Tuning Equation of State Models EOS Tuning Adjustment

Tuning Equation of State Models EOS Tuning Adjustment of EOS parameters to match measured data. A successful EOS tuning is based on common sense, patience, and experience. 1. Data Analysis 2. Data Input 3. Selection of EOS components 4. Weighting 5. Measurement Accuracies 6. Regression 7. § Strategies § Selection of Variables § Step-by-Step Final Consistency Checks Course in Advanced Fluid Phase Behavior. © Pera A/S 1

Data Analysis Always to check the data for validity and consistency! 1. For each individual sample: 2. For all samples: • For reported compositions, verify the mathematical recombination. • Generate general trend plots to identify outliers. • DLE material balance for oils. • • Material balance for slimtube experiments. • Backward and forward material balance for CVD, multi-contact experiments (and potentially swelling experiments). Many quantities are fairly well correlated (e. g. , saturation pressure, GOR, methane content, C 5+ content, C 7+ MW, etc. ). Examples. • K-value plot for separator experiments (Hoffman et. al) • K-value vs. pressure for equilibrium phase split and multicontact experiments. 3. Use Gamma model to fit any available extended compositional analysis. • For any extended compositional analysis with a suspicious tail, replace measured data with model data (See Heptanes Plus characterization). Course in Advanced Fluid Phase Behavior. © Pera A/S 2

Trend Plots – Psat vs. C 1 Course in Advanced Fluid Phase Behavior. © Pera A/S 3

Trend Plots – CGR vs. C 7+ (Gas Condensate) NOTE: CGR Converted to common basis (common process) Course in Advanced Fluid Phase Behavior. © Pera A/S 4

Trend Plots – Density vs. Mw Course in Advanced Fluid Phase Behavior. © Pera A/S 5

Trend Plots – Undersaturated Oil Viscosity vs. Density (at common pressure). Course in Advanced Fluid Phase Behavior. © Pera A/S 6

Data Input Compositions 1. Honor the masses, rather than the moles. • 2. An EOS requires molar compositions. However, PVT labs measure fluid masses and calculate moles using a set of molecular weights that may not have been appropriate. Input compositions up to a selected plus fraction (often C 7+ or C 10+) PVT Experimental Data 1. Input all measured data • Even fluids that are not in-situ representative are important! • For multi-contact and equilibrium phase split experiments input calculated K-values (all light components and one K-value for the whole plus fraction). • Some simulators does not allow the input of all data, in such cases measured data should manually be compared with calculated data. Course in Advanced Fluid Phase Behavior. © Pera A/S 7

Selection of EOS Components and Basic Properties 1. 2. For library components (C 5 and lighter): 3. For heavy plus fraction (typically C 7+ or C 10+): Start with single-carbon-number (SCN) fractions C 7, C 8, … to C 30+ or C 36+. • C 4 and C 5 should be divided into normal- and iso- fractions. • • The PVT program should use standard library EOS component properties for these components. • Intermediate heavy components (C 6 until last heavy plus fraction): • • Component molecular weight (Mw) and specific gravities ( ) should be based on individual component makeup. PVT progam should correlate EOS parameters based on Mw and ( ). Alternatively (less recommended), select number of heavy pseudo components (Typically 3 -10). The selection should be based on equal mass principle (in some PVT simulators this is automated). This selection should be based on an average oil sample, or the heaviest gas sample if only gas samples are available. • The PVT program calculates Mw and for each pseudo fraction, based on the total plus fraction Mw and Gamma distrubution model. • The PVT model use Mw and to estimate the other EOS component properties. • Course in Advanced Fluid Phase Behavior. © Pera A/S 8

Weighting – What Data is Important? Weighting should reflect the importance and the uncertainties in the measured data Reservoir A: Under-saturated oil reservoir Medium sized reservoir Depletion and/or water injection - Reservoir C: Highly under-saturated gas condensate reservoir. High permeability. Primary depletion. - Reservoir B: - Saturated oil reservoir with initial gas cap Large reservoir Gas injection in gas cap, followed by depletion Reservoir D: - Saturated gas condensate reservoir. Low permeability. Potential gas injection followed by depletion. Course in Advanced Fluid Phase Behavior. © Pera A/S 9

