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GUSS14 - 01

Process-mimicking Modeling Considerations

MICHAEL PYRCZ, RICHARD SECH, JAKE COVAULT, TAO SUN, BRIAN WILLIS AND ZOLTÁN SYLVESTER

Chevron Energy Technology Company, Houston, TX, USA

This paper has been selected for presentation for the 2014 Gussow Geosciences Conference. The authors of this material have been cleared by all interested

companies/employers/clients to authorize the Canadian Society of Petroleum Geologists (CSPG), to make this material available to the attendees of Gussow 2014

and online.

ABSTRACT

Process-mimicking modeling methods approximate

sedimentary dynamics to generate numerical descriptions of

reservoir architecture and the spatial distribution of petro-

physical properties. By incorporating stratigraphic rules that

relate to the underlying geologic processes, process-

mimicking methods offer improved representation of

depositional heterogeneity, compared to conventional

modeling approaches. Moreover, since these methods

operate within a geostatistical framework, uncertainty can be

explored effectively by varying geologically meaningful

parameters, whilst maintaining consistency with input data

constraints.

We present background, motivation, advantages, limitations,

and examples of models for deepwater and fluvial

depositional environments, constructed using process-

mimicking methods that span a spectrum of complexity. A

few simple rules included in the modeling workflow are shown

to render continuity and spatial organization to petrophysical

property extremes that is difficult to obtain using other

reservoir modeling methods. When models are strongly

informed by stratigraphic rules, we observe emergent

behavior that differs depending on the geologic concept. As a

result of this effect, an ensemble of models with unique

scenarios and multiple realizations can be quickly produced

and applied to reservoir characterization. Inherent

stratigraphic controls in process-mimicking methods define

models that are hierarchical across almost all length scales of

interest in subsurface applications. Thus information

describing reservoir properties is preserved within the model

regardless of the level of detail explicitly rendered on a grid

(grid-free modeling), and can be rapidly incorporated (down-

scaling) or efficiently removed (up-scaling), as required.

Process-mimicking modeling methods offer a rich data

integration platform for incorporation of geologic concepts

into reservoir modeling. In addition, these modeling methods

enable a variety of modeling applications including;

assessment of the impact of model scale, testing of seismic

resolvability of features, value of information studies, flow

relevance of advanced architecture such as surface-based

interfaces, and numerical analogs for support of multiple

point statistics simulation (MPS) and object-based modeling.

There are limitations and trade-offs between the level of rule

complexity, simplicity of modeling inputs, general applicability

of modeling method and the level of data conditioning

remain. Despite remaining challenges, there is growing

acceptance that process-mimicking methods can significantly

advance reservoir modeling applications when architectural

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complexity is critical to support decision making in reservoir

modeling projects.

INTRODUCTION

Geologic heterogeneity characterization and modeling is

applied to model oil and gas reservoirs for improved decision

making in the face of uncertainty (see textbooks such as

Caers, 2005; Pyrcz and Deutsch, 2014). Many of these

projects are challenged and have a high level of complexity.

Complex subsurface fluid flow patterns associated with

geologic heterogeneity can be specific to depositional setting

of the reservoir deposits and fluid types. This is characterized

by flow barriers, baffles and conduits. Challenges to

development forecasting include: 1) the need to maximize

recovery and limit the number of wells drilled for information

and production, and 2) the difficulty of defining the reservoir

heterogeneity structure from sparse wells and resulting need

to rely on geologic analogues to infer the stratigraphic

architecture. In sparse data situations (e.g. early field

development stages, remote geographic locations, etc.), the

conceptual geologic model can span a multitude of different

possibilities. In such cases, most reservoir management

decisions are most appropriately considered upon the basis

of multiple reservoir models which preserve and test

alternative concept scenarios (Bentley & Woodhead, 1998;

Bentley & Smith, 2008).

Current geostatistical algorithms, object-based or pixel-

based, utilizing spatial continuity defined by semivariograms,

geometric parameters or training images, enable the

reproduction of spatial statistics inferred from available

conditioning data and analogues. They rarely integrate

information about to depositional processes. Indeed, because

conventional geostatistical models are constructed without

reference to time or depositional sequence, their ability to

incorporate sedimentological rules, for the organization of

facies geobodies and intra-body porosity/permeability

heterogeneity, is quite limited. One consequence of such a

limitation is that, unless spatial constraints tediously derived

from alternative depositional interpretations are explicitly

imposed to the simulation, conventional geostatistical

methods only generate low complexity stationary statistical

models, which may not be representative of the full range of

actual reservoir heterogeneity uncertainty (Pyrcz and

Strebelle, 2006).

