process is applied to the more complex 18 channel model usingthe training image shown in Figure 19. The resulting model is shown inFigure 20.

4.2 Oil Recovery Sensitivity to Barrier Discontinuities

As one might expect the addition of holes to the model significantly increasesthe communication between the individual flow units. A sensitivity analysisof the impact of holes on field connectivity was performed by placing a singleinjector and a single producer in the model, changing the hole proportionand hole location, and comparing the results.

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Figure 18: Final 3D model of 2 channel system with holes.

Figure 19: Transfer of depth grid to stratigraphic layer grid for the 18channel model.

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Figure 20: Stochastically simulate holes on a stratigraphic layer grid for the18 channel model with multiple point geostatistics and a training image.

4.2.1 Hole Proportion

First the hole proportion was changed from 0% (complete drape coverage)to 100% (no drape present). The model was simulated until approximately1.25 pore volumes of water were injected and the resulting water cut and oilrecovery verses pore volumes injected were compared. The water saturationprofiles in the 3D models at the end of the simulation are shown in Figure 21and watercut and oil recovery plots are shown in Figure 22. The red line,case000, is 0% hole proportion (complete drape coverage) and the greenline, case100, is 100% hole proportion (no drape present). The oil recoveryfor all proportions between 0% and 100% are bound between these two endcases, case000 and case100. The proportion in this sensivity analysis wascontrolled by the training image and the servo system.

These results show that with approximately 20% proportion and above,there is not a significant different in the amount of bypassed oil. The 20%holes creates a significant amount of reservoir connectivity for this case.

4.2.2 Hole Location

Next, a single hole proportion of 15% was chosen and multiple realizationscreated to demonstrate the difference in water cut and oil recovery as a

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Figure 21: Water saturation profiles in the 3D model at the end of thesimulation show the sensitivity of fractional flow of water and oil recoveryto hole proportion.

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Figure 22: Fractional flow (left) and cumulative oil recovery (right) show thesensitivity of fractional flow of water and oil recovery to hole proportion.

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function of hole location. The water saturation profiles in the 3D modelsat the end of the simulation are shown in Figure 23 and watercut and oilrecovery plots are shown in Figure 24. The red line, case000, is 0% holeproportion (complete drape coverage) and the green line, case100, is 100%hole proportion (no drape present). The oil recovery for all realizations for15% proportion lie between 0% and 100% are bound between these two endcases, case000 and case100.

There is approximately a 20% difference in the oil recovery showing thesignificant impact of the location of these holes.

As a result of this significant impact that the continuity of shale drapeshave on reservoir recovery, it is imperative to correctly characterize theircontinuity. As mentioned in the introduction, a well log or core may providea point measurement to delineate presence or absence of the drape, but doesnot sufficiently sample the reservoir at a scale to determine the complex3-dimensional geometry of these curvilinear surfaces or whether they arecontinuous flow barriers. At the other end of the spectrum, seismic data ismuch to coarse to detect the shale drape.

One way to build a model that may make accurate predictions of reser-voir connectivity would be to use the production data to help to predict theconnectivity of the reservoir (or the uncertainty associated with reservoirconnectivity) based on the shale drape continuity. The next section shows,how using the production data, with the assumed model of shale drape asso-ciation with the channel base, the shale drape connectivity can be perturbedin an automatic history matching process to generate a model of reservoirconnectivity based on hole location.

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Figure 23: Water saturation profiles in the 3D model at the end of thesimulation show the sensitivity of fractional flow of water and oil recoveryto hole location.

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Figure 24: Fractional flow (left) and cumulative oil recovery (right) showthe sensitivity of fractional flow of water and oil recovery to hole location.

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5 Probability Perturbation Method forHistory Matching

The previous section showed the impact of the hole configuration on thereservoir production. It was proposed that production data might be usedto assess the uncertainty in reservoir connectivity as a function of shale drapecontinuity. The next section describes the process whereby drape hole loca-tion can be perturbed until a history match is reached, thereby generating amodel with a connectivity configuration that matches the production data.This history matching approach is a stochastic approach and could be per-formed multiple times to assess the uncertainty in reservoir connectivity.

