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Copyright 2001, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the 2001 SPE Annual Technical Conference andExhibition held in New Orleans, Louisiana, 30 September3 October 2001.

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AbstractThe estimation of oil and gas reserves is necessary for

assessing the value of oil and gas properties, and for meeting

the reporting and disclosure requirements imposed on oil and

gas companies by various governmental and regulatory

bodies. Reservoir simulation is a sophisticated technique of

forecasting future recoverable volumes and production rates,

and is an increasingly popular tool for reservoir management

and optimization. Reservoir simulation is also progressively

being used in the process of forecasting and estimatingreserves. However, as with any reservoir engineering

technique, certain precautions must be taken when relying on

reservoir simulation as the means for estimating reserves.

This paper identifies some of the unique issues encountered in

the reserves evaluation process when reservoir simulation is

utilized, and offers strategies for addressing these issues.

IntroductionThe assessment of a companys reserves is an important

process, regardless of the companys size or corporate

structure. The level of reserves can have a direct impact on a

companys earnings and balance sheet, and can significantly

affect the cost and availability of capital necessary for its

growth.

Reserves are determined using a variety of geological and

engineering methods. Regardless of the evaluation methods

used, however, any estimate of future recovery, no matter how

reasonable, does not necessarily qualify as an estimate of

reserves. Specific criteria must be met to qualify estimated

recoverable volumes as reserves. These criteria are generally

defined in the form of Reserves Definitions.

For an exploration or production company, the value of the

reserves usually constitutes a major portion of the total

company value. Therefore, it is critical that reserves be

estimated as accurately as possible within the constraints

imposed by the relevant Reserves Definitions. As long as the

requirements of the definitions are upheld, reservoir

simulation can be a valuable tool for improving the accuracy

of the reserves estimate. However, due to the nature o

simulation models (their non-uniqueness and complexity) their

use as a tool for this purpose is not always straightforward, as

this paper will discuss.

DiscussionReserves Definitions

Several sets of Reserves Definitions have been published by

various regulatory bodies and professional organizations

throughout the world. Most sets of Reserves Definition

specify different grades of reserves depending on the level of

certainty associated with the estimated recovery of those

reserves. In many systems, the top grade of reserves is

designated as proved reserves. As would be expected

proved reserves require a very high degree of confidence thathe hydrocarbons will actually be recovered. Lower grades o

reserves such as probable or possible require diminishing

standards of certainty.

Examples of two sets of definitions commonly

encountered by companies based or operating in the United

States are 1) those established by the United States Securities

and Exchange Commission (SEC), and 2) those established by

the Society of Petroleum Engineers and the World Petroleum

Congress (SPE/WPC). There are many similarities between

these two sets of definitions, but there are importan

distinctions as well which are beyond the scope of this

discussion.

Publicly held oil and gas companies in the United Statesmust file specific forms with the SEC on a regular basis and

whenever stock is issued. Some of these forms require tha

the company disclose volumes of reserves and the estimated

future income attributable to those reserves. SEC regulation

stipulate that the reserves estimated for such purposes must be

computed in accordance with the definition of proved reserves

contained in Part 210.4-10 (a) of Regulation S-X.

On the other hand, some lending institutions, financia

advisors, and corporate planners work with reserves estimated

SPE 71430

The Adaptation of Reservoir Simulation Models for Use in Reserves CertificationUnder Regulatory Guidelines or Reserves DefinitionsM.R. Palke and D.C. Rietz, Ryder Scott Company

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2 M.R. PALKE, D.C. RIETZ SPE 71430

in accordance with the SPE/WPC Reserves Definitions.

Because these definitions allow for probable and possible in

addition to proved reserves, it is feasible to express the

reserves in terms of a range of possible outcomes, as implied

by the amount of reserves allocated to each classification.

Different grades of reserves are used for different

purposes. In general, proved reserves are used for financialreporting and lending, where the requirement for certainty is

the greatest. However in order to make intelligent business

decisions in activities such as prioritization of capital spending

and property acquisitions, it is also important to recognize and

quantify the amount of probable and possible reserves.

Companies buying or selling assets regularly consider

upside potential, which is usually represented as probable

and possible reserves. The degree to which entities value

these non-proved categories varies dramatically due to the

reduced certainty in recovery of the volumes.

The SPE/WPC definition contains a general requirement

that proved reserves have a reasonable certainty of being

recovered. Other, more specific, criteria must also be met for

reserves to be classified as proved. The definitions forprobable reserves are less stringent, requiring that a general

test of more likely than not be satisfied1.