Reservoir modeling techniques that mimic geologic processes

are amenable to these challenges of subsurface

characterization since they both are strongly informed by,

and honor, the geologic concept. Process-mimicking

methods, known by a variety of names such as event-based

(Pyrcz and Strebelle, 2006), hybrid (Michael et al., 2010), and

process-oriented modeling (Wen, 2005), are a category of

methods that attempt to improve geostatistical modeling

through the integration of sedimentological process rules.

Using these methods, it is possible to build complicated,

hierarchical reservoir models that integrate geologic

concepts, within grid-free frameworks for efficient

geometric-based representation (Hassanpour et al., 2013;

Pyrcz et al., 2012).

While these methods have been the target of various

research groups, they have not entered common practice;

that is, they are not generally available in user-friendly

geological modeling software packages, neither have they

been widely applied for practical problems with research

code. This paper provides motivation for the use of process-

mimicking methods, and discusses limitations, examples, and

applications of these methods, along with discussion. We

offer considerations to encourage the use of process-

mimicking modeling to address practical petroleum reservoir

exploitation problems.

BACKGROUND AND MOTIVATION FOR PROCESS-MIMICKING

MODELS

Stochastic conditional geostatistical simulation methods have

become standard tools in hydrocarbon exploitation

forecasting. Geostatistical models provide spatial

heterogeneity reproduction, data conditioning and

uncertainty characterization through multiple realizations

and scenarios (Deutsch and Journel, 1998; Caers, 2005; Pyrcz

and Deutsch, 2014). These tools attempt to reproduce the

data statistics and inferred spatial patterns within a frame

work of mapped surfaces and deterministically defined

property trends (or a set of frame work and trends scenarios

if uncertain).

Although geologic insights are used to define the large-scale

reservoir framework and intervals for statistical

characterization, methods based on statistical assessment of

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spare data are ultimately limited in their ability to reproduce

realistic geologic complexity patterns.

By contrast, process-based models attempt to refine rock

heterogeneity through a mathematical model of changing

depositional processes and surfaces through time. Patterns of

sediment erosion, transport and deposition are modeled as

the deposits aggrade the reservoir volume (Slingerland and

Kump, 2011; Syvitski, 2012). Common to all of these models

are limitations in the process understanding, the need to

simplify process relationships to run within computational

facilities, and the inaccessibility of initial and boundary

conditions. As a result, these models are unlikely to provide

reservoir prediction with local accuracy. There is simply no

way to exactly reconstruct the basin morphology, input

parameters, and influx rates at the time of reservoir

formation from a system that no longer exists.

Nevertheless, these models are valuable tools for

understanding the complex interplay of various allogenic and

autogenic processes and the resulting reservoir geometry,

trends, and heterogeneity that impact subsurface fluid flow.

For example, numerical models of open-channel flow and

sediment transport provide insights into the distribution of

fine-scale heterogeneities and complex 3D geometries in

fluvial reservoirs (see Figure 1).

Figure 1. A map view of a process-based fluvial meander

model with the preserved sediment grain size indicated by

the color scale. Note the rich complexity in the resulting

heterogeneity.

It is natural to consider the opportunity to merge – or find a

middle ground between – these two modeling approaches to

realize improved complexity in natural resource models and

to maximize the use of geologic knowledge when faced with

sparse local data. This is what the process-mimicking

techniques attempt to do.

The background of process-mimicking approaches is

discussed by Pyrcz and Deutsch (2014). In summary, they

include an evolution from (1) object-based models

(Haldorsen and Chang, 1986; Haldorsen and Lake, 1984;

Stoyan et al., 1987), to (2) object-based models with object

stacking and infill rules to (3) object-based models placed in

time sequence and tracking evolving time surfaces known as

surface-based models (Xie and Deutsch, 2000; Michael et al.,

2010) to (4) surface-based models that track flow paths and

placement rules that mimic erosion and depositional

processes and external controls (Jones, 2001; Patterson et al.,

2002; Pyrcz, 2004; Cojan at al., 2005; Pyrcz et al., 2005; Wen,

2005; Abrahamsen et al., 2008; Leiva, 2009; McHargue et al.,

2011; Sylvester et al., 2011,). In some cases, the focus has

been on the extraction of statistics from the process-based

model to inform the geostatistical model (Miller et al., 2008).

Other examples rely to a greater degree of determinism with

geologic mapping from outcrop and strongly constrained

stacking and filling rules (Sech at al., 2009).

Geostatistics includes a toolkit of simulation methods. It is

convenient to represent the methods on a continuum with

one extreme representing methods that are focused on the

integration of data conditioning and statistics derived from

the data and the other extreme representing methods that

rely on geologic concepts (see Figure 2). Variogram-based

methods would fall on the data conditioning side of the

continuum, given the use of variograms calculated from data

and with geologic concepts assisting with variogram modeling

and trends. Process-based models would fall at the extreme

for geologic concepts without concern for data conditioning.

