spe-2003-203-analisis del error pvt para los calculos de balance de materiales

8/7/2019 SPE-2003-203-Analisis del error PVT para los calculos de Balance de Materiales

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PAPER 2003-203

PVT Error Analysis for

Material Balance Calculations

R.O. Baker, C. Regier, R. SinclairEpic Consulting Services Ltd.

This paper is to be presented at the Petroleum Societys Canadian International Petroleum Conference 2003, Calgary, AlbertaCanada, June 10 12, 2003. Discussion of this paper is invited and may be presented at the meeting if filed in writing with thetechnical program chairman prior to the conclusion of the meeting. This paper and any discussion filed will be considered forpublication in Petroleum Society journals. Publication rights are reserved. This is a pre-print and subject to correction.

ABSTRACT

Very often non-representative/untuned PVT

correlations or incorrect PVT data are selected for use in

material balance calculations. Although the effect of

pressure errors on material balance has been extensively

studied, there is very little discussion of the effect of PVT

errors on material balance calculation in the petroleum

engineering literature. This paper emphasizes the need to

make corrections to laboratory data or correlations to

field data.

This paper therefore addresses the accuracy of the

material balance calculations due to errors in PVT

properties. Systematic and random errors were

intentionally introduced into reservoir properties such as

oil, gas, and water formation volume factors (Bo, Bg, Bw),

solution gas oil ratio (Rs), bubble point pressure (Pb), and

API gravity. The amount of systematic error introduced

was +/-2 and +/-10 percent. A random error from +/-0 to

2% was applied to each PVT value to account for typical

laboratory error. Material balance calculations were

performed using the erroneous PVT data and the

resulting original oil in place (OOIP) and, where

applicable, water influx (We). These error-influenced

results were then compared to a base case. The effects of

different parameters on the errors in calculated OOIP

were examined, including introducing systematic error to

only one PVT property at a time, and using PVT

correlations in place of actual lab data. We also observed

differences in calculated OOIP errors for differen

reservoir drive mechanisms.

The average error observed in the OOIP calculated

from a random +/-0 to 2% error introduced to all PVT

parameters varied from +/-2.7% for a solution gas drivereservoir with a large total pressure drop, to +/-27.6%

for a solution gas drive reservoir with a small tota

pressure drop. Results did not appear to depend directly

on reservoir drive mechanism, but rather were dependen

on the degree of pressure support or total pressure drop

in the reservoir. The larger the decrease in reservoir

pressure, the less sensitiveOOIP calculations are to PVT

PETROLEUM SOCIETYCANADIAN INSTITUTE OF MINING, METALLURGY & PETROLEUM


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error. Also, solution GOR had by far the largest impact

of any PVT parameter on the material balance

calculations. These observations indicate systematic or

random PVT error can cause significant inaccuracies

when using material balance to estimate OOIP and water

influx in certain reservoir situations.

Finally, this paper discusses the use of diagnostic

plots such as OOIP versus time or cumulative oil,

Havlena and Odeh, and measured versus calculated

pressures for showing the impact of error on OOIP

calculations.

INTRODUCTION

To perform material balance calculations, production

data, pressure data, PVT data, and any remaining

reservoir characteristics are required. If any one of these

data sets contains errors or inaccuracies, it will have an

effect on the outcome of the material balance equation.

This paper will investigate the effects and show the

consequences of these errors.

Oil and gas companies earn revenue based on the

amount of oil or gas they produce; accordingly, oil and

gas production is in general measured quite accurately

and the errors in production data are small. As production

data is acquired, it can be used to reduce the uncertainty

of prior original oil in place (OOIP) calculations. One ofthe most commonly used techniques to re-evaluate the

OOIP uses some form of a material balance calculation to

estimate OOIP and production. The effects of pressure

errors on material balance calculations have been

examined by many different individuals, and are

relatively well documented(1,2)

. This paper will examine

the errors introduced to OOIP and water influx

calculations when there are various systematic and

random errors introduced into the PVT data for three

example reservoirs.

CASE STUDIES

Three example reservoirs were selected for use in the

material balance calculation. The first is an Alberta

Cardium solution gas drive system. This example

reservoir has shown little pressure depletion throughout

its history and its PVT data was acquired using laboratory

analysis of fluid samples. This reservoir has therefore not

had any secondary recovery methods applied yet. The

PVT data for this reservoir was acquired using laboratory

analysis of fluid samples.