One goal in the history matching process should be that the resultinghistory matched model should not violate the original geologic concept ofthe reservoir, in this case, hole configuration (shape, size, and proportion).Caers (2002) proposed a method called the Probability Perturbation Method(PPM), where the underlying probabilities of a geostatistical model are per-turbed instead of the model itself. The resulting history matched modelis not only coherent with the initial geologic concept, but also honors thedata used to build the original model, generally hard (well) data and soft(seismic) data.

5.1 Single Region PPM

5.1.1 Methodology for Perturbing Hole Locations

The underlying idea in the probability perturbation method is that there ex-ists a probability model, P (A | B) that was used to generate a geostatisticalrealization of facies, porosity or permeability, for example. This probabil-ity model comes from the 2-point or multiple-point sequential simulationprocess. For this application, P (A | B) is in words the probability of ahole in the shale drape (event A) occurring, given conditioning data (wells,seismic, cores, etc) (B). Perturbing event A directly to match productiondata could lead to a model that does not match input statistics and/or theintended geologic continuity. Instead the probability perturbation methodperturbs the underlying probabilities, P (A | B) instead of the model prop-erties directly.

The underlying probabilities are perturbed by introducing a new proba-bility, P (A | D), that is generated using the production data (D). In words,P (A | D) is the probability of a hole in the shale drape (event A) occurring,given the production data (D). This probability generated using Equation 5.

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P (A | D) = (1 − rD) i(0)(u) + rDP (A) (5)

where rD is a 1-dimensional perturbation parameter, P (A) is the mar-ginal distribution of A, u = (x, y, z) ∈ reservoir is the spatial location in thereservoir, and i(0) is an realization of the indicator (or continuous) randomfunction variable I(u) defined as

I (u) =

{1 if a given facies occurs at u0 else

In the case presented in this paper, the indicator values are (i(u) = 1)is a hole or (i(u) = 0) a shale drape. The complete model realization is i(0)

which is generated using the procedure outlines in Section 4.1.This perturbation is performed through the optimization of a 1-dimensional

”‘free”’ parameter, rD, that is between [0,1] and controls how much the orig-inal model is perturbed. To demonstrate the influence of rD consider thetwo end members of the rD variable. When rD is equal to 1, the originalmodel does not match the production data, and P (A | D) = P (A). A new,equiprobable realization i(1) is generated. When rD is equal to 0, the produc-tion data does not add any additional information and the initial realization,i(0), is retained. A value of rD between 0 and 1 generates a realization thatis a perturbation from realization i(0) toward i(1). For example, rD equal to0.5 would be a blend of the initial realization, i(0) and a new equiprobablerealization, i(1) and is generated from a combined probability, P (A | B,D).The combination is achieved using the Journel tau model (Journel, 2002).

There exists a value for rDopt between [0,1] that matches the productiondata better than the initial realization, i(0). A 1-dimensional optimization isperformed on the parameter, rD to find the optimal perturbation probabilityP (A | D) and subsequently, the optimal realization, i

(1)rDopt(u).

An objective function, O(rD), is evaluated to optimize the perturbationparameter. The objective function is a measure of mismatch between thehistorical production data (D) and the production response predicted fromthe simulation model (DS(rD)). The optimal rD is found by minimizing theobjective function,

rDopt = minrD{O(rD) =∥∥∥DS(rD) − D

∥∥∥} (6)

The workflow for PPM consists of an inner loop and an outer loop.The inner loop finds the optimum realization between the initial realizationand another equiprobable realization. The outer loop consists of replacing

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the initial realization with the previous optimum realization and changingthe random seed. The model space is systematically searched with thisprocedure in a path controlled by a subsequent selection of random seeds,starting with the initial seed to generate, i(0). The iterative loop is repeateduntil the objective function is met and a history match reached.

Finally, this method is applied to perturbing hole locations to match ahistorical production response from field data to predict reservoir connec-tivity.

5.1.2 Simple Model – Single Region PPM with Edges

A simple example is presented to illustrate the process of history matchingthe continuity of the shale drape and its subsequent effect on connectiv-ity between flow units. A reference model is selected with two channelsdiscretized on a small 10x15x7 simulation grid (Figure 25). There is oneinjector in the bottom channel and one producer in the upper channel andhole 5 cells long in the shale drape between the two channels at the far end ofthe model. The producer-injector and hole location forces the injected waterto travel from the injector, through the full extent of the base channel, upthrough the hole and then across the full extent of the upper channel to theproducer. This configuration is ideal to illustrate the impact of correct holeplacement on matching historical production data. If, during the historymatching process, a realization is selected in which a hole is placed directlybetween the injector-producer pair, the water will breakthrough too rapidlyand the model will not minimize the objective function.