This paper focuses on deterministic reserves estimation

incorporating reservoir simulation modeling results. Many of

the issues apply also to the probabalistic reserves setting, but

many other issues, not discussed herein, are unique to

probabalistic reserves estimation2.

Prevalence of Reservoir SimulationOne of the advantages of reservoir simulation is that it enables

an engineer to simultaneously and rigorously consider almost

all of the geological and engineering data pertinent to the

production behavior of the reservoir3. In essence, reservoirsimulation is the construction of a numerical model that is

expected to behave like a particular oil or gas reservoir.

Certain properties of the reservoir (e.g. porosity, permeability,

structure, thickness, etc.) and certain properties of the fluids

contained in that reservoir (viscosity, density, etc.) are

described in numerical terms suitable for input into a

simulation package. Once constructed, a reservoir model is

typically history matched. After the history match is achieved,

the model can be run to predict future performance under a

variety of future development and operating scenarios.

Simulation has become increasingly practical due to

advances in computer software, hardware, and simulation

expertise. There are a number of stable and efficientcommercial programs available, each with its own strengths

and weaknesses. Simulation involves a great deal of

numerical computation; however, as computer power has

continued to increase, it has become feasible to run

increasingly detailed models on relatively inexpensive

hardware. Familiarity with simulation has become more

common as engineers have acquired simulation training and

experience earlier in their education and careers than their

counterparts of previous generations.

We have observed that reservoir simulation has been

increasingly promoted as a means to estimate reserves. I

appears that the use of simulation for reserves estimation is a

logical step in the continued evolution of reserves estimation.

Capabilities and Limitations of Simulation

As with any analysis tool, it is important to recognize the

limitations as well as the capabilities of reservoir simulation

Only then can model results be appropriately interpreted for

estimation of reserves or for any other purpose. As discussed

below, the accuracy of most models is impacted by the

presence of complexities within the reservoir that are no

incorporated into the model.

A model is composed of discrete cells or grid blocks, each

of which represents a specific volume of the reservoir. Each

grid block is assigned certain rock properties that either 1)

dictate the amount and types of fluids originally contained in

that portion of the reservoir (e.g. pay thickness, porosityconnate water saturation, etc.), or 2) control the movement of

fluids into and out of that portion of the reservoir (e.g

permeability, net-to-gross ratio, relative permeability, etc.). In

a model, these parameters are uniform within any given grid

block, whereas in nature there may be considerable variation

within the volume of the reservoir represented by the grid

block. At best, the model block will be assigned values

approximating some type of average for the reservoir over the

volume of the block.

However, it is not always possible to determine the

average block properties with a high degree of reliability

because of the difficulty in directly measuring many of the

reservoir parameters, and the inherent sparseness of the dataIn some instances, undetected reservoir boundaries or

structural features will not be represented in the model

Although geostatistical methods help to improve estimation of

the properties in areas of the reservoir lacking measured data

it is generally not possible to overcome the limitations of the

data set with a high degree of certainty.

Because of the above factors, a model is generally less

heterogeneous than the reservoir it is intended to represent

Unfortunately, heterogeneity in a reservoir leads to uneven

sweep and incomplete drainage, both of which reduce the

recovery of hydrocarbons. Consequently, since a mode

generally understates the degree of heterogeneity present in

the reservoir, the model will tend to overstate the recovery ofhydrocarbons unless compensatory adjustments are made to

the simulation data. For example, homogeneity may be

overestimated, but may be held in check with a lower than

actual overall permeability value or using adverse pseudo

relative permeability curves. Such adjustments are usually

made to achieve a history match. The history matching

process is discussed in greater detail later in this paper.

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Applying Simulation Results toEstimate Proved ReservesReservoir simulation studies are rarely performed with the

objective of estimating proved reserves. Usually, the primary

objective of reservoir simulation is to improve the

understanding of the reservoir, so that the reservoir may be

optimally developed and managed. Frequently, a developmentplan based on proved reserves alone (as compared to the most

likely volumes) would under-develop the field, and in fact

could result in reduced overall production (over the depletion

history of the field). Thus it makes sense to consider the best

estimate of total potential when making development and

management decisions.