The second is also a solution gas drive system. This

reservoir passed through the bubble point pressure during

its production history and has experience a large degree

of pressure depletion throughout the field. The final

example reservoir is a combination drive reservoir with

an initial gas cap which provides most of the pressure

support for the reservoir.

Introduction of Systematic Errors

Laboratory events that may cause these types of error

include instruments calibrated incorrectly or errors in

measurement procedures (human error)(3)

.

Systematic errors were introduced into the reservoir

PVT properties of the three example reservoirs in two

different ways:

One PVT property contained error while all other

PVT properties were held constant at their true

value.

All reservoir PVT properties contained error.

An example of how systematic errors were defined is

shown in Figure 1.

For all three cases (where the foregoing example

reservoirs are respectively designated Case 1, 2, and 3),

systematic errors included sets of values 2% and 10%

above and below the true values of Rs, Bo, Bg, and Bw. As

well, a 2% increase and decrease and a 5% increase and

decrease in bubble point pressure were examined. Errors

were calculated for each PVT parameter individually as

well as all PVT parameters collectively.

For Case 2, in addition to systematic errors, the use of

correlations for values of Rs, B

o, and B

gindividually in

place of the true values was examined. Trials were

performed using the correlation-generated data, and using

the same correlation-generated data but with corrections

applied based on the observed field production data for

the case. The latter method assumes that, because the

reservoir is initially above the bubble point pressure, the

initial production GOR is equal to the initial Rs. To adjust


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the data, each Rs value is multiplied by the ratio of the

correlation-generated Rsi to the actual GOR determined

Rsi. Thus the correlation-generated Rs values are adjusted

to reflect this initial GOR, and values for Bo are

readjusted accordingly.

Introduction of Random Errors

Random errors were also introduced into the PVT data.

These errors were generated using a computer program

designed specifically for this purpose. The program

examined each PVT value and randomly selected a new

value, which was between +/-0 and 2% error from the

correct value. The range of +/-0 to 2% was chosen

because typical lab data typically accounts for a

maximum of +/-1% to 2% error in PVT measurements(4)

.

An example of random errors introduced into PVT

parameters is shown in Figure 2.

The random error generation program was used to

create 20 sets of erroneous PVT data for each of the cases

examined. This allowed for enough trials to obtain a good

average of how random errors in PVT data can affect

material balance results.

Calculation Method

The general form of the material balance equation

(MBE) is commonly expressed as:

( ) ( ) ( ) WePwcS1

fcwcSwcoiBm11BgiBgoimBgBsRsiRoiBoBN +

D

-+++

-+-+-

= Np (Bo + (Rp Rs)) Bg + Wp Wi Gi Bgi.............. (1)

Examining Equation 1 reveals that there are several

components of material balance that can cause errors in

the result. The error in OOIP (N in Equation 1) depends

on drive mechanism, total pressure drop in the reservoir,

pressure measurement accuracy, PVT accuracy, and

production measurement accuracy, or in equation form:

OOIP = f (drive mechanism, DP, Pressure errors, PVT

errors, Production data errors)......................................... (2)

Drive mechanism is a major influence on the error in

OOIP. For example, if a reservoir is under the influence

of a strong gas cap drive mechanism, gas cap expansion

will dominate the MBE. Thus, the MBE should calculate

gas cap volume more accurately than it will calculate

OOIP. In other words, the error bars will be much smaller

for original gas in place (OGIP) than for the OOIP.

A base case calculation was performed for each

reservoir using the existing PVT data to determine the

original oil in place and the water influx for each. The

base case calculations were later used to evaluate the

percentage error in the OOIP and We calculations when

erroneous PVT was used.

Once error was introduced into the PVT properties, the

new data sets were used to recalculate the MBE, which

provided the new OOIP and, in Case 3, water influx

values. Systematic percentage errors were calculated fo

all cases using Equation 3.

ValueCaseBase

ValueCaseBaseValueTrialError%

-

=.....................................(3

Each random error trial was also evaluated using

Equation 3. However, the random error trials were all

averaged together for each case study using the formula:

T

Error

ErrorAbsolute

T

n

n== 1%

%, ...........................................(4

where n represents the trial number and T is the totanumber of trials.