Object-based models would fall closer to geologic concepts

through the use of geometries, but may also attempt to

condition to data through constraints on object geometries

and placement. Multiple point simulation (MPS) methods

span from variogram-based approaching object-based

methods for their ability to integrate geometric information

through the training image. Process-mimicking methods span

from object-based with simple objects and rules to

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approaching physics-based with rules that mimic process. In

this context process-mimicking methods play an important

role in expanding the scope of the geostatistical toolkit.

Figure 2. The continuum of modeling tools from focus on

data conditioning to a focus on geologic concepts.

The selection of the right tool depends on the project goals

and resources available. The project must be doable. In

general, the simplest tool that meets the project objectives is

the right tool. If variogram-based methods are sufficient

then we do not recommend a more complicated method. If

MPS is sufficient then there is no need to consider object-

based or process-mimicking. The feasibility of an approach

must be judged given the final transfer function. For

example, while the variogram-based tools are well

established and often required less work than other tools, the

limitations of the implicit assumptions on the continuity of

extreme property values may have a significant impact on the

model of flow response.

Consideration of geologic complexity and conditioning

density may be applied to select the right tool (see Figure 3).

Complexity is designated as the complexity of the

heterogeneity and the resulting flow paths. For example, a

reservoir with highly complicated configurations of barriers,

baffles and pipes is complex. A reservoir with uniform, piston

type flow displacement has low complexity. Conditioning

represents the spacing and number of wells and the level of

specificity of secondary information. For example, a mature

reservoir with hundreds of wells and / or a reservoir with high

resolution seismic information are densely conditioned. A

deepwater field with less than 10 wells and low resolution

seismic information is sparsely conditioned.

Figure 3. A schematic plot of the best modeling method

relative to data density and heterogeneity complexity (Pyrcz

et al., 2008).

A third axis could be added to the above plot to account for

the degree of amalgamation. For example, in a slope valley

channel setting, as the overall proportion of channels

increases, the reworking of individual channels increases. At

a very high proportion of channels, no individual channel is

preserved and the model only includes short scale

connectivity features. While the complexity of individual

events may be high, the overall heterogeneity complexity of

the preserved features decreases due to amalgamation. For

our present plot, the degree of amalgamation is integrated

into geologic complexity.

These methods mark a major change in the ability to

characterize and reproduce realistic and complicated

reservoir heterogeneity. While research on process-

mimicking methods over the last decade has spread to most

of the major geostatistical research organizations, the

method has not entered common practice. The question

remains, is the technology viable, but some practical issues

are impeding its widespread adoption? Recall the experience

of MPS with the introduction of efficient conditional

probability calculation and storage that was addressed

through the pre-calculation of a search tree from the training

image by Strebelle (2002).

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ADVANTAGES OF PROCESS-MIMICKING MODELS

Process-mimicking methods have important advantages and

challenges. We focus on the advantages and then provide a

discussion of challenges. Note, these are often directly linked

and result from the fact that process-mimicking methods

depart from traditional workflows. Process-mimicking

methods expand the scope of geostatistical methods, but are

not a panacea solution for all reservoir modeling problems.

There are various advantages including: (1) direct integration

of geologic concepts, (2) efficient characterization of

complicated heterogeneity, and (3) more realistic uncertainty

models.

All reservoir models integrate geologic concepts. The grid

framework and trend models are directly constrained by

geologic concepts. Yet, for spatial heterogeneity, within

framework and trends, traditional methods are limited in

their ability to integrate the geologic concepts. Variogram-

based methods reproduce linear features. MPS may improve

connectivity with curvilinear features and ordering relations,

but may not reproduce complicated training images. Object-

based models reproduce geometries, but often with random

or simple clustered stacking patterns. Process-mimicking

methods maximize the integration of geologic concepts using

the language of the geologic experts. The inputs for process-

mimicking models are often rules that describe the geometry,

infills and stacking patterns of geologic depositional bodies.

These are the same parameters measures from outcrop and

shallow seismic studies (McHargue et al., 2010).

Through this efficient use of geologic information, a high

degree of complexity and realism is available. Consider the

model shown below (see Figure 4). It was constructed from

channels with a detailed description of geometry and rules

that govern organized and disorganized stacking patterns.

The resulting connectivity pattern reproduces the

complicated flow response that is typical in deepwater

channel reservoirs.

Figure 4. A process-mimicking model based on rules for the

geometry, infill and stacking patterns of deepwater

channels. The model represents porosity with hot colors

representing high and cold colors representing low porosity.

(Pyrcz et al., 2012).

Furthermore, this complexity is integrated very efficiently.

Efficient coding of geometric models, rules and conditional

routines allows several million cell models to be simulated in

a couple minutes on a regular PC. Complete uncertainty

models through multiple realizations and scenarios are very

practical to build. Contrast this with the time required to

match this complexity with traditional methods. It would

only be possible through detailed mapping of trends, and

stationary regions. The resulting model would be highly

deterministic and the simulation of multiple realizations and

scenarios would be onerous.