As a result, the presumed most likely scenario is most

commonly modeled with the reservoir simulator. Most

likely is a level of recoverable volumes that is more

consistent with proved + probable reserves, rather than proved

alone. This is mainly due to the specific definitions of proved

reserves. One can strongly believe (most likely) that volumes

are present in the subsurface, but based on the proved reserves

definitions, they may not be recognized for proved reservesestimation. Therefore, it is very common that results from a

simulation model cannot be directly applied to the proved

reserves category, even if they are passed through a cashflow

analysis to prove economic viability.

It is not just original hydrocarbon in place that may not fit

the definition of proved reserves. Models may include

pressure support from aquifers or rock compressibility that are

not proved. Numerous other parameters would also fall into

this category. The key is to search for sources of reservoir

drive energy that are not proven to exist. As will be discussed

later, sensitivity studies can be used to root out such

parameters from a history matched model.

Even though reservoir simulation is usually undertaken toforecast recovery and future production rates under the most

likely geological scenario (which may not conform to the

proved reserves definition), simulation can still be utilized in

the estimation of proved reserves if appropriate steps are

taken. There are two approaches for applying the simulation

technique in such a way as to ensure that the definition of

proved reserves is honored in all respects.

First, the model can be modified such that the reservoir

configuration described by simulation data is in strict

compliance with the clear mandates of the proved reserves

definitions. Consider, for example, the case of a reservoir for

which the level of the hydrocarbon-water contact has not been

established from the geological and engineering data. In thissituation, the hydrocarbon-water contact in the model should

be set at the lowest observed occurrence of hydrocarbons

(lowest known oil/gas, or oil-down-to), as specified in the

definition of proved reserves. As long as the other

components of the definition are also honored, the results

generated from this model could be utilized in the estimation

of proved reserves.

The act of modifying a proved + probable model into a

proved model or vice versa can be more difficult than it

sounds. Such a modification to a proved + probable model is

not merely a question of modifying the reservoir description

The planned wells and facilities (manifested through field rate

constraints) must also be adjusted to fit the proved reserves

categories. For instance, if a proved + probable model is

modified to be consistent with proved hydrocarbon in place

the recovery factor might tend to be too high if all of theprobable wells are left within the model.

In addition to the question of constraints, substantia

modifications to the original grid/description could also be

required. For instance, models derived from seismic data

often feature thickening between wells based on reasonable

interpretations of the data. This thickening may or may not be

permitted under the reserves definitions.

We do not recommend, however, that models be originally

constructed to comply with proved reserves definitions

except under special circumstances (litigation, contentious

reserves estimation situations, etc.). In general, constructing a

model in compliance with proved definitions might regrettably

eliminate a great deal of utility in terms of planning and

optimization. It seems likely that it is better to build the largemodel (proved + probable + possible), and then in turn modify

the model, rather than construct a proved model, and have to

add on probable reserves later.

Alternatively, less desirable but perhaps more practical, a

model that is not in compliance with the proved reserves

definition may be used in the estimation of reserves with

appropriate modifications to the simulator results. In thi

situation, the reserves evaluator must perform calculations

external to the model to estimate the recovery that reasonably

approximates what would have been calculated had the mode

actually been constructed in accordance with the proved

reserves definition. An abundance of simulation output data is

necessary in order to perform the required adjustmentsObviously, some of the rigorous nature of the simulation is

lost in the manual process of manipulating the output data.

An example of this second approach occurred, when the

authors were requested to opine on the use of a simulation

model of a field for proved reserves estimation. The field

consisted of stacked reservoirs which were not in vertica

communication except through pipe. The problem arose

because the volumes in the various sands were associated with

different reserves categories based on whether the fault block

they were in had been production tested. Furthermore, the

model volumes were not identical to the volumes certified by

the authors geological associates (due to differences in

interpretation of contact depths and contouring). The modewas calibrated so that the production tests could be reliably

replicated by the model.

The solution used by the authors was to separate the

production streams from the various sands. Production

streams from sands that did not qualify as proved were

eliminated. The remaining proved streams were scaled so tha

their initial rates and ultimate recovery factors were preserved,

but the ultimate recovery factor was appropriate for the

certified OOIP rather than the OOIP present in the model.

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While this approach is not completely rigorous, it at least

relies upon rate forecasts and recovery factors predicted by a

well constructed model. This approach treats the simulated

reservoirs as analogies to the actual reservoirs in terms of

initial rate and recovery factor. It is felt that this approach

does meet all of the requirements of proved reserves

estimation, which the original model, no matter how wellconstructed, did not.