Results of Systematic Error Trials

Case 1

As indicated, the first case examined was a solution

gas drive Cardium pool located in Alberta, Canada

Historically, the pressure depletion is relatively small

having fallen only 14% from initial reservoir pressure

The pools pressure profile is shown in Figure 3. The

reservoir fluid approaches the character of a volatile oil

considering the values of Bo (e.g., Bob > 2.0 as shown inFigure 6), with an API gravity of 46.1. The average

reservoir porosity is 12%. This pool started producing in

1974 and secondary recovery methods have not yet been

applied to the reservoir because of the relatively low

pressure depletion.


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The MBE calculated a base case OOIP of 27.6 MMstb,

which agrees reasonably closely with the government

record of 30 MMstb.

The pool has produced about 800 Mstb during primary

production resulting in a recovery factor to date of about

3%. The production profile and drive indices plots are

shown in Figures 4 and 5.

The drive indices plot shown in Figure 5 indicates that

the solution gas drive mechanism is the dominant drive

index for this system.

The Bo versus pressure is plotted in Figure 6 and

shown to indicate the volatility of the reservoir oil, as

suggested before. The oil formation volume factor

reaches a maximum value at the bubble point of 2.13.

The systematic errors introduced to the PVT dataresulted in a range of errors in calculated OOIP and water

influx values. Table 1 summarizes the systematic error

results for Case 1.

It can be observed from Table 1 that errors in Rs

dominate the errors in OOIP; nevertheless, errors in Bo

and Pb are also quite significant. When all PVT values are

increased by 10%, the error in OOIP is negative, just as

the error in OOIP is when Rs alone is increased. This

effect is mirrored for the trials where all PVT and Rs

alone are decreased.

The smaller errors for the trials when all PVT values

are raised or lowered can be explained by observing that

errors in Bo have the opposite effect on OOIP than errors

in Rs. Thus, when both parameters are changed together,

the effects of one parameter act to offset the effects of the

other.

Finally, we note that for most of the Case 1 systematic

error trials, a +/-2% or +/-10% PVT error resulted in a

much higher degree of error in OOIP. In other words,

there was an amplification of PVT error (% error in OOIP> % error in PVT). This result is due to the relatively

small total pressure drop experienced by the Case 1

reservoir over its production life.

Case 2

The second case examined was also a solution gas

drive reservoir. The difference Case 2 compared to Case

1 is that there is a much greater degree of pressure

depletion and in fact the pressure profile passes through

the bubble point (see Figure 7). This case is a textbook

example from Dake(5). The pool is a tight (K ~5mD),

naturally fractured chalk reservoir located in Texas. The

MBE calculated a base case OOIP of 568 MMstb, whichagrees closely with the value in the textbook of

570 MMstb. This reservoir oil is also somewhat volatile

(Bob = 1.85 rbbl/stb).

The pool has produced 86.4 Mstb during its production

history resulting in a recovery factor to date of about

15%. The production profile and drive indices plots are


The drive indices plot for Case 2 indicates a dominant

solution gas drive mechanism for this system as shown in

Figure 9. Compressible drive energy is also noticeable,but its influence decreases once the bubble point pressure

is reached (in July 1996).

Errors in OOIP were also noticed in Case 2. Table 2

summarizes the systematic error results for Case 2.

Since the reservoir pressure in Case 2 drops below the

bubble point, the effect of introducing error into Bg was

also examined. As expected, results showed that it has an

impact in this case.

In Table 2, variances in Rs dominate the errors, but inthis case it is even more pronounced (in proportion to the

magnitudes of the other errors) than in Case 1. The

creation of a secondary gas cap is potentially the source

of this difference between the two cases. This example

also shows that an increase in Rs causes a decrease in

OOIP, and vice versa.

Errors in PVT Correlations

Trials were also conducted using uncorrected and

corrected correlations in place of various PVT

parameters for Case 2. The corrected versions wereobtained by matching the solution GOR. Table 3 shows

the resulting errors in OOIP using correlations in place of

actual Rs data for Case 2.