This efficient reproduction of complicated features is largely

due to the introduction of emergent features. For traditional

geostatistical methods, the heterogeneity model is

constrained through input statistics, local conditioning and

implicit assumptions of the method. One gets back what was

put in.

For process-mimicking methods the heterogeneity models

result from the combination of input statistics, rules and

conditioning constraints. As discussed in Pyrcz and Deutsch

(2014) there is a continuum of complexity of process-

mimicking methods with different levels of emergent

features. Some methods are simple geometric methods

(drafted rules) that use rules to directly impose the

heterogeneity. Hassanpour and others (2013) provide an

example of this method with meander channel belts that are

completely constrained with geometric inputs. In these

methods, there are no emergent features. Methods that use

the previous event to define the current event (Markov rules)

introduce emergent features. The bank retreat model

applied by Howard (1992), Pyrcz and others (2009) and

Sylvester and others (2010) is an example of this method.

Channels are placed on a grid layers as a function of only the

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previous channel with some additional conditioning

constraint. Surface-based approaches that track the evolving

composite state of the model (topography, local fill type etc.)

with morpho-dynamic rules are rich in emergent features.

Abrahamsen and others (2008), Pyrcz and others (2006) and

Zhang and others (2009) have documented these models.

The efficient reproduction of the complicated features would

not be possible without emergent features.

The process-mimicking models result in more realistic

reservoir connectivity models for complicated reservoir

settings. It is anticipated, that models that underestimate

complexity are responsible for bias in predicted recover

factors and hydrocarbon flow rates. In addition, the detailed

heterogeneity in process-mimicking models often results in

greater sensitivity to well location and realizations and

scenarios. Process-mimicking models may provide a wider

range of possible responses to the transfer function. The

resulting uncertainty models are often wider than predicted

with traditional methods.

In many reservoir settings process-mimicking approaches

offer significant improvements to meet project needs.

Consideration of the capabilities and unique features of

process-mimicking is needed prior to selection as a reservoir

modeling method.

CHALLENGES OF PROCESS-MIMICKING MODELS

It is important to transparently review and discuss the

capabilities, challenges, possible solutions and future

directions of process-mimicking models. Process-mimicking

methods have unique strengths and differences from other

geostatistical methods and are not the solution for all

settings and may require changes in modeling workflows.

This discussion below covers details on the aspects of: (1)

conditioning to well data, (2) conditioning to trends, (3)

emergent features, (4) alignment to grid framework and (5)

generality.

Well Data Conditioning

Although the conditioning of process-mimicking models to

well data is analogous to the problem of conditioning object-

based models, there are additional challenges. The

fundamental object-based conditioning problem is the

placement of relatively large-scale geobodies to match all

available well data without artifacts. This problem has been

known for a long time and has a variety of solutions. Two

step simulations (Shmaryan and Deutsch, 1999; Viseur et al.,

1998) first fit objects to the well data and then complete the

rest of the model avoiding contradictions with the wells to

honor the global proportions. Optimization may be applied

to fit individual objects, characterized by centerlines (Oliver,

2002) or to jointly fit all objects (with simulated annealing,

Deutsch and Wang, 1996). These methods are known to

work reasonably well for sparse data settings (the spacing of

the wells is large relative to the object-based geometries) and

given there are no contradictions between data, object

geometry and the global probability density function. Models

should be checked for conditioning artifacts. Issues with

conditioning object-based models and tests for artifacts have

been discussed by Hauge and Syversveen (2007).

Process-mimicking models often include the added details of

within-geobody variations defined by rule-based

relationships with the external geometry or other large-scale

controls or sequence information to constrain infills (e.g.,

consider the use of stratigraphic systems tracts described by

McHargue et al., 2010 for deepwater slope valley channels).

This adds a level of difficulty for data conditioning, with the

possibility of requiring matching detailed petrophysical infills

with well data. This may be accomplished with two step

simulation, first the geometries and then the infill are

conditioned to wells, but this method is likely to result in local

contradictions between model geometries and infills.

Process-mimicking models can also include stacking rules that

provide valuable information on the arrangement and

connectivity of various geometries. While it is challenging to

condition individual geometries, conditioning groups of

geometries while preserving stacking patterns is potentially

more challenging. This may result in an effective increase in

the size of the geometries, and, as discussed previously, this

renders conditioning more challenging.

Finally, process-mimicking models are forward models.

Geometries are placed in stratigraphic time sequence with

relationships with the previously placed geometries. This

may include only simple stacking rules (discussed above for

Markov rules) or in some cases the strict tracking of evolving

time surfaces with depositional and erosional events

(discussed above as morpho-dynamic rules). In contrast,

object-based modeling works with random placement of

objects is afforded the convenience to perturb individual

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geometries with high level of freedom. The forward model

cannot perturb previous events without changing subsequent

events. Data conditioning is met on an event-by-event basis,

during the formation of the events. As a result, current

models that can be conditioned are largely aggradational and

do not account for large-scale erosion beyond individual

events of limited spatial and time scales.

