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SPE-172434-MS
Probabilistic Material Balance: Application in Green Field
DevelopmentPlanning
Hammed Shittu, Ejeru Kemelayefa, and Ejika Emeka, Chevron
Nigeria limited
Copyright 2014, Society of Petroleum Engineers
This paper was prepared for presentation at the SPE Nigeria
Annual International Conference and Exhibition held in Lagos,
Nigeria, 0507 August 2014.
This paper was selected for presentation by an SPE program
committee following review of information contained in an abstract
submitted by the author(s). Contentsof the paper have not been
reviewed by the Society of Petroleum Engineers and are subject to
correction by the author(s). The material does not necessarily
reflectany position of the Society of Petroleum Engineers, its
officers, or members. Electronic reproduction, distribution, or
storage of any part of this paper without the writtenconsent of the
Society of Petroleum Engineers is prohibited. Permission to
reproduce in print is restricted to an abstract of not more than
300 words; illustrations maynot be copied. The abstract must
contain conspicuous acknowledgment of SPE copyright.
Abstract
The authors have used this paper to demonstrate how material
balance was applied in field developmentplanning for a green gas
field. In this work, we have used one of the reservoirs as case
study.
Deterministic tank model was initially built for the reservoir
using MBAL. Petrophysical properties,aquifer parameters and
relative permeability data were all added into the model. Well flow
models weregenerated using PROSPER and then imported into MBAL.
Facility constraints were imposed, anddeterministic prediction run
was performed.
Key impacting parameters on the recovery factor were assessed,
and corresponding ranges wereestimated for each. A probabilistic
prediction workflow was developed and applied to the
deterministicmodel. This uses experimental design to generate
multiple runs with the aid of OpenServer. Response/proxy function
for gas recovery was then generated and tested for consistency with
observed data.
Multiple Monte Carlo runs were then done using Crystal ball, and
the 10th, 50th and 90th percentileswere extracted. The
corresponding parameters for these respective percentiles were then
tested inMBAL to check for reliability. Finally, all reservoirs
were rolled-up using GAP, and the recoveryfactors were checked for
consistency with MBAL.
The recovery factors (P10, P50 and P90) from the probabilistic
material balance work were thencompared with results from
grid-based simulation work done on the reservoir. The figures were
furthercompared with estimates from local and global analogues, as
well as analysis done by a third-party.
Results from the MBAL work compared reasonably with recovery
factors from the other methods.Probabilistic material balance
approach helps to remove bias/anchoring while estimating a range
of
outcomes for recovery factor. It also gives reasonable
estimates, as demonstrated by the closeness ofresults with other
methods. However, it is not a replacement especially for the
grid-based simulation, butshould rather be a complement.
The methodology has been successfully applied to other gas
fields and reliable results were alsoobtained. The work was equally
adapted to more complex systems as multi-tank models.
Reservoir OverviewRoja is a virgin gas condensate reservoir
located in a field offshore Niger Delta with about 90 ft
waterdepth.
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Reservoir producibility was demonstrated by Drill Stem Tests
(DST) obtained from 3 wells. Thereservoir is over-pressured, with
pressure to datum ratio of 0.53 psi/ft. Liquid obtained during the
DSTshave 56API density and 75 STB/MMSCF condensate to gas yield
ratio.
The workflow for the probabilistic material balance modeling
done for Roja is shown in Fig. 1. Thetheory and application of
material balance, sub-surface forecasting and
probabilistic/stochastic methodshave been discussed extensively in
literature (Dake 1978, Ahmed 2005, Nwaokorie 2012, Vahedi
2005,Diamond 2011, Galecio 2010 and Wolff 2010). The authors do not
intend to discuss them in this work.
Deterministic MBAL Modeling and Uncertainty AssessmentTable 1
shows the input parameters used in building the deterministic
material balance model. Composi-tonal PVT modeling was done, and
some results are captured in Fig. 2. Coreys relative permeability
wasused with hysteresis option. Rock compressibility (comp.) was
obtained from local analogue correlation.Inflow performace and
vertical lift curves were generated in PROPSERmodel for the well
and importedinto the MBAL file. Surface constraints were also
imposed in MBAL to capture pressure drops throughthe well head to
delivery point.