Reservoir A – What Data is Important? Reservoir A: - - Under-saturated oil reservoir Medium sized reservoir Depletion and/or water injection PVT Measurements: - Multi-Stage Separator Experiments (SEP) - Constant Composition (CCE) - Differential Liberation (DLE) - Oil Viscosity Measurements (VISC) Key Data: Sampling: - Bo and GOR from SEP experiment. If the well is tested: - Oil densities (CCE, DLE). - Bottom-hole samples - Oil viscosities (CCE, DLE). - Separator sample - Oil shrinkage and Solution GOR from DLE. - Gas Z-factor - Oil compressibility (CCE). - Bubble-point pressure (EOS tuning). If well not tested: - MDT - Mini DST Course in Advanced Fluid Phase Behavior. © Pera A/S 10

Reservoir B – What Data is Important? Reservoir B: PVT Measurements: - Multi-Stage Separator Experiments (SEP Oil & Gas) - Constant Composition (CCE Oil and Gas) - Differential Liberation (DLE Oil) - Constant Volume Depletion (CVD Gas) - Backward multi-contact experiments (Oil and Injection Gas). Sampling: - Oil Viscosity Measurements If the well is tested: - ECM experiment (Oil and Gas) - TBP (From reservoir oil) - Saturated oil reservoir with initial gas cap Large reservoir Gas injection in gas cap, followed by depletion - Bottom-hole samples - Separator sample Key Data: (Addition to Res A) - ECM - Vaporization of oil - CVD gas compositions - Equilibrium oil and gas composition at GOC (ECM oil and gas). If well not tested: - MDT - Mini DST Course in Advanced Fluid Phase Behavior. © Pera A/S 11

Reservoir C – What Data is Important? PVT Measurements: Reservoir C: - Highly under-saturated gas condensate reservoir. High permeability. Primary depletion. Sampling: - Constant Composition (CCE) - Constant Volume Depletion (CVD) - Multi-Stage Separator Experiments (not required for lean systems). Key Data: - Gas z-factor - Producing gas composition (amount of C 7+ in gas). - Cumulative amount of gas produced from CVD. - Separator oil densities (C 7+ characterization). - Dew-point pressure (only for EOS tuning) If the well is tested: - Separator sample If well not tested: - MDT - Mini DST Course in Advanced Fluid Phase Behavior. © Pera A/S 12

Reservoir D – What Data is Important? PVT Measurements: Reservoir D: - Constant Composition (CCE) - Constant Volume Depletion (CVD) - Multi-Stage Separator Experiments - Multi Contact Vaporization - Viscosity measurements (Separator Oil, at reservoir p, T) Sampling: - IFT measurement. If the well is tested: - Slim-tube Experiments (for rich, near critical fluid systems only). - TBP (Stock Tank Oil) - - Saturated gas condensate reservoir. Low permeability. Potential gas injection followed by depletion. Separator sample If well not tested: - MDT Key Data (Addition to Res A) - Mini DST - Oil vaporization (injection) Relative oil volume (blockage) Oil viscosity (blockage) Course in Advanced Fluid Phase Behavior. © Pera A/S 13

Accuracy in Measured Data • Saturation pressure: Generally within +/- 5 bar. • Gas condensate might have larger uncertainties. Gas Z-factors: • After checking with Standing. Katz, accuracy should be within 1 -3%. Stock tank oil densities: • Within 1% • • STO (and C 7+) Molecular Weight Generally within 5% • Not uncommon to see variation between different labs of 5+%. Reservoir oil densities: • Pycnometer densities generally within 1 -2%. • DLE densities within 2 -4% (except last stage!). Separator Bo • Generally 1 -2%. Separator GOR • Within 2% • Lean gas condensates, 4 -5% • Beware of gas leakage • • Course in Advanced Fluid Phase Behavior. © Pera A/S 14

Accuracy in Measured Data • Saturation pressure: Generally within +/- 5 bar. • Gas condensate might have larger uncertainties. Gas Z-factors: • After checking with Standing. Katz, accuracy should be within 1 -3%. Stock tank oil densities: • Within 1% • • STO (and C 7+) Molecular Weight Generally within 5% • Not uncommon to see variation between different labs of 5+%. Reservoir oil densities: • Pycnometer densities generally within 1 -2%. • DLE densities within 2 -4% (except last stage!). Separator Bo • Generally 1 -2%. Separator GOR • Within 2% • Lean gas condensates, 4 -5% • Beware of gas leakage • • Course in Advanced Fluid Phase Behavior. © Pera A/S 15