The reference model was forward simulated to generate reference watercut, cumulative oil production and bottom hole pressure of the producercurves. These curves were used in the history matching process. The objec-tive function was:

O(rD) = w1

√√√√∑Ni=1 (WCUTS

rD − WCUThist)2

[WCUThist]N

+ w2

√√√√∑Ni=1 (WBHPS

rD − WBHPhist)2

[WBHPhist]N(7)

where WCUT is the water cut in the producing well and WBHP is thebottom hole pressure of the producer, w1 and w2 are the weights assignedto each separate parameter for the calculation of the objective function. To

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Figure 25: Synthetic model to demonstrate PPM with holes

commence the history matching process, a hole training image was chosenthat matched the size and shape of holes in the reference model. Thistraining image is shown in Figure 17. The training image grid is 30x30.

After 18 outer loop iterations with approximately 5 inner loop iterationseach, an optimal solution was obtained. The final results are shown inFigure 26. The reference model is shown in red, the initial guess shownin blue, and the final history matched model shown in green. Note that,although a history match has been reached, the hole location in the historymatched model and the reference model are not identical. The reason forthis discrepancy is that the location of the holes in the history matchedmodel are only important in the region where the two channels overlap.The remaining holes do not play a part in the history matching result. Asmodels become more complex with multiple contact surface between faciesbodies, this type of discrepancy will result in significant differences in historymatched models.

5.2 Multi-Region PPM

Reservoirs often have more than one well, and these wells usually have differ-ent responses due to the geological complexity and the well configuration.Typically, production data from one well (area) may be history matched

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Figure 26: History match results for simple 2 channel model. History matchobtained by perturbing hole location. Water cut (upper left), producerbottom-hole pressure (upper right), cumulative oil production (lower left)and final matched model (lower right).

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while production data from another well (area) is not. In Section 5.1, theSingle-Region PPM treats the whole reservoir as one region and uses a sin-gle perturbation parameter rD for entire reservoir. As a result, the wholereservoir is perturbed by a similar amount (Hoffman, 2005). If the amountof perturbation is too large for the area around history-matched well loca-tion, the match of this well will be destroyed. This will reduce the efficiencyof the history matching for the entire reservoir, or if the reservoir is verycomplicated, some wells might not be history matched at all. To overcomethis problem a Multi-Region PPM was proposed (Hoffman, 2005) which al-lows different amounts of perturbation to be applied to various areas of thereservoir.

5.2.1 Methodology

The idea of Multi-Region PPM is to perturb the properties that influenceproduction data for one region differently than the properties that affect pro-duction for another region by optimizing perturbation parameter for eachregion. The workflow for Multi-Region PPM is similar to the Single-RegionPPM, that is, it also consists of an inner loop and an outer loop. The in-ner loop finds the optimum realizations between the initial realization andan equiprobable realization. The outer loop consists of replacing the initialrealization with the previous optimum realization and changing the randomseed. However, there are two differences in optimization procedure: the firstdifference is that the objective function is calculated differently since mul-tiple perturbation parameters are defined instead of one parameter; conse-quently, the second difference is that Multi-Region PPM optimizes multipleparameters jointly while Single-Region PPM optimize one parameter.

Defining multiple parameters To perform Multi-Region PPM, the fieldproduction data needs to be split into K distinct units, D = {D1, D2, . . . , Dk},where a unit is a set of production data that is influenced by properties inthe same region. In other words, if the wells are located closely and havesimilar responses, these wells will be grouped together as one unit. Corre-spondingly, the area around these wells is defined as one distinct region.

Similarly, the simulated production data is divided into the same num-ber of units, DS =

{DS

1 , DS2 , . . . , DS

k

}. A single perturbation parameter is

assigned to each unit, and they are denoted as {rD1, rD2, . . . , rDk} whereK is the total number of distinct units to be matched. The objectivefunction defined in Single-Region PPM O(rD) now is rewritten in term of{rD1, rD2, . . . , rDk} as O(rD1, rD2, . . . , rDk) and can be decomposed into

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O(rD1, rD2, . . . , rDk) =K∑

k=1

Ok(rDk) (8)

Ok(rDk) =∥∥∥DS

k − Dk

∥∥∥ (9)

where Ok(rDk) denotes the objective function for each unit. The objec-tive is some measure of mismatch between historical production data andsimulated one. In this study, the mismatch is calculated by the least squareerror.

