ESTIMATION OF UNCERTAINTY ESTIMATION OF UNCERTAINTY IN GAS-CONDENSATE SYSTEMS IN GAS-CONDENSATE SYSTEMS

RESERVES BY MONTE CARLO RESERVES BY MONTE CARLO SIMULATIONSIMULATION

Jakub Siemek, Stanislaw NagyJakub Siemek, Stanislaw NagyAGH University of Science and TechnologyAGH University of Science and Technology,,

FacultyFaculty of Drilling and Oil-Gasof Drilling and Oil-Gas, , Kraków, PolandKraków, Poland

AGH Univ. of Science & AGH Univ. of Science & Technology Technology

in Krakow (Poland)in Krakow (Poland)

OverviewOverview AAn impact of improper condensate n impact of improper condensate

sampling on calculation of gas and sampling on calculation of gas and condensate reserves of gas-condensate reserves of gas-condensate system is presented. condensate system is presented.

PProbabilistic methods in reserves robabilistic methods in reserves estimation (proven, possible, estimation (proven, possible, probable). probable).

Sensitivity of CGR during Sensitivity of CGR during recombination of stream process on recombination of stream process on liquid and gas reserves has been liquid and gas reserves has been shown. shown.

Appraisal of Oil and Gas Appraisal of Oil and Gas FieldsFields

Investors have an interest in Investors have an interest in appraising propertiesappraising properties

Appraisal is of two basic forms: Appraisal is of two basic forms: Reserves Reserves Cash FlowCash Flow

ReservesReservesQuantities of petroleum from known accumulations Quantities of petroleum from known accumulations

available for production and quantities which are available for production and quantities which are anticipated to become available within a practical anticipated to become available within a practical time frame through additional field development, time frame through additional field development,

technological advances, or exploration.technological advances, or exploration.

SourceJanuary 1996 issue of the SPE Journal of Petroleum Technology and in the

June 1996 issue of the WPC (World Petroleum Congresses) Newsletter.

ReservesReserves

The SPE formulates rules for estimating The SPE formulates rules for estimating reservesreserves

Reserves are volumes that will be Reserves are volumes that will be produced under current operating produced under current operating practices, prices, taxes, costs, etc.practices, prices, taxes, costs, etc.

Three categories of reserves: Three categories of reserves: Proved, Proved, Probable Probable PossiblePossible

Proved is most importantProved is most important

Types of reservesTypes of reserves

Identifying reserves as proved, Identifying reserves as proved, probable, and possible has been the probable, and possible has been the most frequent classification method most frequent classification method and gives an indication of the and gives an indication of the probability of recovery. probability of recovery.

Because of potential differences in Because of potential differences in uncertainty, caution should be uncertainty, caution should be exercised when aggregating exercised when aggregating reserves of different classifications.reserves of different classifications.

Type of reserves -contType of reserves -cont

Reserves may be attributed to either Reserves may be attributed to either natural energy or improved recovery natural energy or improved recovery methods. methods.

Improved recovery methods include all Improved recovery methods include all methods for supplementing natural energy methods for supplementing natural energy or altering natural forces in the reservoir or altering natural forces in the reservoir to increase ultimate recovery.to increase ultimate recovery.

Type of reserves -contType of reserves -cont

Examples of such methods are pressure Examples of such methods are pressure maintenance, cycling, waterflooding, maintenance, cycling, waterflooding, thermal methods, chemical flooding, and thermal methods, chemical flooding, and the use of miscible and immiscible the use of miscible and immiscible displacement fluids. displacement fluids.

Other improved recovery methods may be Other improved recovery methods may be developed in the future as petroleum developed in the future as petroleum technology continues to evolve.technology continues to evolve.

Proved ReservesProved Reserves

Must be at least 90% likely to be Must be at least 90% likely to be producedproduced

Must be based on actual production Must be based on actual production tests or similar highly reliable tests or similar highly reliable informationinformation

May be reported to various agencies, May be reported to various agencies, stockholders and the general publicstockholders and the general public

Are “estimated’ and change with timeAre “estimated’ and change with time

Probable and Possible ReservesProbable and Possible Reservesand and ResourcesResources

Rarely reported outside companyRarely reported outside company Useful to keep track of future Useful to keep track of future

opportunitiesopportunities Measures of exploratory successMeasures of exploratory success ResourcesResources are NOT expected to be are NOT expected to be

produced unless some critical produced unless some critical factor (usually economics) factor (usually economics) changes in the futurechanges in the future

ReservesReserves

Petroleum reserves definitions are not Petroleum reserves definitions are not static and will be revised as additional static and will be revised as additional geologic or engineering data become geologic or engineering data become available or as economic conditions available or as economic conditions changechange