Trends

Various methods have demonstrated conditioning to vertical

trends through constraints on the rate of model aggradation

and the distribution of facies within individual events (Pyrcz

et al., 2009; Michael et al, 2009; Sylvester et al., 2010). Due

to the forward nature of these models, some form of

forecasting is necessary to improve vertical trend match.

Events deposit over the current model layer and may cut into

previous layers. This must be integrated to properly

constrain the aggradational rate and avoid bias in the trend

model. This is in contrast to an object-based model that may

randomly add and remove objects at any stratigraphic

position in the model grid to match a vertical trend.

Conditioning to areal trends is also a challenge shared with

object-based modeling methods that is made more

complicated by the need to adhere to stacking rules and / or

interactions between the forward modeling progression of

depositional events. In most cases only somewhat naïve,

smoothed, generalized areal trends or boundaries in a

depositional area have been reproduced.

Conditioning is possible in sparse data settings, but given the

power of these models to efficiently produce complicated

architectures (see in the examples and applications below),

we acknowledge the role of unconditional process-mimicking

models for the use as analogue models and training images.

These analog models avoid any conditioning limitations and

may provide a framework for extracting statistics or as analog

models to test concepts (Michael et al., 2010).

Emergent Features

As discussed previously, emergent features allow for efficient

reproduction of geologic concepts. These models produce

features beyond conditioning data, limited spatial continuity

models and trend information. Emergent behaviors impose

structure that may not be expected prior to running the

model.

For many practical reservoir modeling problems it may be

preferable to simplify the rule set to dampen large scale

emergent features and to enable the reproduction of the

basic, required architectural concepts. This allows for a clear

connection from inputs to the output model. To more fully

explore uncertainty models, advanced rules may be applied,

to produce a numerical laboratory with complicated

emergent behaviors (Pyrcz et al., 2006, Sylvester et al., 2010).

Two components of emergent behaviors are: (1) new

heterogeneities that are not imposed directly and (2) drift

from the initial seed architectures. The second is a concern as

it may be considered an artifact of mismatch of the seed form

and the rules. This may be dealt with through inversion for

the modeling parameters given the seed form or by running

the rules until the form stabilizes and removing the

transitional products (Howard, 1992). Regardless, this is a

challenging area of research and the extent of the predictive

value and reasonable applications needs to be confirmed

with natural settings and more complete physics-based

modeling (Oreskes et al., 1994).

Alignment to Grid Framework

The grid framework introduces important stratigraphic

information into reservoir models. Top and base surfaces

represent important constraints on volumetrics. They are

usually mapped from a combination of well and seismic data

and the stratal relationships between top and base surfaces

are represented through the layering within the grid.

Traditional geostatistical models then anchor their statistical

heterogeneities to this grid. Departures from this grid are

limited to very local features such as patterns that represent

local channel scours and fills. This is done for good reason; it

honors the important stratigraphic input and supports good

flow simulation that is dependent on the layer alignment with

the primary flow directions.

Process-mimicking models in some cases generate their own

gradients as an emergent behavior. Even a simple

aggradational surface-based model (e.g. Xie and Deutsch,

2001), is theoretically known to increase surface undulations

as events at added until a point of saturation (Barabási and

Stanely, 1995). These surface undulations are represented by

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geometries that cross multiple grid layers and may violate the

stratigraphic concepts. Furthermore, the resulting

nonstationarity in these features with low undulation at the

base of the model and constantly higher undulation after

saturation is an artifact (see Figure 5). This has been solved

by integrating rules that compensation and capture natural

healing process in aggradational settings.

Alignment to the top surface in the presence of aggradational

features may be important. If the top surface is non-

erosional, local features in the top surface may indicate the

placement of specific event geometries. The honoring of this

information is a challenge given the forward nature of the

modeling method. It is a challenging inversion problem to

guide the forward model to match the target configuration

along the top surface. Current methods are limited to

assuming the top surface is erosional and unrelated to the

architecture below the surface or to tweak the placement

rules to improve match with the top surface.

Generality of Process-Mimicking Models

As illustrated in the following section, the process-mimicking

modeling methods and associated rules are highly specific to

depositional environments. Unlike other geostatistical

methods, it is not anticipated that a single algorithm would

be applicable to a broad set of settings. The process rules

must be tuned to the processes that operate in a certain

depositional environment. This may be seen as an

advantage, as this tuning represents the integration of

important stratigraphic and process information.