As presented before, one rDk corresponds to one region. So a specificvalue will be assigned to all grid nodes within one given region. To do this,first the geometry of regions should be defined. This could be done in manyways (Hoffman, 2005). In this study, a streamline method will be used.

Once rDk values are assigned to each grid node, u, they can be used tocalculate the soft probability P (A | D) as follows:

P (A | D) = (1 − rDk)i(0)(u) + rDkP (A) (10)

where A is for example, ”hole occurs”. P (A | D) is defined for the entirereservoir, R, with its local value depending on the region definition. Similarto the Single-Region PPM, P (A | D) is combined with P (A | B) usingJournel’s tau model to get a new probability profile. This new probabilitymodel is used to create a new realization, irDk(u).

Optimizing multiple parameters As previously stated, the objectivefunction Ok(rDk) is calculated for each unit (region) separately. This al-lows multiple rDk values to be modified. During optimization procedure,all K rDk values are updated based on the production data from one singleflow simulation. The rDk for each unit is determined by performing onestep of a one-dimensional optimization routine. But since there are multi-ple parameters, this one step is performed K times (Hoffman, 2005). Thestopping criteria or convergence is based on the overall objective calculatedby summing the multiple individual objectives Equation 10.

In the PPM method, the most CPU consuming part is the flow simula-tion. However, for Multi-Region PPM, the multiple perturbation parame-ters rDk are updated in parallel through one single flow simulation, and theflow simulation is performed only once per iteration which is the same asthe Single-Region PPM. Therefore, the Multi-Region PPM may have muchfaster convergence than the Single-Region PPM because it allows different

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amount of perturbation to be applied to different areas of reservoir for thesame number of flow simulations.

5.2.2 Simple Model – Mutli-Region PPM with Edges

A simple three-channel case is provided to better understand the Multi-Region PPM and to demonstrate how this algorithm can be applied toperturb edge properties. Some of the information used in this exampleis provided in Figure 27. The model with 12x15x10 grid includes 3 chan-nels (Figure 27a) that inter-cut with each other. Because of levee slump orother geological process, shale drape were often deposited on these channeledges. The location of these shale drapes will strongly affect the fluid flowin the reservoir. This example will apply Multi-Region PPM to perturb theshale drapes location on these channel edges to obtain history match of thereference data.

For simplification, one channel is treated as one region. Because the basechannel is completely connected with the background shale, its edge prop-erties are assumed to be determined and will not be perturbed. As a resultthere are two regions: the middle channel is region one and the top channelis region two. Figure 27b shows the edge model of these three channels.Similar to the simple model used in Single Region PPM (See Section 5.1),these 3D channels edges are projected onto 2-D surfaces (Figure 27c), andthe shale drape location will be perturbed on these surfaces.

To set up a reference model, a holes training image (Figure 27d) with100x100 grid is chosen instead of shale training image. This is because theshale coverage is as high as 90% in this case, thus shale is treated as back-ground. Using this training image, the multiple point simulation algorithmsnesim is applied to create the reference holes distribution model. Figure 27eshows one realization of the holes distribution for region one, and Figure 27fis one realization for region two. It should be noticed that (1) the dimensionof the holes training image is 100x100, while the simulated holes model isonly 12x15, so even simulated holes show larger size in the model than thetraining image, in fact the holes have the same actual dimension; (2) sinceonly those holes located on the edges where the two channels connect impactfluid flow, the holes that are not distributed on the overlapping part of thechannel are filtered out in Figure 27e & f for better visualization. The 2Dsurface model then is projected back onto the 3D channel edges (Figure 28),and the edge properties are expressed by transmissibility with 0 indicatingshale occurrences and 1 as holes presence.

One injector injects water into the base channel, one producer P1 pro-

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Figure 27: Reference model setting. (a) 3-channel geological model; (b) Edgemodel for this geological model; (c) three 2D surfaces corresponding to 3channels; (d) holes training image with 10% holes; (e) one holes distributionrealization for region one; (f) one holes distribution realization for regiontwo.