Use of any of the correlations resulted in substantial

errors if they were not corrected to match solution GOR.

However, when the corrections were applied, the

resulting OOIP values calculated were much closer to the


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true value. Because the oil in this example is a lighter

Texas oil, the Lasater (for Rs) and Dindoruk (for Bo)

correlations (both tuned to that type of crude) are the

most appropriate in this case.

Table 4 summarizes errors in OOIP calculated for

Case 2 when various Bo correlations were used in place

of the actual PVT data.

The results listed in Table 4 indicate that Bo

correlations do not cause major errors in OOIP calculated

using material balance, especially if the correlation used

is the most applicable to the type of oil being studied.

Case 3

The final reservoir examined has a combination drive

mechanism with an initial gas cap. The reservoir is

located in the Westerose Field in central Alberta, Canada.

The pools pressure profile is shown in Figure 10. It is a

light oil with a gravity of 42 API. The initial gas cap has

a free gas to oil volume ratio m ~ 0.48. This pool started

producing in 1954 and has had gas and water injection as

secondary recovery methods. The MBE calculated a base

case OOIP of 188 MMstb, which agrees closely with the

known value of 185 MMstb.

The reservoir has produced a total of 146 MMstb of oil

and 269 Bscf of gas. The recovery factor to date is

approximately 79% OOIP.

The production profile and drive indices plots are


The drive indices plot shows that there is influence

from solution gas, the gas cap, and the aquifer. However,

the gas cap influence is the most significant. The aquifer

provides only moderate support.

Systematic error results for OOIP and We are shown in

Table 5.

In Case 3, it is evident that the systematic errors in Bg

have a huge impact on OOIP. This is to be expected for

this case: the reservoir was initially at the bubble point

pressure, and there was a large primary gas cap (m =

0.48). Also, the most significant drive mechanism for this

reservoir is gas cap expansion, indicating that the MBE

should be much more sensitive to Bg than to the other

parameters.

When systematic error was applied to Bw in Case 3

very little error in OOIP and We was observed. Error in

OOIP was minimal, ranging +/-0.4%. The error in the

calculated water influx was also minimal compared to

Cases 1 and 2. Error in We was +/-7% when compared to

the base case. The explanation as to why B w has such aminimal effect on the MBE is that Bw is only encountered

in the underground removal term of the MBE. Although

the water formation volume factor introduces error into

the water production and injection values, considering

that Bw is usually a small number (Bw 1.01), a +/-2% or

+/-10% error in Bw is trivial to the overall MBE.

Errors in Bo did not significantly impact the OOIP

calculated in Case 3 as compared to errors in Rs. Error in

Bo did, however, have the greatest impact on the water

influx calculated when it was increased or decreased by10%.

RESULTS OF RANDOM ERROR TRIALS

Discussion

Table 6 lists the maximum, minimum, and average

errors in OOIP over the 20 random error trials for each o

the three cases.

The errors in Case 1 were much larger than the errors

observed for Cases 2 and 3. As noted, the explanation for

this is that the pressure drops over the production history

in Cases 2 and 3 were much larger than the pressure

drops over the production history of Case 1. The larger

pressure drops in Cases 2 and 3 mean that the differences

in PVT values used to calculate the OOIP over various

points in the production history are larger in proportion to

the size of the errors; thus, the errors in the PVT values

have less of an impact on the overall result. Case 3 had

the lowest errors in OOIP due to randomly induced PVT

errors because it is the least volatile of the three oils and

also had a substantial pressure decrease. As previously

noted in the Case 1 discussion, lack of pressure drop

amplifies errors in PVT (%error in OOIP > % error in

PVT); in Cases 2 and 3 with larger pressure drops

(greater than 30%), the error in PVT is roughly equal to

the error in OOIP.


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Diagnosing Errors

If there are sufficient pressure measurement points, it

is convenient to use a plot such as OOIP versus time (6) (or

cumulative oil produced), pressure versus time, or

Havlena and Odeh(7) to show the amount oftotal error in

the OOIP values calculated, and thus to help indicate themagnitude of errors that may exist in PVT values,

pressure measurements, and production. It is also very

common that, on plots of OOIP versus time or cumulative

oil, the early time points show a wide range of OOIP, but

with elapsed time or pressure depletion, the that range of

OOIP narrows. Figure 13 shows a plot containing two

sets of OOIP versus time data for Case 2. One data set

(the more consistent one) is the calculation of OOIP at

each time interval using the actual PVT data for Case 2.