More problematic is the ability for robust operation in a wide

range of model inputs for a given setting. Given the

previously discussed challenges in conditioning, it is quite

possible for these methods to fail if conditioning data is not

sparse or if data is inconsistent with each other or the rules.

Solutions include: (1) check data and model consistency

before modeling and correct, (2) post-processing to locally

correct models, (3) acceptance of model conditioning

imprecision or (4) do not applying process-mimicking

methods in dense data settings. Ensuring consistency

between data and rules requires is a good method to mitigate

and requires some pre-work, but results in improved models.

Consider that with traditional cell-based geostatistical

methods such contradictions will result in artifacts that may

be hidden by the stochastic simulations. Efforts to check

consistency between all information sources should be

required for all modeling methods.

Emergent features (as discussed previously) are a strength of

process-mimicking methods, but care must be taken to build

good rule sets and to confirm their behavior match natural

settings.

Figure 5. A process-mimicking model based on rules for the

geometry, infill, and compensation stacking for deepwater

lobes. The model represents depo-facies with lobe inner

(orange), lobe medial (yellow) and lobe outer (green) along

with local mud drapes (brown). No healing rule was

applied. Note the increase in surface gradients (evident by

tracking mud drapes) from the base to the top of the model.

Compare with Figure 7 below with healing rule applied.

These emergent features may include long rage trends away

from data. Consider the example of a process-mimicking

model of a deepwater slope valley (as shown in Figure 6

below). The channels are realistically confined to the valley.

The resulting model may indicate focusing of channels at

specific locations within the slope valley system due to the

interactions of channel placement rules and slope valley and

data constraints in the model. Compare this to traditional

geostatistical methods that do not include features beyond

the data, trend constraints and limited stationary statistical

descriptions. Consider what features come from data, from

the spatial, and from the rule-based model. Once again

confirmation of the model behavior with natural settings is

essential.

In general, it is straightforward to apply simple process-

mimicking models as reservoir modeling tools. The more

complicated rule-based systems have remained as numerical

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laboratories for testing concepts, comparison to, and

abstraction of full process models. Methods that extract

detailed statistical descriptions from process-based models

into more conventional geostatistical methods through

detailed trends and statistical inputs are also possible

solutions. However, such statistics may be limited, or the

extracted trends may contradict local data. While these

differences from traditional geostatistical methods are

significant, practical modeling examples are available and

demonstrate value when applied judiciously.

EXAMPLES OF PROCESS-MIMICKING MODELS

Process-mimicking models have been applied to deepwater

and fluvial settings. This is motivated by the complicated

heterogeneity / connectivity and knowledge of the

sedimentologic/stratigraphic processes (McHargue et al.,

2010).

Deepwater Examples

The application of process-mimicking modeling to deepwater

slope valley channel systems has been demonstrated by

McHargue and others (2010). In general, these models focus

on constraining a set of stacked channels and linked channel

infills to well data and the mapped slope valley boundaries

(see Figure 6). The work of McHargue and others provides a

good description of the stratigraphic rules, including the use

of disorganized and organized channel stacking and the

associated channel fills. This model uses morpho-dynamic

rules as the composite surface from channel erosion and

aggradation impacts subsequent channel positions through

avulsion and confinement.

Figure 6. A process-mimicking model based on rules for the

geometry, infill, avulsion and erosion rules of deepwater

channels. The model represents depo-facies with channel

axis (orange), channel off-axis (yellow) and channel margin

(green) (McHargue et al., 2010).

In these models, channels are anchored to the existing grid

layering, ensuring reproduction of the grid framework.

Channels are sequentially added to the model and may erode

and / or aggrade sediments. The rules steer channels

through the slope valley from proximal to distal to match

data and under the slope valley boundary constraints. These

models are practical for sparse data reservoirs. The rules

result in highly realistic heterogeneity models. The change in

channel fill fraction produced a very good transition from

disorganized to organized channel stacking patterns. Of

course, dense data would be problematic. Global

proportions and vertical trends are honored through

constraint on the aggradation rate.

Since the slope valley region is applied to constrain the

channel, irregularity in the bounding surface of the slope

valley is problematic. For example the lack of contiguous

paths at the base of the slope value in a grid layer contradicts

the assumption that channels are anchored to the grid layers

and continuously pass from the proximal to the distal end of

the slope valley. This requires clean-up of the slope valley

boundary model to ensure a continuous conduit along the

base of the slope valley.

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This model, with associated channel stacking rules, may

provide improved prediction away from wells and an

improved assessment of channel-to-channel connectivity.

Detailed channel fills may also be important for flow

heterogeneity. These models may provide improved

prediction and uncertainty models with application of a

transfer function such as flow simulation.

Deepwater lobes are also important reservoir targets. Pyrcz

and others (2005) demonstrated the use of process-

mimicking methods for modeling deepwater lobes. These

methods rely strongly on the concept of surface-based

modeling with morpho-dynamic rules for compensation and

healing.