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duces oil from the middle channel, and another producer P2 produces fromthe top channel (Figure 28). The channel reservoir has constant porosity(20%) and permeability (1000mD). The model is a two-phase oil-water sys-tem. The viscosities of oil and water are 1.0 centipoise (cp). The densityof the oil is 40lb/ft3 and the water density is 62.24 lb/ft3. The oil-waterrelative permeability curves are shown in Figure 29. To enhance the impactof holes on flow, the oil and water mobility is set to 1 and there is no gravityand capillary pressure present.

There are two rDks, one for Well P1 and one for Well P2. After 1200days production, the production profiles of two producers are displayed inFigure 30. These two wells show very different responses. Since water firstreaches region one (middle channel), then goes up to region two (top chan-nel), Well P1 in region one has earlier breakthrough time and thus higherbottom hole pressure (BHP). These production data is used as referencedata. Next, the Multi-Region PPM algorithm described previously will beapplied to match reference data.

Figure 28: Edge model with holes distribution. Green box is injector, yellowboxes are producers

An initial realization is generated that is constrained only to the staticdata. Here since there is no well data available, the static data indicates thegeological information provided by the training image (Figure 27d)). Once

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Figure 29: Relative permeability for simple 3-channel example

the initial model is constructed, the flow simulation is completed on thisrealization using flow simulator eclipse (Schlumberger, 2004). The mismatchbetween reference data and simulated data is calculated. If the mismatch isbelow the tolerance, the history match is achieved. Otherwise, the algorithmthen optimizes rD1 and rD2 and thus the holes distribution is modified.The other model properties such as porosity and permeability remain fixedat their initial values. The standardized least square error between thereference water cut and simulated water cut is calculated as the mismatchvalue. Once the error is less than 0.2, the matching procedure is stopped. Inthis example, the error between the initial realization and the reference datais 7.03 which is larger than 0.2. Hence the hole locations will be modifiedusing Multi-Region PPM.

The algorithm then changes the random seed and enters the inner loop.It starts with an initial guess for rD1 and rD2. In this example, 0.3 is used.Two objective functions are calculated, one for rD1 and another for rD2.Then the optimization routine chooses the next rD1 and rD2 by bisection,and the same process is used to calculate the objective function values. Thethird point is also found by bisection, and their mismatches are calculated.Now, there are enough points to do parabolic interpolation. The remainingrDs are determined by either parabolic interpolation if it is well behaved, or

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Figure 30: Top: the oil saturation model; Bottom: the water cut and wellbottom hole pressure profiles for two producers

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by bisection. Once the optimization method has converged, the rD1and rD2

values, their summed mismatch value, and the realization that best matchthe data are returned to the main program. The program will replace theinitial realization with this optimum realization and changes the randomseed, then repeating the same optimization procedure until the summedmismatch reaches the tolerance 0.2.

Figure 31 shows the initial realization and the final best matched real-ization of the holes distributions. Figure 32 provides the oil production rate,water cut and the bottom hole pressure data for the three models (reference,initial and best matched). For Well P1, the water breakthrough for the ini-tial guess is later than for the reference. This is because the simulated holelocations in region one (left one of the two initial guess maps) are furtheraway from the injector compared with the reference model. As a result, thewater travels longer time to reach Well P1. On the other hand, for WellP2 which produce from top channel (region two), the water breakthroughfor the initial guess is much earlier than for the reference. This is becausethe hole location in region two (right one of the two initial guess maps) ismuch closer to the injector compared with the reference model, thus thewater travels to the Well P2 in a short time. However, the hole locations inthe best matched realization are almost the same as the reference model, anexcellent history matching is achieved.

The history match requires 32 outer iterations and around 120 flow simu-lations. Figure 33 shows the objective function value for the outer iterations,and Figure 34 shows one outer iteration profile and two inner iteration pro-files within this outer iteration. For the outer loop, the objective functionvalues drop rapidly for the first few iterations. However, it does have manylong periods where the model does not improve and it takes a large numberof iterations to reduce the last small amount in the objective function.