Key impacting parameters on recovery identified were water and
gas relative permeability end-points( and respectively), trapped
gas saturation (Sgr), aquifer size (outer/inner radius Rd) and
aquiferpermeability (kaq). Table 2 enumerates the range of input
values for these key parameters.
The range of relative permeability end-points for gas and water
were obtained from core data. Residualgas saturation low-mid-high
values were also taken from SCAL analysis, and these lie within the
rangeof global analogue data after Hamon et al., 2001 (see Fig. 3).
Range of input for aquifer size was estimatedfrom geology map on
the low end, and the likely extent of aquifer beyond map data on
the higher end.
Figure 1Probabilistic material balance workflow
Table 1Input Parameters for Deterministic MBAL model
Parameter SMwi Rd kaq nq nw no Rock Comp. (1/psi)
Values 0.3 0.2 3 500 0.3 0.3 0.3 2 2 2 2.00E-06
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Aquifer permeability range was selected using petrophysical data
from wells penetrating hydrocarbon andaquifer.
Figure 2Some Results from Compositional PVT Matching for Roja
Reservoir Fluid Sample
Table 2Input Parameters for Probabilistic MBAL
Variable Rd kaq Sgr
Low 0.50 0.15 7.1 1620 0.43
Mid 0.33 0.30 3.0 815 0.28
High 0.11 0.49 1.0 168 0.17
* Low case was assigned highest aquifer size/permeability
because of reduction in recovery for gas reservoir in strong
aquifers; Rd represents the ratio ofradius measured from centre of
reservoir to edge of aquifer and assumes concentric reservoir and
aquifer; aquifer size is equal to times the reservoirsize.
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Probabilistic Forecast: Experimental Design and Proxy
GenerationFive-variable D-Optimal table was set-up for , and kaq as
shown in Table 3. SampleVisual Basic codes used for this work are
written below:
Where n is number of runs, k is row preceding the first row
where actual data for low-mid-high valuesare intended for
population; m is the first column value for the first variable in
the D-Optimal table; v isthe number of variables; R1:R2 are the
cells where the actual low-mid-high values are intended
forpopulation; L is a fixed value, equal to m1-2, where m1 is the
lowest value of m; A, B, C are the rowscontaining the actual low,
mid, high values of the variables. (This step entails creating a
table in Excelthat captures the actual low-mid-high values for the
variables: in this work, they have been capturedbetween rows A, B,
C and columns j-L and j-Lv-1.)
The OpenServer macro was generated using DoSet and DoGet
commands in addition to someVisual Basic commands. The authors have
not published the codes used for this step. This is because weare
not aware of the policies of Petroleum Experts (PETEX) relating to
this, even though we havedeveloped the codes entirely in-house.
Figure 3Literature data on maximum trapped gas saturation versus
porosity (after Hamon et al., 2001) Circles with orange fill are
data from Rojareservoir and another sand in the same field.
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Table 3Five-Variable D-Optimal Matrix.
Figure 4Response surface versus MBAL prediction results Figure
5Results from 100,000 Monte Carlo runs
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Once the D-Optimal-cum-MBAL macros were generated, we proceeded
to perform the probabilisticruns. Response equation that relates
the recovery factor from the runs to the variables was then
generatedusing QuickProxy, a Chevron in-house tool.
ResultsThe response surface calculations versus respective
outputs from the MBAL runs are shown in Fig. 4,showing a good
correlation. This gave us confidence to use the proxy, and so we
proceeded to generate100,000 Monte Carlo simulation runs. Below is
the response surface equation from this exercise:
Recovery Factor
The 10th, 50th and 90th percentiles from the Monte Carlo runs
are shown in Fig. 5, with values 61%,71% and 75% respectively.