The other (more erratic) data set is the same plot with

random +/-0 to 2% errors in the PVT data.

Note that, for each data set, the initial computed OOIP

values in Figure 13 are generally too high, but as time

progresses, the material balance calculation settles out to

its reasonably consistent value. This is because the

reservoir initially has only experienced a small total

pressure drop at these early points in time, and therefore

small errors in PVT or pressure measurements are greatly

amplified during the initial part of the curve. This is

another demonstration of how material balance

calculations can contain large errors for reservoirs with a

small total pressure drop, and how large pressure drops

help make the material balance more accurate.

From Figure 13, it is also easy to see that random

errors in the PVT data translate into random errors in the

computed OOIP with time and wider error bars for OOIP.

The Havlena and Odeh plot shown in Figure 14

demonstrates the effect of PVT error as well. We have

found the use of Havlena and Odeh plots to be a valuable

diagnostic tool when examining results from the MBE

solution. When error was introduced into the PVT data,

the curve did not fit the data as accurately. Caution must

be used when interpreting the plot. Unlike an OOIP

versus time plot, where the uncertainty in OOIP can be

clearly seen, the uncertainty shown on a Havlena and

Odeh plot is not as obvious. This is due to the later points

which are more heavily weighted and therefore the error

is dampened and not as visible(8).

Another diagnostic tool used to evaluate the accuracy

of the MBE is a plot of both actual pressure (field data)

and calculated pressure (from MBE) versus time.

Generally, if there is a good pressure match between the

two curves, there can be more confidence in the MBE.

Shown in Figure 15 is a plot of measured pressure and

calculated pressure for Case 2. Initially, the curves do not

match exactly due to some uncertainty in OOIP. Once

this uncertainty (error) is minimized, the match between

the pressures significantly improves.

CONCLUSIONS

The results from this work indicate that the impact of

PVT errors on material balance calculations can be

significant if the decrease in reservoir pressure over the

production history of the reservoir is quite small, or if the

oil is highly volatile. These results are also a good

indication of one of the reasons why a reservoir should

have a significant amount of production and pressure loss

before it becomes a good candidate for analysis using the

MBE.

Making use of available information such as

production data, results from infill drilling and

surveillance measurements (current reservoir pressureand contact levels), as well as ensuring that the PVT data

for the field agrees with that from the production data can

help to narrow down the possible results for a material

balance calculation. It is also important to compare initial

produced gas oil ratio to PVT data and make necessary

corrections(9)

. Using diagnostic plots such as OOIP versus

time, Havlena and Odeh, or calculated pressure with

measured pressure can help indicate how much error

there is in a material balance calculation, and therefore

can help determine the reliability of the results of the

calculation.

While software packages exist that greatly simplify the

task of performing material balance calculations, these

packages cannot be used blindly. A reservoir engineer

must have a good understanding of the fundamentals of

the MBE, and apply this knowledge to the software

package to produce the best results in cases with small


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pressure depletion. In particular, this applies to the

selection and adjustments of any correlations used in the

calculations.

NOMENCLATURE

N = volume of original oil in place in the reservoir,

stb

Bo = oil formation volume factor, rbbl/stb

Boi = initial oil formation volume factor, rbbl/stb

Rsi = initial solution gas oil ratio, scf/stb

Rs = solution gas oil ratio scf/stb

Bg = gas formation volume factor, rbbl/scf

m = ratio of the volume of the initial reservoir gas

cap to the volume of the original oil in place,

rbbl/rbbl

Bgi = initial gas formation volume factor in thereservoir, rbbl/scf

cw = compressibility of the water in the aquifer,psi-1

Swc = connate water saturation, fraction

cf = compressibility of the formation rock, psi-1

P = change in volumetric average reservoir pressure,

psia

We = cumulative water influx, rbbl

Np = cumulative volume of oil produced, stb

Rp = ratio of cumulative gas produced to cumulative

oil produced, scf/stb

Wp = cumulative produced water, stb

Wi = cumulative injected water, stb

Gi = cumulative injected gas, scf

ACKNOWLEDGEMENTS

The authors would like to acknowledge the fine

contributions of many individuals in the reservoir

engineering literature regarding the techniques of

material balance analysis as well as the Alberta

Energy and Utilities Board for providing an excellent

database for production data. The authors would also like

to acknowledge Eric Denbina and Trisha Anderson for

their assistance and many helpful suggestions in making

this paper a reality.

