investigation of compositional grading in petroleum...

RESERVOIR SIMULATION

Investigation of Compositional Grading in

Petroleum Reservoirs

Zhangxing Chen

University of Calgary


Outline •  Importance of the Research •  Factors Leading to

Compositional Variations •  Compositional Grading •  Theory •  Numerical Experiments •  Conclusions


Importance of the Research

•  Initialization of simulation:

-  Mechanical equilibrium -  Chemical equilibrium


Importance of the Research (cont’d)


Importance of the Research (cont’d)

•  Accurate modeling of composition variation highly affects:

-  Reserve estimation -  Design of production and

development strategies


Factors Leading to Composition Variation

•  Gravity: gravity segregation.

•  Thermal diffusion: light components to warm zones and heavy ones to cold zones.

•  Incomplete hydrocarbon migration/mixing: complete mixing takes time.

•  Natural convection: leading to an increase of horizontal compositional variation.

•  Dynamic flux of water aquifer contacting only a part of reservoir: creating a sink for continuous depletion of light components (e.g., methane)


Factors Leading to Composition Variation (cont’d)

•  Asphaltene precipitation during migration: leading to different layers with different permeability to host different types of oil.

•  Biodegradation varying laterally and vertically: causing significant variation in H2S content and API gravity of the reservoir.

•  Reservoir compartmentalization: causing loss of pressure and fluid communication between adjacent fault blocks.


Factors Leading to Composition Variation (cont’d)

•  Partial barriers: causing limited fluid and pressure communication.

•  Genesis: related to source rocks. •  Capillary forces: having an effect on fluid

distribution in systems with pore radius in the order of 1 micron.

•  Artificial issues: e.g., miscible gas injection


Processes and Time Scales Affecting Fluid Compositions

•  Multiple processes that affect fluid properties: –  Reservoir charge/filling, fluid mixing through Darcy flow/advection/

diffusion, gravity segregation, biodegradation, fractionation, and differential leakage of gas vs. oil.

•  Different time scales (key to understanding the relative significance of fluid data to reservoir segmentation studies): –  Charge/filling of reservoirs: geological time - several millions of

years –  Biodegradation: thousands to hundreds of thousand of years –  Molecular diffusion: 1 to 100 million years –  Pressure diffusion: hundreds or even thousands of years –  Convective flow: thousands to million years


Importance of the Research (cont’d): Understanding Reservoir Fluid Compositions

Time scale


Difficulties in Modeling Compositional Variation

•  We do not have enough physical/chemical understanding of these phenomena.

•  Boundary conditions are changing continually.

•  Mathematical models may be so complex or even unknown.


Compositional Grading

•  Gravity •  Thermal diffusion (Soret

effect) •  Capillary effects


Theory

•  Classical theory •  New general theory


Classical Theory

•  Constraint of chemical equilibrium for an isothermal system (Gibbs, 1876):


Classical Theory (cont’d)

•  Constraint of chemical equilibrium for a nonisothermal system (Faissat, et al., 1994):


New General Theory

•  Mass conservation


New General Theory (cont’d)

•  Diffusive mass flux:


Relationship between classical and new theories

•  For an isothermal system, the classical constraint of chemical equilibrium can be obtained from the pressure diffusion.

•  For a non isothermal system, it can be obtained from the thermal diffusion.


Simulation Approach •  R&D Program: Have developed a software package that

integrates geological processes (source rock maturation, hydrocarbon generation, migration, charge/filling, etc.) with reservoir processes (fluid mixing, advection, diffusion, gravity segregation, biodegradation, etc.).