Accuracy in Measured Data, cont. • DLE GOR (Released gas) • • Last stage (bleeding process) should not be weighted! Generally within 3 % • Gas composition C 6+ content not accurate! • • CVD gas compositions: • High quality laboratories should get C 7+ within +/- 0. 2 mole-%. • Material balance check is ALWAYS needed – a lot of bad data exists. • CVD cumulative gas produced. • Generally within 2 -3 recovery-% • CCE and CVD oil relative volumes: • Within 5% for volatile oil and rich gases. • Large errors can be expected for very lean and near-critical fluids. Minimum Miscibility Pressure: • High quality measurements should give oil recoveries above MMP higher than 95% • With a well-designed experiment (pressure selection) MMP should be within +/- 5 bar. Oil viscosities: • Large uncertainties, generally 1020% Gas viscosities: • Usually not measured Course in Advanced Fluid Phase Behavior. © Pera A/S 16

Accuracy in Measured Data, cont. • DLE GOR (Released gas) • • Last stage (bleeding process) should not be weighted! Generally within 3 % • Gas composition C 6+ content not accurate! • • CVD gas compositions: • High quality laboratories should get C 7+ within +/- 0. 2 mole-%. • Material balance check is ALWAYS needed – a lot of bad data exists. • CVD cumulative gas produced. • Generally within 2 -3 recovery-% • CCE and CVD oil relative volumes: • Within 5% for volatile oil and rich gases. • Large errors can be expected for very lean and near-critical fluids. Minimum Miscibility Pressure: • High quality measurements should give oil recoveries above MMP higher than 95% • With a well-designed experiment (pressure selection) MMP should be within +/- 5 bar. Oil viscosities: • Large uncertainties, generally 1020% Gas viscosities: • Usually not measured Course in Advanced Fluid Phase Behavior. © Pera A/S 17

Regression Strategies § Use as few regression variables as needed, and try to exercise good engineering judgment. § Try to choose regression variables that have both relatively high impact and relatively high uncertainty, such as binary interaction parameters, correlation parameters, and the properties of the heaviest pseudocomponents. § Keep the regression variables bounded within their estimated uncertainties. § Do not regress on the physical properties of the pure components (C 5 -), with the exception of volume shift of C 1 and C 2 (to match gas Z-factors at high pressures > 500 bar) § Don’t match viscosity data simultaneously with PVT data. It will only compromise the fit of the PVT data. Successful regression requires considerable trial and error. Keep trying different regression variables, initial values, and/or data weightings. If the results continue to be unsatisfactory, look for possible inconsistencies in the data. § Course in Advanced Fluid Phase Behavior. © Pera A/S 23

Regression Strategies § Use as few regression variables as needed, and try to exercise good engineering judgment. § Try to choose regression variables that have both relatively high impact and relatively high uncertainty, such as binary interaction parameters, correlation parameters, and the properties of the heaviest pseudocomponents. § Keep the regression variables bounded within their estimated uncertainties. § Do not regress on the physical properties of the pure components (C 5 -), with the exception of volume shift of C 1 and C 2 (to match gas Z-factors at high pressures > 500 bar) § Don’t match viscosity data simultaneously with PVT data. It will only compromise the fit of the PVT data. Successful regression requires considerable trial and error. Keep trying different regression variables, initial values, and/or data weightings. If the results continue to be unsatisfactory, look for possible inconsistencies in the data. § Course in Advanced Fluid Phase Behavior. © Pera A/S 24