Figure 7. A process-mimicking model based on rules for the

geometry, infill, and compensation stacking and healing

rules of deepwater lobes. The model represents depo-facies

with lobe inner (orange), lobe medial (yellow) and lobe

outer (green) along with local mud drapes (brown).

This deepwater lobe model covers a practical target for

reservoir modeling (see Figure 7). This model is readily

conditioned to sparse well data through iteration of lobe

placement weighted by the compensation rule. A challenge

for lobe modeling is a tendency for gradients to emerge in

the model that may violate the stratigraphic framework and

cause issues with flow simulation. The application a healing

rule in the form of a smoothing model applied to previous

surfaces may be carefully tuned to dampen this effect, while

preserving important features (compare Figure 7 and Figure

5).

Fluvial Examples

Fluvial meandering process-mimicking models have been

demonstrated by Cojan and others (2005) and Pyrcz and

others (2009). Conditional fluvial meander modeling

methods have been described by Cojan and others (2005).

Recent work from Sech and others has illustrated the use of

process models to impose stacking rules and stratigraphically

inspired infills to build realistic braided and meandering

fluvial models (see Figures 8 and 9). These models include

the realistic evolution of abandoned channel fills and all the

associated reservoir facies.

These examples demonstrate the high degree of

heterogeneity and complexity that may be incorporate into

reservoir models; this aspect motivates the application of

process-mimicking models. In many cases, such models

provide enhanced flow forecasts, through a step change in

the integration of geologic concepts that would not be

practical without process-mimicking methods.

APPLICATION OF PROCESS-MIMICKING MODELS

The above examples of process-mimicking models can be

passed through conventional reservoir modeling workflows

to model the petrophysical properties required for the

transfer function (typically flow simulation and / or

volumetric calculations). In fact, these models are improved

with detailed porosity and permeability trends from the rules

for infills within the modelled geometries resulting in

improved prediction and uncertainty models.

A conditional deepwater lobe model realization was

constructed with depofacies, porosity and permeability. The

model is conditional to 2 wells and shown flattened and with

vertical exaggeration to improve clarity. The facies model

includes inner, medial and outer lobe is shown in Figure 7.

The porosity model is constrained by internal lobe trends (see

Figure 8). Shale drapes are shown as dark blue lines and the

proximal lobe axes are shown with hot colors.

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Figure 8. A porosity model based on a process-mimicking

model for deepwater lobe with detailed within-facies

property trends. The range is from 2% (blue) to 20% (red).

A conditional process-mimicking braided fluvial realization is

another example. Rules-based conditional abandonment fills

are modeled to provide the general framework. Shale trends

within the remaining sandy component provide a detailed

sand and shale model (see Figure 9).

Figure 9. A sand (yellow) and shale (grey) facies model from

a process-mimicking method for braided fluvial reservoirs.

Note the abandoned channel fills that form significant

barriers and the lesser shale fills within the sandy fills.

Within the sand component, detailed trends are applied to

model porosity and permeability. A lithofacies model (see

Figure 10) illustrates a rich model with barriers, baffles and

conduits.

Figure 10. A lithofacies model based on a process-mimicking

model for a fluvial braided setting with detailed within-

facies property trends.

As discussed by Pyrcz and Deutsch (2014) and Pyrcz and

others (2012) the ability to efficiently and easily build a large

suite of process-mimicking, hierarchical, information rich,

detailed numerical conditional representations of reservoir

architecture is useful in conventional reservoir geostatistics.

Other potential applications include training images and non-

stationary statistics.

Exhaustive training images are required by MPS to calculate

the large number of required conditional probabilities for

specified data events. It is natural to consider the use of

methods such as process-mimicking. Note that

nonstationarity and complexity in training images may

degrade the quality of MPS realizations without careful

implementation and local constraints. In fact, the best

practice is to construct simplified training images and impose

nonstationarity in the MPS simulation. Given this

consideration, we do not universally recommend process-

mimicking models for MPS training images, in some cases

more simplified methods such as the training image libraries

and generators should be considered (Pyrcz et al., 2007;

Maharaja, 2008). Process mimicking methods can be applied

to generate simplified training images. A simple disorganized

channel model was constructed with channel asymmetry,

planform and placement rules (see Figure 11). These models

include a variety of depositional coordinate and trend

information that could be applied to provide refined facies

models and also auxiliary variables to improve training image

reproduction (Chugunova and Hu, 2008).

12

Figure 11. A simple disorganized deepwater channel training

image generated with a process-mimicking method that

uses channel geometry and infill rules.

The facies model for deepwater lobes (see Figure 7) could

function well as a more complicated training image. The

simulation implementation should be tuned and checked to

ensure good reproduction of salient features. Furthermore,

continuous MPS requires methods to generate realistic

continuous training images. The use of rule-based

hierarchical trends provides a good source for continuous

training images (for example see Figure 8).