The objective function value for both inner iterations does not decreasemonotonically due to the non-continuous nature of the holes distributions(Figure 33). The optimum realization is not always the last one. In thisexample, the first realization is the optimum one. Since the best realizationis obtained based on the overall objective function value, the lowest objec-tive value for single unit may not be retained. In this example, the bestrealization is the first one, while for rD2 the lowest objective is the thirditeration. We also should notice that these two rDs have different values atthe same iteration procedure due to a different well response in each region;and the optimized rD values are usually different too.

To compare the efficiency of the Multi-Region PPM with the Single Re-gion PPM, the Single Region PPM is run for this example. The reference

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Figure 31: Initial realization and best realization. The blue color indicatesholes and the background gray is shale. Pink dots are well locations

Figure 32: Production profiles for three models: reference, initial guess andbest match

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Figure 33: The optimization profile for Multi-Region PPM

model and the production data are the same as used for Multi-Region PPM,the training image is also the same (Figure 27d). The Single Region PPMstarts with the same initial guess as Multi-Region PPM (Figure 31 left).The standardized least square error between the reference water cut andthe simulated water cut is calculated, and once the error is below 0.2, thehistory matching will stop. Figure 35 shows the best matched realizationand Figure 36 compares the production data profiles for both methods. Aswe observe, for this very simple reservoir model, these two approaches pro-vide similar results, and they match the history production data very well.Figure 37 shows the outer loop optimization profiles for Multi-Region PPMand Single Region PPM. The optimization profile using Multi-Region PPMdrops very fast than the one using Single Region PPM. The Single Re-gion PPM takes 45 outer iterations and around 225 flow simulations whileMulti-Region PPM takes 32 outer iterations and around 120 flow simula-tions. Even though these two approaches can provide the same good historymatched model, the Multi-Region PPM is much more efficient. As for thecomplicated reservoirs with multiple wells, at least in terms of efficiency, weshould choose Multi-Region PPM to perform the history matching

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Figure 34: Top: One outer iteration; Bottom: two inner iterations of tworDk values for this outer loop of Multi-Region PPM

46

Figure 35: One best matched realization using Single Region PPM

Figure 36: Production profiles for four models: Reference, initial guess, bestmatched using Multi-Region PPM, best matched using Multi-Region PPM

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Figure 37: Outer iterations for both methods

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6 History Matching the Shell Model

Two different cases were run where PPM was performed with only a singleregion and with multiple regions on the 18 channel model. The history matchparameter was the location of the holes in the shale drapes by matchingwater cut and bottom hole pressure of the producing well. The location ofthe channel bodies; hence, the shale drape location, was fixed.

Waterflooding with one PPM region The more complex 18 channelmodel was used to demonstrate how the complexity of flow unit connectivitydue to holes in the shale drapes could be history matched. A simple testwas generated to test the shale drape history matching methodology on thismore complicated model. The process was as follows:

1. Select a hole size (1/3 height of the channel and 3/4 the width of achannel), shape (elliptical) and proportion of 15%. These are the samehole configurations as shown in Section 4.1.2, Figure 20

2. Choose a single realization with the hole configuration described in Step1 and name it the ”‘truth”’ case. Figure 38. Flow simulate this real-ization and use this production as the historical production to match.

3. Select a new seed that changes only the hole location and use this modelas the initial guess.

4. Proceed with the history matching process until a history match is reached

The ’truth’ model is flow simulated with two wells, an injector and aproducer, as a water flood from one end of the model to the other. Theinjector is controlled on water injection rate and the producer is controlledby total liquid rate in the simulation. The fluid properties of the model werevery simple with a unit mobility and no gravity. Figure 38 shows the modelafter 1 year of production, along with a water cut curve for the field for fiveyears of production. This is the production history that will be matchedduring PPM.

Note that the character of the water cut curve is similar to what wasobserved for the extreme case of continuous shale drapes at the base ofeach channel where as the water for each flow unit breaks through to theproducer, there is a bump up in the water cut curve. In this case, therebumps in the curve are related to groups of flow units that were createdwhen holes generated communication between units.

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Figure 38: The reference model with 18 channels. Hole location (top), watercut curve (middle), and water saturation profile after 1 year (bottom).

50

A history match was performed for the first year of production and theremaining four years were treated as target for prediction. At one yearof production, approximately 35% of the oil was already recovered in thefield. The hypothesis was that if the model could be history matched signifi-cantly into the water flooding process, then the history match process of onlychanging the hole location should be able to predict reservoir connectivityand subsequent future production.