Regression Strategies § Use as few regression variables as needed, and try to exercise good engineering judgment. § Try to choose regression variables that have both relatively high impact and relatively high uncertainty, such as binary interaction parameters, correlation parameters, and the properties of the heaviest pseudocomponents. § Keep the regression variables bounded within their estimated uncertainties. § Do not regress on the physical properties of the pure components (C 5 -), with the exception of volume shift of C 1 and C 2 (to match gas Z-factors at high pressures > 500 bar) § Don’t match viscosity data simultaneously with PVT data. It will only compromise the fit of the PVT data. Successful regression requires considerable trial and error. Keep trying different regression variables, initial values, and/or data weightings. If the results continue to be unsatisfactory, look for possible inconsistencies in the data. § Course in Advanced Fluid Phase Behavior. © Pera A/S 25

Regression Strategies § Use as few regression variables as needed, and try to exercise good engineering judgment. § Try to choose regression variables that have both relatively high impact and relatively high uncertainty, such as binary interaction parameters, correlation parameters, and the properties of the heaviest pseudocomponents. § Keep the regression variables bounded within their estimated uncertainties. § Do not regress on the physical properties of the pure components (C 5 -), with the exception of volume shift of C 1 and C 2 (to match gas Z-factors at high pressures > 500 bar) § Don’t match viscosity data simultaneously with PVT data. It will only compromise the fit of the PVT data. Successful regression requires considerable trial and error. Keep trying different regression variables, initial values, and/or data weightings. If the results continue to be unsatisfactory, look for possible inconsistencies in the data. § Course in Advanced Fluid Phase Behavior. © Pera A/S 26

Regression Strategies § Use as few regression variables as needed, and try to exercise good engineering judgment. § Try to choose regression variables that have both relatively high impact and relatively high uncertainty, such as binary interaction parameters, correlation parameters, and the properties of the heaviest pseudocomponents. § Keep the regression variables bounded within their estimated uncertainties. § Do not regress on the physical properties of the pure components (C 5 -), with the exception of volume shift of C 1 and C 2 (to match gas Z-factors at high pressures > 500 bar) § Don’t match viscosity data simultaneously with PVT data. It will only compromise the fit of the PVT data. Successful regression requires considerable trial and error. Keep trying different regression variables, initial values, and/or data weightings. If the results continue to be unsatisfactory, look for possible inconsistencies in the data. § Course in Advanced Fluid Phase Behavior. © Pera A/S 27

Regression Strategies § Use as few regression variables as needed, and try to exercise good engineering judgment. § Try to choose regression variables that have both relatively high impact and relatively high uncertainty, such as binary interaction parameters, correlation parameters, and the properties of the heaviest pseudocomponents. § Keep the regression variables bounded within their estimated uncertainties. § Do not regress on the physical properties of the pure components (C 5 -), with the exception of volume shift of C 1 and C 2 (to match gas Z-factors at high pressures > 500 bar) § Don’t match viscosity data simultaneously with PVT data. It will only compromise the fit of the PVT data. Successful regression requires considerable trial and error. Keep trying different regression variables, initial values, and/or data weightings. If the results continue to be unsatisfactory, look for possible inconsistencies in the data. § Course in Advanced Fluid Phase Behavior. © Pera A/S 28

Regression Variables § Binary Interaction Parameters (BIPs) (C 1 -C 7+): § Large effect on saturation pressure calculation (especially last C 7+ fraction). § Less effect on VLE compositions! § § § If there is a substantial amount of non-HC components, the BIPs between the non-HC and C 7+ can be used as a regression parameter. Maximum change in any multipliers to C 1 -C 7+ BIP should be within [-2, 2]. Tc, Pc: § § Effects saturation pressure and VLE compositions. Changes in Tc, Pc should be consistent (this can be easliy be obtained by regressing only on Tb, if the simulator allows Tc and pc to be updated from Tb). Tc, pc for the heaviest pseudo-component has a large impact on the dew-point pressure. Maximum change 5% (possibly up to 15% for the last pseudo component). NB: Check K-values! Course in Advanced Fluid Phase Behavior. © Pera A/S 29

Regression Variables § Binary Interaction Parameters (BIPs) (C 1 -C 7+): § Large effect on saturation pressure calculation (especially last C 7+ fraction). § Less effect on VLE compositions! § § § If there is a substantial amount of non-HC components, the BIPs between the non-HC and C 7+ can be used as a regression parameter. Maximum change in any multipliers to C 1 -C 7+ BIP should be within [-2, 2]. Tc, Pc: § § Effects saturation pressure and VLE compositions. Changes in Tc, Pc should be consistent (this can be easliy be obtained by regressing only on Tb, if the simulator allows Tc and pc to be updated from Tb). Tc, pc for the heaviest pseudo-component has a large impact on the dew-point pressure. Maximum change 5% (possibly up to 15% for the last pseudo component). NB: Check K-values! Course in Advanced Fluid Phase Behavior. © Pera A/S 30