Case Study A: A Light Oil

•  A North Sea reservoir •  The thickness of reservoir: 200m •  Reference pressure and temperature

at 3,000m: 40 MPa and 320 K •  Temperature gradient: 0.02 K/m •  Components: C1--C10+


Case Study A (cont’d) Depth (m) 3000 3050 3100 3150 3200

C1 % 68.861 63.6557 60.1561 57.4384 55.2189

C10+ % 5.231 8.9845 11.9898 14.5655 16.8147

P (MPa) 40 40.252 40.528 40.820 41.122

dens (kg/m3) 478.28 542.57 580.50 606.88 626.49

Pb (MPa) 35.474 31.862 29.520 27.539 25.892

Rs (Sm3/Sm3) 1132.5 655.1 482.5 389.5 330.7

Bo (m3/Sm3) 3.962 2.665 2.208 1.966 1.815


Case Study A (cont’d)

Pref (bar) Tref (K) Error OIP %

320 400 39.77

336.79 395.0175 44.47

353.58 390.035 48.75

370.37 385.0525 52.73


Case Study B: A Black Oil Two-Phase

•  Location: the Azadegan oil, southwest of Iran.

•  Components: C1—C7+ •  Temperature gradient: 0.01 K/m,

which is normally considered isothermal.


Case Study B (cont’d)

Depth (m) 3000 2950 2900 2850 2800 C1 % 36.47 72.4079 74.2365 75.6161 76.7778 C7+ % 33.29 0.7870 0.4672 0.3052 0.2093 P (bar) 240.000 237.136 236.198 235.310 234.455

Dens (kg/m3) 654.72 198.37 185.41 177.33 171.41 Pb (bar) 194.102 - - - - Pd (bar) - 233.482 191.729 156.929 124.729

Rs (Sm3/Sm3) 152.880 - - - - Bo (m3/Sm3) 1.541 - - - -

T (K) 400 400 399 399 398 MW of C7+ 218 209.13 201.84 195.28 189.33

GOC depth (m) 2955 - - - -


Case Study B (cont’d)

Condition

Without Plus Fraction

Change with Depth

Isothermal

Error OIP% 31.18 39.33


Case Study C: Single Phase

•  Location: the Azadegan oil, southwest of Iran.

•  12 Components: H2S, N2, CO2, C1, C2, C3, iC4, nC4, iC5, nC5, C6, C7+

•  Reference pressure and temperature at 3,000m: 175 Bar and 370 K

•  Temperature gradients in x, y, and z directions: 0.003, 0.004, -0.035 K/m.


Case Study C (cont’d) Component Mole% H2S 0.04 N2 0.4 CO2 1.44 C1 29.59 C2 7.36 C3 5.39 iC4 0.91 nC4 2.98 iC5 1.43 nC5 1.78 C6 1.4 C7+ 47.28


Case Study C (cont’d)


Case Study D: Analytical Solution

yr

yr

yr

yr

yr

yr


Case Study E: Diffusive Mixing

0 0.5 1

2 myr

80 myr

20 myr

400 myr


Case Study F: n-Component


Case Study G: Rayleigh Number


Case Study H: Reservoir with Baffle for n-Component Mixing

nC4 mole fraction

C1 mole fraction

Kx = 100 md in reservoir Kx = 10, 1, 0.1, 0.0001 md in baffle

Kz = 10 md in reservoir Kz = 1/10 of Kx in baffle

Pressure gradient (atm)


Case Study H: Reservoir with Baffle for n-Component Mixing (cont’d)


Case Study I: Effect of Pressure and Thermal Diffusions

Equilibrium at t = 19 million years with pressure and thermal diffusions

Equilibrium at t = 17 million years with pressure diffusion

Equilibrium at t = 20 million years with thermal diffusion


Conclusions •  The effect of compositional grading is magnificent and cannot

be ignored; its effect is more pronounced as the fluid becomes near-critical.

•  Ignoring change in composition can lead to huge errors in OIP calculations as much as 50% of the real number.

•  The temperature gradient must be included in calculations as it has a remarkable effect on compositional grading and the change of physical properties with depth.

•  Molecular weight and so all other properties of the plus fraction can change with depth, which cannot be ignored.

•  Gravity causes the fluid and the plus fraction to become heavier towards the bottom while the temperature gradient does the opposite.

•  Pressure equilibration seems fastest.

investigation of compositional grading in petroleum...

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