The 3D hole configuration of the history matched model next to the’truth’ model is shown in Figure 39. It is clear that these models have dras-tically different hole locations. However, plots of water cut, bottom holepressure of the producer, cumulative oil production and oil rate are shownin Figure 40 and show the results of the historical data (black), initial guess(red) and final history matched model (blue). These plots show that thehistory matching process has succeeded in matching the production history.But, how well does it predict the overall reservoir connectivity? The pre-diction for three out of four of these parameters show some departure fromthe reference, even though the match in the first year is very good.

The history matching process was able to match the first bundle of chan-nels or flow units connected by holes. However, later in the simulation phase,water reaches the producing well from a different set of bundled flow units.Therefore, matching the water production profile in the first year of historydoes not guarantee a fully accurate prediction of total reservoir connectivityfor this case.

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Figure 39: The 3D and select channel map view of the ’holes’ following thesuccessful history matching process. The top images are the ’Truth’ caseand the bottom images are the History-Matched model.

52

Figure 40: Plots showing the comparison of the prediction following thehistory matching of 1 year. Water cut (top left), bottom hole pressurein the producer (top right), cumulative oil recovery (bottom left) and oilproduction rage (bottom right). The ’truth’ model is shown in black, theinitial guess in red, and the 1-year matched result shown in blue.

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7 Summary

This paper presented the methodology for modeling, upscaling and historymatching discontinuous thin shales and reservoir connectivity using faciesand edges through the following processes:

• Defining a 3D edge property to capture the very fine-scale

• Upscaling to a grid that preserved the flow unit connectivity for 100%shale connectivity

• Perturbing the edge continuity using PPM by changing hole locationto match production history

It was demonstrated that a history match could be achieved that pre-dicted a model of reservoir connectivity to match the first year of the pro-duction data. Additionally, it was demonstrated that the multi-region PPMcould potentially achieve the same history match more quickly. This is ageneral approach that can be applied to many different depositional systems.

8 Future Work

The research presented in this paper contains many simplifications for thepurpose of demonstration of methodology for assessing and history matchingshale drape continuity. For example, petrophysical properties (porosity andpermeability) within the channels are held constant, the channel locationsare fixed and shale drapes are associated with the bases of these fixed chan-nels within a single channel belt, perturbation of the shale drape continuitywas only performed on hole location, and the shale drapes were consideredas categorical properties; sealing or non-sealing.

In light of these simplifications, future research will include the followingaspects:

• Perturbation of hole proportion and hole location by region

• Partially sealing (continuous) edge properties

Reservoir modeling will be added into the proposed workflow to closethe loop. The work includes:

• Model the location and connectivity of multiple scale features such ascanyons, channel belts and channel bodies

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• Sensitivity study to determine the communication between multi-scalefacies bodies and which scales most significantly impact the produc-tion, and what combination of production data should be used for theobjective function

• Explore method for constructing edge models in conjunction withchannels generated from geostatistical techniques, that is, generatingedge models for channels without fixed locations

• Generating multiple history matched models for uncertainty analysis

Finally, to define regions, a streamline method is proposed.

• Streamline simulation is fast and can be performed on relatively largemodels

• Streamlines can asses the reservoir connectivity, thereby defining thereservoir regions during the history matching process

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References

[1] Voelker, J. The Use of the Conventional Well Model toPredict the Effect of Discrete Fracture Network Flow onReservoir Flow Performance. SCRF Annual Meeting Re-port 5, Stanford Center for Reservoir Forecasting, Stan-ford, CA 94305-2220, May 2004.

[2] Caers, J., Krishnan, S., Wang, Y. and Kovscek, A. R.:”‘A Geostatistical Approach to Streamline-Based HistoryMatching,”’ Soc. Pet. Eng. Journal pp. 250-266, Septem-ber 2002.

[3] Journel, A. G.: Combining Knowledge from DiverseSources: an Alternative to Traditional Data IndependenceHypothesis, Mathematical Geology, Vol. 34, Iss. 5, July2002.

[4] Hoffman, T.: Geologically Consistent History MatchingWhile Perturbing Facies, Ph.D. Dissertation, StanfordUniversity, May 2005.

[5] Geomodeling Technology Corporation, SBED Manual,2006.

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