Immature ReservoirsThe status of a reservoir represented by a simulation model

can range from immature to mature depending on the

stage of depletion at the time the model is to be used for the

estimation of reserves. For the remainder of this paper, we

shall discuss the considerations for using models at these

extreme ends of the maturity spectrum, although many

reservoirs will actually fall between the two extremes. As will

be evident from this discussion, the reserves estimator will

require an understanding of the concepts involved in reservoir

simulation as well as experience in the application of the

Reserves Definitions in order to utilize the model resultsproperly for this purpose.

Immature reservoirs have limited or no actual production

history. In some cases, the history is limited to formation tests

of various wells.

When building models of such reservoirs, it is necessary to

rely primarily on geophysical and geological data to set the

reservoir size and characteristics. A history match of the

model to the reservoir is easy to obtain since there are few if

any performance points to be matched. Because it is so easy

to obtain, however, the match is not very meaningful in terms

of calibrating and improving the reliability of the model.

It is unlikely that the most likely estimate of

hydrocarbons in place will adhere to the pertinent guidelinesfor proved reserves. The proved reserves definitions contain

specific rules that limit the reservoir area to be considered in

the reserves assessment. These rules place restrictions on

assumptions regarding the position of the water-hydrocarbon

contact, the extent of the reservoir defined by logged and

tested wells, and so forth. Furthermore, the model is probably

being constructed for purposes such as optimization, or

facilities design, rather than proved reserves estimation alone.

As a result, most models of immature reservoirs are unlikely

to be acceptable for the purposes of proved reserves

estimation.

However, even models not built in accordance with the

Reserves Definitions are helpful for estimating thehydrocarbon recovery efficiency to be used in the volumetric

calculation of reserves. Important to this process is the use of

the model to study the sensitivity of recovery to certain

reservoir characteristics not explicitly governed by the

reserves definition (e.g. relative permeability, drive

mechanism, pore volume compressibility, etc.). The use of

simulation in this fashion is referred to as performing

sensitivity studies. The understanding gained by sensitivity

studies will aid in the determination of the hydrocarbon

recovery efficiency that is reasonably certain to be attained

Unless contradicted by analogy data (or experience) it would

be legitimate to use a value of recovery efficiency established

by such means in the estimation of proved reserves

particularly if one treats this information in their analysis as

another analogous reservoir.

Furthermore, in many cases it is simple enough to modifythe non-proved-volumes model that was used for planning

purposes, to contain a proved volume in place for the purposes

of a proved reserves forecast.

Mature Reservoirs & History MatchingA mature reservoir is one that has produced long enough to

develop well-established production and pressure trends. A

history match of a model of a mature reservoir is usually more

difficult to obtain than for an immature reservoir, but is more

meaningful in terms of enhancing model reliability.

There are two basic components of a successful history

match. First, the model properties should be set such tha

simulated reservoir pressure levels are reasonably close to

measured field pressures at the proper time and location withinthe reservoir. Second, model properties should be set such

that simulated produced fluid ratios (water cuts and gas-oi

ratios) and contact movements are reasonably close to the

observed fluid ratios and contact movements overall, and in as

many individual wells as is possible.

A match to pressure alone is necessary but may not be

sufficient to definitively establish the size of the reservoir. For

example, a small reservoir connected to a gas cap or a large

aquifer can exhibit pressure behavior similar to a large

reservoir connected to a small aquifer. Furthermore, the

reservoir pressure behavior is sensitive to fluid composition

and phase changes. This means that any error in the fluid

characterization can cause a significant error in the size of thereservoir required to achieve the pressure match. Thus, unless

the presence and size of a gas cap and aquifer are known from

independent geological information and the fluid

characteristics are known with reasonable certainty, the

pressure match alone does not guarantee a unique and correc

solution for the reservoir size.

On the other hand, a model that matches both pressure

behavior and produced fluid ratios has a much better chance o

providing a correct representation of the actual reservoir. A

match to observed pressures and water cuts for example, will

require a reservoir/aquifer combination of particular size and

relative proportions, thus reducing the range of possible

solutions.The quality of a history match is also an important

consideration for gaining confidence in a models ability to

predict future reservoir behavior. For example, a model with a

good field history match, but a poor well-by-well match

would generally be less trustworthy than a model where both

the field data and the individual well data were matched

Further, if a well-by-well match was obtained by adjusting the

model properties in the vicinity of existing wells, the model

would not be expected to give reliable predictions for

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conditions significantly different from those already

encountered (e.g. the drilling of infill wells). Whenever

possible, localized changes used in the history match should

be propagated in a reasonable fashion to new well locations.