REFERENCES

1. Walsh, M.P., Effect of Pressure Uncertainty on Material

Balance Plots, SPE paper 56691, 1999.

2. McEwan, C.R., Material Balance Calculations with Wate

Influx in the Presence of Uncertainty in Pressures, SPEJ

June 1962.

3. Williams, J.M., Getting the Best Out of Fluid Samples,

JPT, September 1994.

4. Bu, T. and Damsleth, E., Errors and Uncertainties in

Reservoir Performance Predictions, SPE paper 30604

presented at the 1995 SPE Annual Technical Conference

and Exhibition, Dallas, TX, October 22-25, 1995.

5. Dake, L..P., The Practice of Reservoir Engineering, Elsevie

Science B.V., 1994.

6. Campbell, J.M.: Oil Property Evaluation, Prentice-Hall Inc

September 1959.

7. Havlena, D. and Odeh, A.S., The Material Balance as an

Equation of a Straight LinePart II, Field Cases, JPT, July

1964.

8. Tehrani. D.H., An Analysis of Volumetric Balance

Equation for Calculation of Oil-in Place and Water Influx,

SPE paper 5990.

9. Clark, N.J., Adjusting Oil Sample Data for Reservoi

Studies, JPT, February 1962.

10. Wang, B., and Hwan, R.R., and Bowman II, G.W

OILWAT: Microcomputer Program for Oil Materia

Balance With Gascap and Water Influx, SPE paper 24437

presented at the Seventh SPE Petroleum Compute

Conference, Houston, TX, July 19-22, 1992.

11. Pletcher, J.L., Improvements to Reservoir Material Balance

Methods, SPE paper 62882 presented at the 2000 SPE

Annual Technical Conference and Exhibition, Dallas, TX

October 1-4, 2000.

12. Carlson, M.R., Tips, Tricks and Traps of Material Balance

Calculations, JCPT, December 1997.

13. Galas, C.M.F., Confidence Limits of Reservoir Parametersby Material Balance, paper 94-035 presented at the 45

t

Annual Technical meeting of the Petroleum Society of CIM

Calgary, AB, June 12-15, 1994.

14. Epic Consulting Services Ltd., Theory and Pract ice o

Material Balance User Manual, internal company

publication, 2001; Public version, May 2002.


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15. Craft, B.C. and Hawkins, M.F., Applied Petroleum

Reservoir Engineering, Second Edition revised by R.E.

Terry, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1991.

16. Hwan, R.R., Improved Material Balance Calculations by

Coupling with a Statistics-Based History Matching

Program, SPE 26244, presented at SPE PetroleumComputer Conference, New Orleans, July 11-14, 1993.