Reserves may be attributed to either Reserves may be attributed to either

natural energy or natural energy or improved improved recovery methodsrecovery methods

Facts

ReservesReserves

Geological complexityGeological complexity Stage of developmentStage of development Degree of depletion of the Degree of depletion of the

reservoirsreservoirs Amount of available dataAmount of available data Regulatory and economic conditionsRegulatory and economic conditions

Amount of Reserves depend upon

Current SPE Definitions-Current SPE Definitions-1997+1997+

Interpretation of P90,P50 and P10 for reserves accounting using SPE probability method

0

10

20

30

40

50

60

70

80

90

100

0 20000 40000 60000 80000 100000STB Recoverable

Pro

ba

bili

ty

Proved = P90 = 5,000 STB

Probable = P50 = 30,000 - 5,000 = 25,000 STB

Possible = P10 = 1,000,000 - 30,000 = 970,000 STB

Reserves StatusReserves Status

reserves

Proved Unproved

Probable Possible developed undeveloped

Producing Non-producing

Important!

RESERVES

Proved Unproved

Developed Undeveloped PossibleProbable

Producing

Non-producing

Probability > 90%

Probability > 50% Probability > 10%

more uncertain

Reserves Classification

Monte Carlo SimulationMonte Carlo Simulation A mathematical technique such as Monte A mathematical technique such as Monte

Carlo Simulation may be used to perform Carlo Simulation may be used to perform a large number of random, repetitive a large number of random, repetitive calculations to generate a range of calculations to generate a range of possible outcomes for the reserves and possible outcomes for the reserves and their associated probability of occurrence.their associated probability of occurrence.

See: See: Newendorp, 1975, Newendorp, 1975, Davidson&Cooper ,1979, Rubinstein, Davidson&Cooper ,1979, Rubinstein, 1981, Iman et al. 1980, Smith & Buckee 1981, Iman et al. 1980, Smith & Buckee 19851985

Classic Reserve Estimation Classic Reserve Estimation of Condensate Systemof Condensate System

The most classic attitude in estimation of reserves The most classic attitude in estimation of reserves of gas, oils and gas-condensate systems is of gas, oils and gas-condensate systems is presented in Arps (1956) Craft& Hawkins (1959). presented in Arps (1956) Craft& Hawkins (1959). This approach is rather deterministic with use of This approach is rather deterministic with use of single – average parameter estimation (Arps, single – average parameter estimation (Arps, 1956, Craft& Hawkins, 1959) or based upon 1956, Craft& Hawkins, 1959) or based upon numerical integration of geologic properties maps numerical integration of geologic properties maps The two main equation for volumetric reserve The two main equation for volumetric reserve estimation are following:estimation are following:

(1)(1) (2)(2)

(1 ) /wHCN V NTG S FVF

(1 ) /HC wN V NTG S FVF

(1 ) /w gHCG V NTG S B

Monte Carlo simulationMonte Carlo simulation

Using Monte Carlo simulation of gas and Using Monte Carlo simulation of gas and condensate reserves, it is possible to condensate reserves, it is possible to construct probability density function construct probability density function (e.g. fig.2), which may be useful to fix (e.g. fig.2), which may be useful to fix proven (P90), possible (P50) and proven (P90), possible (P50) and probable (P10) type of reserves. The MC probable (P10) type of reserves. The MC simulation is done usually using 1000-simulation is done usually using 1000-3000 random sampling or Latin Cube 3000 random sampling or Latin Cube procedures (Garb 1988, Iman et al. procedures (Garb 1988, Iman et al. 1980).1980).

Fig. 2 Probability density function Fig. 2 Probability density function of condensate reservesof condensate reserves

Probabilistic Methods Applied to Probabilistic Methods Applied to the Gas-Condensate and Volatile the Gas-Condensate and Volatile

Oils FieldsOils Fields To compute volumetric estimation of To compute volumetric estimation of

reserve by means probabilistic tools reserve by means probabilistic tools following equation may be used. following equation may be used.

where D- domain covering the reservoir, where D- domain covering the reservoir,

IR(x,y,z) =1 inside reservoir and IR(x,y,z) =1 inside reservoir and

IR(x,y,z) =0 outside reservoir, IR(x,y,z) =0 outside reservoir,

NTG (x,y,z)- net to gross ratio, NTG (x,y,z)- net to gross ratio,

φ (x,y,z) – porosity, φ (x,y,z) – porosity,

Sw (x,y,z)- water saturation, Sw (x,y,z)- water saturation,

FVF (x,y,z) –formation volume factor.FVF (x,y,z) –formation volume factor.

