1. Day 4 – Part 1: Lumping and De-lumping
Pseudoization (Lumping)
Black Oil Models
De-lumping (Black-Oil to Compositional)
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2. Successive Reduction of Number of EOS Components
Pseudoization
Successive Reduction of Number of EOS Components
Key Questions:
Which components to group, and how?
Pseudo component properties.
Regression strategies.
How many components should be used?
EOS9  EOS4 C
PC1 1 C2 C3
PC2 C4 C5 C6
PC3
PC3 F1 F2 F3
PC4
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3. Pseudoization – Which components to group?
Always group in a stepwise manner, and check predictions after each regression step.
Lump components that are most similar first. E.g.:
Iso- and normal fractions (i-C4 and n-C4, i-C5 and n-C4)
N2 (*) and C1
Co2 (*) and C2
(*) If the reservoir fluid, or the injection gas contains more than about 2% of a non-hydrocarbon component, this component must be kept as a separate component.
Try lumping the light components first, i.e. keep the heavy pseudo components separately until the last few steps.
Avoid pseudoizing to the point of deteriorating predictions. It is usually better to pseudoize too little than to pseudoize too much.
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4. Pseudo Component Properties
Pc, Tc and  can be determined by Kay’s mixing rule:
Coats has suggested an approach that preserves the volumetric behavior at undersaturated conditions, by ensuring that the mixture EOS constants A and B are unchanged by the pseudoization.
Any PVT package should automatically calculate the pseudo properties (based on some set of mixing rules)
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5. Pseudoization – Regression Strategies.
Always group in a stepwise manner.
Regress to maintain the best possible fit of the original (full) EOS model, instead of the actual experimental data!
Expand the data range in pressure, temperature and composition space.
At each pseudoization step, regress only on properties of the new pseudo components introduced at that stage. (However an update of the C1 – heavy component BIPs can be made at every stage).
We reccomend regressing on pc, Tc for the new grouped components at each stage. In addition, the BIPs between the C1 pseudo fraction and the heavy pseudo components should be updated at each stage.
An alternative approach to changing Tc, pc is to regress directly on the a and b parameters (Coats).
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6. Pseudoization – Regression Strategies, cont.
Check model predictions at the end of each step (compare against original model predictions).
Internal model consistency (monotonic properties and K-values) should be verified at the end of each step.
Test for possible three-phase solutions at reservoir conditions.
The final pseudoized EOS model should ideally be tested with reservoir simulation (full-field or sector model simulations).
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7. Pseudoization – How many components?
Depends on the complexity of the fluid, and the process being simulated.
For depletion processes, 3 – 4 pseudo components are usually sufficient (e.g. black-oil) – provided the model was generated properly.
For more compositional sensitive processes, like gas injection, 5 – 8 components should be sufficient.
For highly compositional sensitive processes (e.g. slimtube simulation for determination of miscibility conditions), 9 – 15 components might be required.
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8. Pseudoization Scheme Example
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9. Black Oil Models
Black-Oil models are a special case of a two-component mode, where the components are surface- oil and gas.
The model assumes constant component surface densities.
The “component” PVT properties are associated with a fixed reservoir temperature and a given surface process.
Component PVT properties are tabulated as function of pressure and Rs (oil) or rv (gas).
Rs (and rv) represents a “measure” of the fluid composition.
Res Oil
Process
Vgo, mgo, g
Voo, moo, o
Vo, mo, o
Vgg, ngg
Process
Vog, nog
Res gas
Vg, ng
Phases : Oil & Gas
Components: STO Oil & Surf. Gas
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10. Generation of Black Oil Tables
Black oil tables can be generated directly from laboratory experiments.
Saturated properties for the reservoir oil (Rs and Bo) can be derived by combining DLE and Multi-stage separator data.
Undersaturated oil compressibility (original pb) can be taken from a CCE experiment.
Now a days, it is common to generate black oil PVT tables based on an (tuned) EOS model.
Whitson Torp method: Equilibrium oil and gas from a depletion experiment are passed separately through the surface process, and the black oil properties at each pressure stage are calculated.
For an oil reservoir with a gas cap, the gas cap gas should be used to generate the gas PVT table, and the reservoir oil should be used to generate the oil PVT table.
For gas injection, the PVT table of the reservoir oil should be extrapolated by using a swelled oil.
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11. Generation of Compositional Streams
Where are compositional information needed?
Challenges:
Reservoir engineering management.
Gas injection.
Production allocation.
Pipeline calculations
Pressure loss, liquid dropout, etc.
Surface process simulations.
Process facility design
Product forecasting.
Product quality control.
Production optimization.
Tie in of different wells, reservoirs or fields.
Optimize surface process and product quality (blending).
Most reservoir models are black-oil models!
Have only two products: “surface oil” & “surface gas”
Multi-reservoir & field development.
Different reservoir models.
Gas injection.
Multiple fluid models.
Different black-oil models.
Reservoir EOS models
Detailed surface process EOS.
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12. Conversions Zi Zi Sij(p,T) From Compositional to Black Oil
From Black Oil to Compositional
Gas
Gas
Sep
Sij(p,T) Zi Zi
Oil
Oil
(p, T)
The BOz split-factors are generated from the compositional information that were “lost” when the black-oil tables were generated.
The BOz conversion factors are typically functions of pressure (BO depletion stage pressures).
Black oil tables are generated by EOS models by simulating depletion experiments.
Detailed compositional information at each pressure stage is “lost” in the black oil tables.
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13. Split Factors BOz Conversion
q1 = qg
q2 = qo z2 qg .
Sij qo zn
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14. Gamma Distribution Function
A finite number of discrete reservoir C6+ fractions are first fit by a four-parameter continous Gamma distribution model
The continous Gamma distribution model of C6+ is then discretized into a finite number of process-defined fractions.
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15. Split Factors and Gamma Distribution Function
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16. Example - CO2 Immiscible Injection BOz Conversion
North Sea 2D Sector Model.
Highly undersaturated, low API oil.
1 horizontal producing well in lower-structure.
1 gas injection well in upper-structure.
BOz conversion of black-oil surface gas and oil rates.
Compare with E300 model results.
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17. CO2 Immiscible Injection
High permeability.
Low API & low Rs-pb oil.
One horizontal producer.
One updip injector.
Black-Oil E100 model gives approximately the same results as EOS E300 model:
GOR, Qo, Qg, P = f(time)
Gas Breakthrough
After 5 years.
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18. CO2 Immiscible Injection BOz Conversion
Flowing composition is thought to consist of a mixture of:
CO2 injection gas
CO2 swelled oil (xiso), with solution GOR = Rsso
for all GOR > Rsso
CO2 injection gas
Swelled oil (xiso)
qo, qg
CO2 swelled oil (xiso), with solution GOR = Rsso
Original oil (xioo), with solution GOR = Rsoo
for all Rsoo < GOR < Rsso
Original oil (xioo)
Swelled oil (xiso)
qo, qg,
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19. CO2 Immiscible Injection Comparison of Converted vs
CO2 Immiscible Injection Comparison of Converted vs. Simulated Molar Rates
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