The history match technique should be focused on making

logical adjustments to model parameters that are consistent

with geological and engineering evidence.We should recollect however, that history matching is

generally a somewhat subjective process, and it is unlikely

that any two engineers would arrive at the exact same solution.

Furthermore, it is normal that certain parameters that have a

limited impact upon the history match would have a dramatic

impact upon the predictions from the same model. Aquifer

dimensions are perhaps the most obvious of such parameters.

It may be surprising, but original hydrocarbon in place is

frequently another such parameter!

Thus the authors strongly recommend that any parameters

suspected of falling into this category be tested through the

use of sensitivity studies so that the engineer who estimates

reserves can study the possible range of future recovery

forecasts.Many times the OOIP modeled for a history matched

mature reservoir does not comply with the Reserves

Definitions. For situations where a model has been history-

matched to field pressures and fluid ratios, and where there is

virtually no other way to match observed reservoir behavior,

the model would generally be a reliable tool for estimating

proved reserves. Sensitivity studies are a reliable tool for this

analysis. In all other cases, the size of the reservoir in the

model should be scaled back as necessary to prevent the

modeled reservoir from exceeding the size implied by the

criteria of the Reserves Definitions.

It would be wise to remember that reserves from very

mature reservoirs are often based solely on the application ofempirical decline curve methods, and are not necessarily tied

to geological-volumetric analysis of original hydrocarbons in

place. In such a case, it is not critical that the original

hydrocarbons within the model comply with the Reserves

Definitions. Thus, in cases where there is compelling

evidence that the model is representative (reasonable

predictions, and a high quality history match) the model

results should be used in a manner consistent with the use of

traditional production trend analysis, even though the original

hydrocarbon in-place cannot be fully reconciled with the

reserves definitions. Meaning that the model should not be

discounted because every detail cannot be explained.

However, this is only appropriate for cases where reservescould otherwise be assigned without respect to volumetric

analysis. As usual, the model results should be considered in

the context of all available data.

Model AppropriatenessWhen using a model to estimate reserves, it is imperative that

reasonable assumptions be made with regard to future

development and operations of the reservoir. As with any

determination of proved reserves, environmental, regulatory,

contractual, market, and other types of practical factors mus

be taken into account when estimating the likelihood and

timing of future development and operational changes

Assumptions related to future wellhead pressures, the drilling

of future wells, etc. should be made with these practica

factors in mind.

It is also important to recognize situations where thephysical processes governing reservoir behavior are expected

to be different in the future than they have been in the past

and to adjust expectations for the model accordingly. For

example, if a model has been matched to the history of a

reservoir that has produced primarily under solution gas drive

there will be less confidence in that models ability to predic

reservoir performance under waterflood than if the reservoir

were to continue to produce under solution gas drive. The

match under solution gas drive provided assurance that the

factors important under that depletion regime (such as gas-oi

relative permeability functions) were reasonably correct in the

model. If there were little or no water movement or

production to match in the past, however, the model would no

have been tested for the adequacy of factors such as the water-oil relative permeability functions, which would impact the

performance under waterflood. Observations from analog or

nearby fields or laboratory test data could be incorporated into

the model to improve the confidence when forecasting under

different depletion mechanisms.

As a final check, the evaluator should verify that the

transition from historical to predicted production is smooth if

the model is run as a status quo, or do nothing case. An

abrupt change at the end of history is indicative of an

inappropriate model, even if the history match appears to be

reasonable in all other respects.

Mixed Reserves CategoriesThus far, we have focussed on down-grading a proved +

probable model for use in proved reserves estimation. There

are many other permutations that are interesting. In general, i

is best that an acceptable proved + probable or proved +

probable + possible model be developed, history matched, and

forecast. This model would then be modified for the highe

category runs. The probable reserves would be the incremen

between the proved and proved + probable reserves (as

determined through cashflow analysis of the simulation

results), and the possible reserves, if desired, would be the

final increment between proved + probable + possible

reserved and the proved + probable reserves. As a warning

though, removing hydrocarbon volumes from a historymatched models can have unforeseen consequences that must

be investigated. The authors have seen cases where rate

forecasts from proved reserves reach higher rates than the

reserves forecasts from the history matched proved + probable

model, despite featuring less OOIP and fewer wells. This

could be caused by mobility contrasts between the cases, and

enhanced contact with the aquifer when bands of hydrocarbon

are removed from a history matched model

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There are other means of modeling the different categories.