( , , ) (( , , ) ( , , )(1 ( , , )) / ( , , )R wDN I x y z x y z NTG x y z S x y z FVF x y z dxdydz

Sensitivity Analysis Sensitivity Analysis

There are several uncertain factors There are several uncertain factors related to definitions of reserves in the related to definitions of reserves in the gas/condensate/oil systems. Caldwell & gas/condensate/oil systems. Caldwell & Heater (2001) and Bu &Damsleth Heater (2001) and Bu &Damsleth (1996) claim that 75% of uncertainty of (1996) claim that 75% of uncertainty of reserves is linked to structural, reserves is linked to structural, geological properties (fault description, geological properties (fault description, tops on seismic velocity etc) and only tops on seismic velocity etc) and only 25% to the petrophysical properties. 25% to the petrophysical properties.

Sensitivity AnalysisSensitivity Analysis…… Some of possible errors in volumetric Some of possible errors in volumetric

reserve calculation are presented in the reserve calculation are presented in the table 1 - based on Detable 1 - based on De Sorcy (1980), Sorcy (1980), Smith&Buckee(1985), Bu&Damsleth Smith&Buckee(1985), Bu&Damsleth (1996) papers. (1996) papers.

In the table it is not taken into In the table it is not taken into consideration grading compositional consideration grading compositional effect or non-representative sampling of effect or non-representative sampling of hydrocarbon fluid or compositional hydrocarbon fluid or compositional grading (CG). In grading case the grading (CG). In grading case the uncertainty of FVF may rise up to 50% uncertainty of FVF may rise up to 50% (Siemek&Nagy 2004).(Siemek&Nagy 2004).

Table 1 Possible uncertainties of field variables Table 1 Possible uncertainties of field variables used in reserve and risk analysisused in reserve and risk analysis

Approx. range of accuracy (%) Source of Estimate

DeSorcy (1979)

Smith&Buckee (1985)

Bu&

Damsleth (1996)

Drill holes ±10-20 ±10 Geoph.data ±10-20 ±15

Area

Reg. Geol. ±50-80 ±50 Cores ± 5-10 ±8 Logs ±10-20 ±30

Pay thickness

Reg. Geol. ±40-60 ±50 Cores ± 5-10 Logs ±10-20 ±15 ±5 Prod. Data ±10-20 ±8 Drilling Cuttings

±20-40

Porosity

Correlation ±30-50 ±50 Cap. Press. ± 5-15 Oil Cores ± 5-15 ±20 Sat. logs ±10-25 ±8 ±20

Water Saturation

Correlation ±25-30 ±50 PVT ± 5-10 ±10 ±2 FVF Correlation ±10-30 ±20

Reserve Volume Reserve Volume EstimationEstimation After After ArpsArps(1956) recommendation, (1956) recommendation,

reserve volume may be evaluated by reserve volume may be evaluated by planimetering or numerical planimetering or numerical integrating (Simpson, trapezoidal, integrating (Simpson, trapezoidal, pyramidal), horizontal and vertical pyramidal), horizontal and vertical slices. The descriptions of real slices. The descriptions of real porous model systems are much porous model systems are much more complicated.more complicated.

Reserve Volume Reserve Volume EstimationEstimation

The properties of rock may spatially vary: The properties of rock may spatially vary: verticalvertical laterally. laterally.

Assuming uncertainty in the structure and Assuming uncertainty in the structure and volume of reservoir minimum three volume of reservoir minimum three scenarios have to be prepared: pessimistic scenarios have to be prepared: pessimistic (minimum value, most likely and optimistic (minimum value, most likely and optimistic (highest value). (highest value). These values may be used later in the These values may be used later in the Monte Carlo simulation of reservesMonte Carlo simulation of reserves

Sensitivity to Porosity and to Sensitivity to Porosity and to Effective Pay Thickness (Net Effective Pay Thickness (Net

to Gross)to Gross) The parameters like porosity and effective pay The parameters like porosity and effective pay

thickness depend on type of geological thickness depend on type of geological heterogeneity of rocks. heterogeneity of rocks.

There are three different types of There are three different types of heterogeneity in sandstones heterogeneity in sandstones different depositional units in the same reservoir, different depositional units in the same reservoir, lateral & multiple reservoirs apparently “blanket” lateral & multiple reservoirs apparently “blanket”

sands, sands, shale “breaks” of indeterminate aerial extends) and shale “breaks” of indeterminate aerial extends) and

There are two typesThere are two types heterogenity heterogenity in in carbonate reservoirs carbonate reservoirs lateral discontinuities in pay zones, lateral discontinuities in pay zones, very erratic – sometimes vugular – porosity.very erratic – sometimes vugular – porosity.