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Trial Error In OOIP

All PVT +10% -6.5%

All PVT -10% 8.0%

Rs +10% -28.3%

Rs -10% 54.7%

Bo +10% 38.8%

Bo -10% -24.6%Pb +2% -18.1%

Pb -2% -4.7%

Table 1: Systematic Case 1 Trials and Result

Trial Error In OOIP

All PVT +10% -16.0%

All PVT -10% 22.5%

Rs +10% -16.0%

Rs -10% 22.5%Bo +10% 10.0%

Bo -10% -8.6%

Bg +10% -7.9%

Bg -10% 11.3%

Pb +2% -3.5%

Pb -2% 11.1%

Table 2: Systematic Case 2 Trials and Results

Rs CorrelationUsed

OOIP Error forUncorrectedCorrelation

OOIP Error forCorrected

Correlation

Standing 121.3% 56.9%

Vasquez & Beggs 194.7% 50.3%

Lasater 66.1% 9.4%

Petrosky 257.0% 42.4%

Dindoruk 46.3% -1.24%

Table 3: Errors in OOIP Using Correlations for Rs

Bo Correlation Used OOIP Error

Standing -3.3%

Vasquez & Beggs -8.3%

Petrosky -14.2%

Dindoruk 0.9%

Table 4: Errors in OOIP Using Correlations for Bo


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Trial OOIP Error We Error

All PVT +10% -7.9% 39.7%

All PVT -10% 9.7% -39.7%

Rs +10% -9.4% -45.5%

Rs -10% 10.6% 48.7%

Bo +10% 1.2% 88.1%Bo -10% -1.3% -87.6%

Bg +10% 17.1% -394.0%

Bg -10% 2.4% 196.4%

Bw +10% 0.4% -6.9%

Bw -10% -0.4% 6.8%

Table 5: Systematic Case 3 Trials and Results

Case 1 Case 2 Case 3

Maximum 56.9% 9.5% -2.4%Minimum 0.0% 0.2% 0.1%

Average 27.4% 3.0% 1.2%

Table 6: Max, Min, and Average Random Errors for OOIP for each Case for2% PVT Error

Rs

Pressure

Bubble pt.

True value

-10% of True value

+10% ofTrue value

Figure 1: Example of Systematic Error


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11

Rs

Pressure

Bubble pt.

True value

Figure 2: Example of Random Error

Pressure vs Time

0

500

1000

1500

2000

2500

3000

3500

4000

4500

1973 1975 1976 1978 1979 1980 1982 1983

Date

Pressure(p

sia)

Figure 3: Pressure Profile of Case 1 Reservoir

Cumulative Production

0

100

200

300

400

500

600

700

800

900

1973 1976 1979 1982 1984

LiquidProduction

(Mstb)

0

500

1,000

1,500

2,000

GasProduction

(MMscf)

Oil Water Gas

Figure 4: Cumulative Production for Case 1


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Calculated Drive Indices

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1974 1975 1977 1978 1979 1981 1982

DriveIndice

s

Solution Gas Gas Cap Sum Indices

Figure 5: Drive Indices Plot for Case 1

Bo vs. Pressure

0.0

0.5

1.0

1.5

2.0

2.5

0 1000 2000 3000 4000 5000 6000 7000 8000

Pressure (psia)

(rbbl/stb)

Bo

Figure 6: Plot of Bo vs. Pressure for Case 1

Pressure vs Time

0

1000

2000

3000

4000

5000

6000

7000

8000

1994 1995 1996 1997 1998 1999 2000 2001

Date

Pressure(psia)

Figure 7: Pressure Profile for Case 2


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13


0

20

40

60

80

100

1994 1995 1997 1998 1999 2001

LiquidProduction

(MMstb)

0

50000

100000

150000

200000

250000

300000

GasProduction(M

Mscf)

Oil Gas


Calculated Drive Indices vs Time

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1995 1995 1996 1997 1997 1998 1999 1999 2000

DriveIndices

Solution Gas Compressible Sum Indices

Figure 9: Drive Indices Plot for Case 2

Pressure vs Time

0

500

1000

1500

2000

2500

3000

19 54 19 60 1 966 19 72 1 978 19 84 1 990 19 96

Date

Pre

ssure(psia)

Figure 10: Pressure Profile for Case 3


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14


0

20

40

60

80

100

120

140

160

1952 1957 1962 1968 1973 1979 1984 1990 1995 2001

LiquidProdu

ction

(MMstb)

0

50

100

150

200

250

300

GasProduction

(Bscf)

Oil Water Gas


Calculated Drive Indices

0.0

0.2

0.4

0.6

0.8

1.0

1 95 2 1 95 7 1 96 2 1 96 8 1 97 3 1 97 9 1 98 4 1 99 0 1 99 5

DriveIndices

Soln' Gas Gas Cap Water Sum Indices

Figure 12: Calculated Drive Indices for Case 3

(OOIP)MB=568MMstb

(OOIP)MB=570MMstb

(OOIP)MB=568MMstb

(OOIP) Volumetric= 570MMstb

(OOIP)MB=568MMstb

(OOIP)MB=570MMstb

(OOIP)MB=568MMstb

(OOIP) Volumetric= 570MMstb

Figure 13: OOIP vs. Time for Case 2, With and Without PVT Error


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spe-2003-203-analisis del error pvt para los calculos de balance de materiales

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