Regression Variables, cont. § Average C 7+ Molecular Weight: § § § Will affect the saturation pressure (especially dew-point). Also density, mainly because of the molecular weight – specific gravity relationship. Volume Shift: § § § C 7+ molecular weight of specific input feeds can be used as regression variable, due to uncertainty reported molecular weights. Effects ONLY densities. Temperature dependent volume shifts can be used, if STO densities and reservoir oil densities cannot be matched with a single set of volume shift factors (use two sets of volume shifts). Zc. Visc (or alternatively Vc. Visc) § Used exclusively for viscosity calculations. § Initial estimate of Zc. Visc should be close to 0. 3. § Maximum change +/- 20% § NB: Check individual component viscosities (continuous increasing with molecular weight). Course in Advanced Fluid Phase Behavior. © Pera A/S 31

Regression Variables, cont. § Average C 7+ Molecular Weight: § § § Will affect the saturation pressure (especially dew-point). Also density, mainly because of the molecular weight – specific gravity relationship. Volume Shift: § § § C 7+ molecular weight of specific input feeds can be used as regression variable, due to uncertainty reported molecular weights. Effects ONLY densities. Temperature dependent volume shifts can be used, if STO densities and reservoir oil densities cannot be matched with a single set of volume shift factors (use two sets of volume shifts). Zc. Visc (or alternatively Vc. Visc) § Used exclusively for viscosity calculations. § Initial estimate of Zc. Visc should be close to 0. 3. § Maximum change +/- 20% § NB: Check individual component viscosities (continuous increasing with molecular weight). Course in Advanced Fluid Phase Behavior. © Pera A/S 32

Regression Variables, cont. § Average C 7+ Molecular Weight: § § § Will affect the saturation pressure (especially dew-point). Also density, mainly because of the molecular weight – specific gravity relationship. Volume Shift: § § § C 7+ molecular weight of specific input feeds can be used as regression variable, due to uncertainty reported molecular weights. Effects ONLY densities. Temperature dependent volume shifts can be used, if STO densities and reservoir oil densities cannot be matched with a single set of volume shift factors (use two sets of volume shifts). Zc. Visc (or alternatively Vc. Visc) § Used exclusively for viscosity calculations. § Initial estimate of Zc. Visc should be close to 0. 3. § Maximum change +/- 20% § NB: Check individual component viscosities (continuous increasing with molecular weight). Course in Advanced Fluid Phase Behavior. © Pera A/S 33

Regression Step by Step 1. Fit TBP-Data or STO densities from Separator tests (MSF) by tuning of the Soreide characterization factor. 2. Fit only the measured saturation pressure by changing BIPs C 1 -C 7+ fractions. § Try first with a common multiplier for all C 7+ pseudo components. If needed, use several multipliers for different groups (E. g. , use a separate multiplier for the heaviest component). 3. If further regression is required, we recommend to tune on the following two groups (1) All but the last pseudo components, (2) the last pseudo component using the following regression parameters. 1. Tc and Pc or Tb (maximum 5 -10% change) 2. BIP (the BIPs can be negative but C 1 -C 7+ BIPS should generally have a trend. 4. With multiple samples, regression the Mw of C 7+ might be used as a regression parameter. When Mw of C 7+ is used as a regression parameter the mass of C 7+ should be maintained. 5. When a satisfactory match of all important PVT data is obtained, regress on Zc to match oil viscosities. Course in Advanced Fluid Phase Behavior. © Pera A/S 34