Sensitivity to Water Sensitivity to Water SaturationSaturation

The water saturation is usually computed The water saturation is usually computed from well logs using some of simply formulas from well logs using some of simply formulas (Archie, Humble, etc.). (Archie, Humble, etc.).

Based on the computed data is possible to Based on the computed data is possible to determine characteristic of distribution determine characteristic of distribution (vertical/lateral) or estimate triangular (vertical/lateral) or estimate triangular distribution with distribution with minimal, minimal, most likely and most likely and maximum water saturation.maximum water saturation.

Sensitivity to FVFSensitivity to FVF … … The following phenomena may be important for The following phenomena may be important for

evaluation of sensitivity of Formation Volume Fluid evaluation of sensitivity of Formation Volume Fluid (FVF): improper well conditioning, sample (FVF): improper well conditioning, sample contamination, inadequate or poor PVT analysis, contamination, inadequate or poor PVT analysis, inappropriate fluid model. In case of improper inappropriate fluid model. In case of improper sampling of gas condensate system (e.g. with non sampling of gas condensate system (e.g. with non stable CGR) the PVT properties may mask current stable CGR) the PVT properties may mask current estimation of HCIIP. estimation of HCIIP.

The errors of estimation may reach up to +/-50% or The errors of estimation may reach up to +/-50% or more. The influence of incorrect well conditioning more. The influence of incorrect well conditioning (e.g. inappropriate CGR) is given in the fig. (e.g. inappropriate CGR) is given in the fig. 2 and 3, 2 and 3, the impact of false CGR on gas phase properties is the impact of false CGR on gas phase properties is small (below 4% in presented case, fig. 4), but is small (below 4% in presented case, fig. 4), but is extremely high in case of condensate yield +70% and extremely high in case of condensate yield +70% and -20% (fig.3).-20% (fig.3).

Table 2. The summary of geological date and PVT Table 2. The summary of geological date and PVT data data

used in sensitivityused in sensitivity

Min. Most likely

Max.

Volume [108 m3] 1.800 2.00 2.200 NTG [-] 0.810 0.90 0.990 PHI [-] 0.135 0.15 0.165 SW [-] 0.270 0.30 0.330 OilFVF[m3/m3] 11.35 18.98 25.26 GasFVF[m3/m3] 0.0057 0.0058 0.006

0

Table 3 Prototype of gas-condensate Table 3 Prototype of gas-condensate system system

(Walsh &Raghavan, 1994)(Walsh &Raghavan, 1994)

Component Mole fraction [-]

Nitrogen (N2) 0.0223

Methane (C1) 0.6568

Carbon Dioxide (CO2) 0.0045

Ethane (C2) 0.1170

Propane (C3) 0.0587

Iso-Butane (iC4) 0.0127

Normal Butane (nC4) 0.0168

Iso-Pentane (iC5) 0.0071

Normal Pentane (nC5) 0.0071

Hexane (C6) 0.0098

C7+ 0.0872

Table 4 Comparison of reserve using Monte Carlo Table 4 Comparison of reserve using Monte Carlo simulation based upon crisp and triangular simulation based upon crisp and triangular

distribution of FVF distribution of FVF for condensate and gas phasesfor condensate and gas phases

Condensate reserves [106 Sm3]

Gas reserves [109 Sm3]

Type of

reserve Triangular Crisp Triangular Crisp

P90 8.33 9.085 29.73 29.74

P50 9.94 9.932 32.28 32.51

P10 17.7 12.15 39.15 39.77

ExamplesExamples

Based upon triangular presented in the table 2 Based upon triangular presented in the table 2 - - MC MC simulation has been performed. simulation has been performed.

Triangular distribution favor the estimated maximum Triangular distribution favor the estimated maximum point taken from the model parameter prefers any point taken from the model parameter prefers any random pseudo-generated value from the variable random pseudo-generated value from the variable range. range.

The Latin Hypercubic sampling (LHC) has been chosen, The Latin Hypercubic sampling (LHC) has been chosen, because LHC method reduces the number of samples because LHC method reduces the number of samples and variance(Rubinstein, 1981, Iman et al. 1980). and variance(Rubinstein, 1981, Iman et al. 1980).

One run in full triangular distribution of all parameters One run in full triangular distribution of all parameters (PVT1) and one additional simulation run for crisp PVT (PVT1) and one additional simulation run for crisp PVT data (PVT2) for each phase has been performed. data (PVT2) for each phase has been performed.