Figure 6Pareto chart showing relative impact of
uncertainties
Table 4Selected Output Parameters for Probabilistic MBAL
Variable Rd kaq Sgr
P10 0.50 0.28 3.7 1000 0.38
P50 0.35 0.30 3.5 600 0.31
P90 0.11 0.49 2.6 168 0.18
Table 5Comparison of Recovery Factors (RF) with Other
Methods
Percentile ED MBAL (%) Simulation (%) Local Analogue (%) Third
Party (%)
P10 61 65 70 70
P50 71 66
P90 75 73
Note that values for local analogue and third party are based on
deterministic evaluations
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Fig. 6 is the Pareto chart, indicating that the aquifer size has
the highest impact on the recovery factor.The key parameter values
that replicated the P10, P50 and P90 recovery factors were then
selected. Thesewere in turn tested in MBAL (and ultimately in the
GAP full-field roll-up) a step which is iterative to ensure that
the parameters indeed represent models that produce the recovery
factors. Table 4 showsvalues for the P10, P50 and P90 models
selected.
BenchmarkingRecovery factor from this method was compared with
numbers from other methods. Table 5 shows thecomparion of the
probabilistic MBAL (ED MBAL) recovery factors with those from other
methods.
The first benchmark was against recovery factors obtained from
grid-based simulation done indepen-dently on the same
reservoir.
Another of such is the benchmark against a local analogue gas
condensate reservoir with similar ageand depositional environment.
Roja reservoir compares favourably, having better properties
relative to theanalogue. In addition, Roja is over-pressured at
shallower depth, while the analogue is normally pressured.
The third benchmark was against an independent assessment done
by a third party.In addition to these, the results from this work
were benchmarked against some global analogues (as
shown in Fig. 7), where the numbers lie within reasonable range
of the data.
ConclusionsProbabilistic material balance, as shown in this
work, is a reliable method for estimating a range recoveryfactors,
where there is need to build uncertainties into impating
parameters. Adding a probabilistic stepto the use of material
balance analysis eliminates bias and prevents anchoring. The
results from themethod compare reasonably with other methods.
When applied, the results should be benchmarked against other
data/methods to further build confi-dence in the reliability of the
forecasts.
Figure 7Benchmarking of MBAL recovery factors against global
condensate analogues
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The method can have limitations in terms of application to
highly heterogenous three-phase fluidsystems, although reasonable
results have been obtained in some cases.
AcknowledgementsThe authors would like to thank Chevron Nigeria
Limited (CNL) for the permission to publish theinformation. We
would also like to thank the management of CNLs JV E&AD and Gas
DevelopmentAsset Team for their encouragement towards this
work.
Nomenclature
Comp. CompressibilityED Experimental DesignGAP General
Allocation Package (a PETEX tool)kaq Aquifer permeability
Relative permeability to gas end-pointRelative permeability to
water end-pointRelative permeability to oil end-point
MMSCF Million Standard Cubic Feetng Coreys exponent for gasnw
Coreys exponent for waterno Coreys exponent for oilPVT Pressure
Volume TemperatureRd Outer to Inner radius ratioSCAL Special Core
AnalysisSTB Stock Tank BarrelSwi Water Saturation Trademark
sign
Subcripts
g, w, o gas, water, oilaq aquifer
Greek
Porosity
References1. Hamon, G., Suzanne, K., Billiote, J. and Trocme, V.
2001: Field-Wide Variations of Trapped
Gas Saturation in Heterogeneous Sandstone Reservoirs, Paper
71524 presented at 2001 SPEAnnual Technical Conference and
Exhibition held in New Orleans, Louisiana, 30 Sep-3 Oct.
2. Vahedi, A., Gorjy, F., Scarr, K., Sawiris, R., Singh, U.,
Montgomery, P., Clinch, S. and Sawiak,A. 2005: Generation of
Probabilistic Reserves Distributions From Material Balance
ModelsUsing an Experimental Design Methodology, IPTC Paper 11009
presented at the InternationalPetroleum Technology Conference held
in Doha, Qatar, 21-23 Nov.
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Vienna, Austria 23-26 May.
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4. Galecio, R. A. and Huerta, V. A. 2010: Traditional
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Production Modelling User Manual
SPE-172434-MS 9
Probabilistic Material Balance: Application in Green Field
Development PlanningReservoir OverviewDeterministic MBAL Modeling
and Uncertainty AssessmentProbabilistic Forecast: Experimental
Design and Proxy GenerationResultsBenchmarkingConclusions
AcknowledgementsReferences