Regression Step by Step 1. Fit TBP-Data or STO densities from Separator tests (MSF) by tuning of the Soreide characterization factor. 2. Fit only the measured saturation pressure by changing BIPs C 1 -C 7+ fractions. § Try first with a common multiplier for all C 7+ pseudo components. If needed, use several multipliers for different groups (E. g. , use a separate multiplier for the heaviest component). 3. If further regression is required, we recommend to tune on the following two groups (1) All but the last pseudo components, (2) the last pseudo component using the following regression parameters. 1. Tc and Pc or Tb (maximum 5 -10% change) 2. BIP (the BIPs can be negative but C 1 -C 7+ BIPS should generally have a trend. 4. With multiple samples, regression the Mw of C 7+ might be used as a regression parameter. When Mw of C 7+ is used as a regression parameter the mass of C 7+ should be maintained. 5. When a satisfactory match of all important PVT data is obtained, regress on Zc to match oil viscosities. Course in Advanced Fluid Phase Behavior. © Pera A/S 35

Regression Step by Step 1. Fit TBP-Data or STO densities from Separator tests (MSF) by tuning of the Soreide characterization factor. 2. Fit only the measured saturation pressure by changing BIPs C 1 -C 7+ fractions. § Try first with a common multiplier for all C 7+ pseudo components. If needed, use several multipliers for different groups (E. g. , use a separate multiplier for the heaviest component). 3. If further regression is required, we recommend to tune on the following two groups (1) All but the last pseudo components, (2) the last pseudo component using the following regression parameters. 1. Tc and Pc or Tb (maximum 5 -10% change) 2. BIP (the BIPs can be negative but C 1 -C 7+ BIPS should generally have a trend. 4. With multiple samples, regression the Mw of C 7+ might be used as a regression parameter. When Mw of C 7+ is used as a regression parameter the mass of C 7+ should be maintained. 5. When a satisfactory match of all important PVT data is obtained, regress on Zc to match oil viscosities. Course in Advanced Fluid Phase Behavior. © Pera A/S 36

Regression Step by Step 1. Fit TBP-Data or STO densities from Separator tests (MSF) by tuning of the Soreide characterization factor. 2. Fit only the measured saturation pressure by changing BIPs C 1 -C 7+ fractions. § Try first with a common multiplier for all C 7+ pseudo components. If needed, use several multipliers for different groups (E. g. , use a separate multiplier for the heaviest component). 3. If further regression is required, we recommend to tune on the following two groups (1) All but the last pseudo components, (2) the last pseudo component using the following regression parameters. 1. Tc and Pc or Tb (maximum 5 -10% change) 2. BIP (the BIPs can be negative but C 1 -C 7+ BIPS should generally have a trend. 4. With multiple samples, regression the Mw of C 7+ might be used as a regression parameter. When Mw of C 7+ is used as a regression parameter the mass of C 7+ should be maintained. 5. When a satisfactory match of all important PVT data is obtained, regress on Zc to match oil viscosities. Course in Advanced Fluid Phase Behavior. © Pera A/S 37

Regression Step by Step 1. Fit TBP-Data or STO densities from Separator tests (MSF) by tuning of the Soreide characterization factor. 2. Fit only the measured saturation pressure by changing BIPs C 1 -C 7+ fractions. § Try first with a common multiplier for all C 7+ pseudo components. If needed, use several multipliers for different groups (E. g. , use a separate multiplier for the heaviest component). 3. If further regression is required, we recommend to tune on the following two groups (1) All but the last pseudo components, (2) the last pseudo component using the following regression parameters. 1. Tc and Pc or Tb (maximum 5 -10% change) 2. BIP (the BIPs can be negative but C 1 -C 7+ BIPS should generally have a trend. 4. With multiple samples, regression the Mw of C 7+ might be used as a regression parameter. When Mw of C 7+ is used as a regression parameter the mass of C 7+ should be maintained. 5. When a satisfactory match of all important PVT data is obtained, regress on Zc to match oil viscosities. Course in Advanced Fluid Phase Behavior. © Pera A/S 38

Final Internal Model Consistency Checks • Always scrutinize the values and trends of the component properties (in particular, molecular weight, boiling point, specific gravity, critical temperature and pressure, acentric factor). • Check the equilibrium K-values for some near-critical flash calculations, to make sure they are predicted in the correct order (continuously decreasing with molecular weight). • If possible, make a thorough search for any reservoir conditions under which the tuned EOS would try to predict three-phase behavior. Retune, if necessary. Course in Advanced Fluid Phase Behavior. © Pera A/S 39