There may be opportunities to utilize process-mimicking

models to extract or constrain traditional spatial continuity

models such as semivariogram models and indicator

semivariogram models and transitional probabilities. This

ensures consistency with geometric concepts.

Another application is to calculate non-stationary statistics

such as trends and locally variable azimuths from process-

mimicking models and apply them to guide conventional

geostatistical models. This may be useful considering the

complexity in inferring consistent, detailed, locally variable

azimuth models, given local constraints and the preservation

of information within process-mimicking models that allows

for the rapid generation of these non-stationary models.

The process-mimicking methods are geometrically

parameterized methods with geometric descriptions of

surfaces, geometries and centerlines. While this is

conveniently anchored to a grid, this is independent of the

grid. This allows for efficient refinement of the model, down

scaling through the use of the geometric descriptions and

rules to describe higher resolution features locally or globally.

In fact, these geometric descriptions could be used to build

detailed surfaces that constrain the grid to the surface-based

heterogeneity from the process-mimicking model (e.g., Fitch

et al., 2014; Sech et al., 2009).

In a more advanced application, the process-mimicking

model(s) are treated as numerical analog models for the

reservoir of interest. Once this decision is made, a variety of

applications are possible including, extraction of architectural

relationships, well risk analysis and value of well data.

Admittedly this application relies on strong assumptions of

the chosen models being analogous and characterizing

appropriate models of uncertainty.

13

Figure 12. A fluvial meander process-mimicking model

developed by Willis and Tang (2010). The preserved

architecture, included geobody geometry and internal

trends are compared for various rules and parameters.

It may be useful to understand the relationships between

architectural parameters and reservoir parameters such as

volumetrics, connectivity and flow under local constraints.

With a detailed set of realistic architectural models and their

emergent behaviors this is possible.

Willis and Tang (2010) provide a summary of meander

channel architecture and connectivity as a function of various

stacking parameters such as aggradation rate and the degree

of meander loop translation and migration (see Figure 12).

These unconditional process-mimicking models have

provided very useful concepts for heterogeneity, with

identification of reservoir body geometry and the infill trends.

It was demonstrated that the type of deposits on the

concave-bank area of channels, the type of channel cutoff

and abandonment fill and the rate of channel aggradation

determines the connectivity of course-grained reservoir

geobodies. Channel stacking rules have a significant impact

on recovery factor. Translation dominated meander

architecture results in a higher recovery factor than

expansion dominated (see Figures 13 and 14). The results of

this model provide useful inputs into reservoir models,

including geometries for object-based modeling and training

images for MPS.

Figure 13. Streamline subsurface flow simulations after 0.4

pore volumes of water (blue) displaced oil (red) for a

translation dominated meander process mimicking model

(from Figure 12). The recovery factor is 32%.

Figure 14. Streamline subsurface flow simulations after 0.4

pore volumes of water (blue) displaced oil (red) for an

expansion dominated meander process mimicking model

(from Figure 12). The recovery factor is 17%.

In another case, the preservation potential of components of

the element fill may be quantified, for example the fraction

of axial channel lag preserved in a aggrading and meandering

channel model. There are much more complicated

experiments possible, such as quantifying reservoir

connectivity for various types and frequencies of channel

avulsion (see Pyrcz et al., 2012 for examples of these

applications).

Journel and Bitnavo (2004) and Maharaja (2007) developed

methodologies for exploring NTG uncertainty through spatial

bootstrap from reservoir models. In a similar manner, a

proposed well design may be applied to suite of process-

mimicking models to calculate the resulting probability

distribution of any associated well result of interest, such as

the net pay length, average NTG, proportion of above specific

thresholds, number of isolated units etc. If information is

available concerning well site selectivity in the analog models,

this may be imposed with a selectivity bias surface that

adjusts spatial bootstrap sampling rates.

CONCLUSION

Process-mimicking modeling methods allow for a major

change in the ability to integrate geologic stratigraphic and

process information into reservoir models. While the

methods have been under development for the last decade,

their widespread application has not been realized beyond

demonstrations and specialty projects by some academic and

industrial research organizations.

14

With improved awareness and minor changes in workflows

current process-mimicking methods are ready for broad use.

Many of the required workflow changes, including checking

data and concept consistency, are best practice and should

be applied regardless of choice of modeling method.

Process-mimicking methods are well suited to sparse data

settings, with known geologic concepts and the need for

efficient modeling of multiple scenarios and realizations to

support uncertainty modeling and ultimately decision

making. While future developments will improve these

process-mimicking methods, judicious application of these

methods in the current state is anticipated to fill an

important gap for reservoir modeling.

ACKNOWLEDGMENT

The authors would like to recognize Chevron Energy

Technology Company for supporting the research on this

topic and allowing for this publication.

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