Fig. 4 Sensitivity of gas reserves error Fig. 4 Sensitivity of gas reserves error for over- and underestimation of CGRfor over- and underestimation of CGR

Fig. 3 Sensitivity of condensate reserves error Fig. 3 Sensitivity of condensate reserves error for over-for over- a and underestimation of CGRnd underestimation of CGR

ExamplesExamples……

The preparation of gas and condensate The preparation of gas and condensate phases has been done using flash phases has been done using flash procedure described in Nagy (1996, procedure described in Nagy (1996, 2002) using Peng-Robinson equation 2002) using Peng-Robinson equation of state (EOS) type (Tsai&Chen,1998, of state (EOS) type (Tsai&Chen,1998, Nagy 2002) (is standard conditions). Nagy 2002) (is standard conditions).

Data of gas-condensate systems Data of gas-condensate systems composition are presented in the tab. composition are presented in the tab. 2 (from Walsh&Raghavan 1994). 2 (from Walsh&Raghavan 1994).

ExamplesExamples……

The two calculations of reserves has The two calculations of reserves has been presented (fig. 5-6) for both been presented (fig. 5-6) for both condensate and gas phase. condensate and gas phase.

It is evident based on observation of fig. It is evident based on observation of fig. 5, that introducing possible 5, that introducing possible inaccuracies into the Oil Formation inaccuracies into the Oil Formation Volume Factor based upon earlier Volume Factor based upon earlier estimation of improper CGR estimation estimation of improper CGR estimation (±40%) causes movement of “true” (±40%) causes movement of “true” probability cumulative curve and its probability cumulative curve and its “scouring”. “scouring”.

Fig. 6 Estimation of P90, P50 & P10 type of gas Fig. 6 Estimation of P90, P50 & P10 type of gas reserves: PTV1 – with high uncertainties in reserves: PTV1 – with high uncertainties in

estimation of CGR; estimation of CGR; PVT2- true recombination sampling PVT2- true recombination sampling

Fig. 5 Estimation of P90, P50 & P10 type of condensate Fig. 5 Estimation of P90, P50 & P10 type of condensate reserves: PTV1 – with high uncer tainties in CGR; reserves: PTV1 – with high uncer tainties in CGR;

PVT2- true recombination sampling PVT2- true recombination sampling

ExamplesExamples……

The comparison of proven and possible The comparison of proven and possible and probable reserves for condensate and probable reserves for condensate and gas phase is given in the table 4. and gas phase is given in the table 4. The movement of P90 reserves is 8.3%. The movement of P90 reserves is 8.3%.

The effect is negligible for gas phase – The effect is negligible for gas phase – as is presented in the fig. 6 and tab. 4. as is presented in the fig. 6 and tab. 4. The maximum error of calculation is The maximum error of calculation is below 0.3% (!). below 0.3% (!).

The errors for P10 for condensate The errors for P10 for condensate phase are -45% and for gas phase 1.6%. phase are -45% and for gas phase 1.6%.

ConclusionsConclusions

Evaluation of uncertainties in the Evaluation of uncertainties in the estimation of geological reserves estimation of geological reserves based upon Monte Carlo method based upon Monte Carlo method is important in cases where full is important in cases where full compositional simulation (FCS) compositional simulation (FCS) or material balance with constant or material balance with constant volume depletion (MBE CVD) is volume depletion (MBE CVD) is not performed.not performed.

Conclusions …Conclusions … Impact of improper estimation of PVT Impact of improper estimation of PVT

data (well conditioning, sample data (well conditioning, sample contamination, inadequate or poor PVT contamination, inadequate or poor PVT analysis, and inappropriate fluid analysis, and inappropriate fluid model) on GIIP/OIIP may be model) on GIIP/OIIP may be significant. significant.

Other uncertainties in estimation of Other uncertainties in estimation of hydrocarbon liquid reserves using hydrocarbon liquid reserves using reservoir simulation may be caused by: reservoir simulation may be caused by: data inaccuracies; data coverage; data data inaccuracies; data coverage; data smoothing/interpolating; numerical smoothing/interpolating; numerical solution limits. solution limits.

Conclusions …Conclusions …

The effect of improper CGR estimation The effect of improper CGR estimation may be of range of 10% in case of P90 may be of range of 10% in case of P90 reserve and may expand up to -45% for reserve and may expand up to -45% for P10 reserve for condensate phase.P10 reserve for condensate phase.

The sensitivity to the FVF of gas-The sensitivity to the FVF of gas-condensate system for gas phase is condensate system for gas phase is negligible and could be omitted.negligible and could be omitted.

Thank you Thank you for your attention !for your attention !