One is to create separate models. One that contains only

proved category hydrocarbons, a second that includes only

probable hydrocarbons, and a third (if so desired) that contains

only possible category reserves. The models would be run

separately, and reserves estimated based on three separate

streams. This approach is less desirable however, because itwould tend to underestimate interference between categories

through the reservoir and through facilities and wellbores.

ConclusionsIn general, simulation results should be treated as if they are

actual results from an analog field. If the simulation model is

very detailed, properly constructed, and well history matched,

then the model can be treated as a nearly perfect analog. If the

model or its history match are less impressive, then the results

can be treated as a less directly comparative analog. Thus it is

our conclusion that when incorporating simulation modeling

results into reserves estimation, the model should be treated as

additional data, rather than the sole source of data.

Additionally we reach several more particular conclusionsrelated to the incorporation of simulation modeling results into

reserves estimation.

1. Although reservoir simulation is a sophisticated technique,

it does not always produce reliable or applicable results,

especially in situations where data are sparse or of poor

quality.

2. Reservoir simulation should be used to improve the

understanding of a reservoir, but should not be used to

circumvent the terms of the Reserves Definitions. Reservoir

simulation is increasingly being used as a tool for reserves

estimation, but reservoir simulation results do not necessarily

constitute reserves estimates.

3. Simulation models are typically designed to capture themost likely reservoir description.

4. Because most likely is a level of confidence generally

associated with proved + probable reserves, models are

generally not designed to estimate proved reserves.

5. Aside from OOIP/OGIP, other types of reservoir energy

may be present in a model that do not qualify as proved, or

even probable in nature.

6. Models that are not in compliance with proved reserves

definitions can be modified to comply with the definitions, but

this process may be difficult.

7. Such modifications (# 6 above) may require substantial

alteration of the simulation grid/description, and require

attention to the development plan (wells and constraints)applied to the model.

8. Results from models that are not in compliance with proved

reserves definitions can also be used through the alteration of

the simulation output itself. This requires a great deal o

simulation output and may provide less rigorous solutions.

9. For immature reservoirs, simulation is useful primarily for

estimation of the hydrocarbon recovery efficiency, and to test

the limits in terms of uncertain parameters (permeability

aquifer support, OOIP, OGIP).

10. Some parameters will be uncertain, even in a historymatched model. These parameters may strongly influence the

prediction mode results. The impact of uncertain parameters

should be studied through the use of sensitivity runs.

11. Models of mature reservoirs should feature reasonable

history matches before they are accepted for reserves

purposes. The uniqueness and the quality of the history match

affect the confidence to be placed in a models ability to

predict future performance, and thus dictate the models

appropriate usage in the process of estimating reserves.

12. If the original hydrocarbon in place violates any reserves

definitions, sensitivity studies should be used to assure that the

original hydrocarbon in place is strictly necessary for history

matching before a model is accepted for reserves estimation

Under certain conditions, history-matched models can beuseful for confirming and resolving the in-place volume and

the recoverable reserves for mature reservoirs.

13. When using a model to estimate reserves, it is imperative

that reasonable assumptions be made with regard to future

development and operations of the reservoir.

14. Care must be taken in estimating reserves when a model is

used to assess the impact on recovered volumes caused by the

introduction of a process not included in the history match of

the reservoir.

15. A do nothing or status quo predictive run is required to

test a history matched model. If a history matched model doe

not smoothly transition between the historical data to the

predictive mode, it may need to be modified before it can beused to estimate reserves.

AcknowledgmentsWe extend our thanks to Kent Williamson, Don Roesle, and

Ron Harrell for valuable assistance granted writing this paper

We also thank Ryder Scott Company for supporting the

publication of this paper.

References1. Petroleum Reserves Definitions, Published by the SPE and

WPC, Richardson TX (1997).

2. Acuna, G.H., and D.R. Harrell: Adapting ProbabalisticMethods to Conform to Regulatory Guidelines, paper 63202

presented at the 2000 Annual Technical Conference andExhibition, Dallas, Texas, October 1-4.

3. Mattax, C.C. and Dalton, R.L.: Reservoir SimulationMonograph Series, SPE, Richardson, TX (1990).