Si-Yong Lee

Model development & Aneth site example

What is a model?

A model is a simplified representation of realityor any device that represents a system.

Why model?

- Predictive application (predicting the consequences of a proposed action)

- Interpretive application (understanding system dynamics)

- Generic application (analyzing processes in generic/hypothetical settings)

What types of models?

Conceptual Model: Qualitative description of system

Mathematical Model: Mathematical description of system- Analytical solution- Numerical solution

Physical Model: e.g. core flooding experiment

Modeling Protocol

Define Problem

Conceptual model

Mathematical model

Computation

Comparison with field data

Results

Model Calibration

Model Redesign

Define the problems/objectives

• Site selection

- storage capacity

- Injectivity

- Plume distribution (AOR)

• Monitoring design

• Uncertainty/Risk assessment

Data Collection

• Hydrologic data (local & regional)

• Geologic data (e.g., stratigraphy, formation tops, faults/fractures, tectonic information, and seismic events)

• Geophysical data (e.g., well logs, seismic survey)

• Rock properties (por, perm, relative perm, Pc, bulk density, Young’s modulus, Poisson’s ratio, mineralogy, etc)

• Fluid properties (salinity, pH, density, viscosity, mutual solubility, brine chemistry, isotope, etc)

• Well information (location, vertical/horizontal, perforation interval, injection/production history, bottom hole pressure, etc)

Conceptual Model

Cross-bedded aeolian Navajo Ss(outcrop in Devil’s canyon, UT)

Conceptual modelof the cross-bedded bedform

3D cross-bedded bedform

Grain flow (dune)Wind ripple (interdune)

Grid building

An optimally-sized model domain should :

- Encompass all the major flow units (formations of interest – injection zone, overlying and underlying formations)

- Include the injection, monitoring, and any production wells

- Lie within the extent of pressure response area

- Be tractable computationally

Grid resolution (dx, dy, dz)

Grid resolution vs. computational efficiency

Should include heterogeneity, well configuration, and sufficient accuracy in the changes of results (pressure & saturation).

Coarsening of model grid further from the injection well (no more than 1.5 times the previous nodal spacing).

Grid coarsening could create numerical dispersion.

Assigning property parameters

- Single value in a cell (REV, scale issue)

- Sparse data in space (especially horizontal direction)

- Heterogeneity

- Property upscaling

Heterogeneity and Aniostropy

Heterogeneity : Variations through space

Aniosotropy : Variations with the direction of measurement at any given point

(

Heterogeneity and Aniostropy

(x1,z1)

(x2,z2)

kx

kz

Homogeneous, Isotropic Homogeneous, Anisotropic

Heterogeneous, Isotropic Heterogeneous, Anisotropic

Approaches to generate heterogeneity

Deterministic approach: parameter values are known with certainty (single solution)

Stochastic approach: uncertainty in parameter values (ranges in solution)

Actual Geology

Layer Cake Model

Stochastic/Geostat. Model

Stochastic Approaches

• Continuous HeterogeneityGaussian model (mean, variance, and variogram)Fractal model

• Discrete HeterogeneityFacies model with indicator geostatisticsDepositional simulation

Process imitation (mathematically-based equations)Structure imitation (probabilistically-based)

• Mixed Heterogeneity (continuous + discrete)

x y

z

Core description (LLNL site)

(TPROGS1)

TProGS Realization

x y

z

(TPROGS1)

TProGS Realization(largest connected channel body)

x y

z

Spatial Covariance of LnK

Lag(m)

Covariance of LnK

0. 20. 40. 60. 80. 100. 120.

0.0

5.0

10.0

15.0

20.0

25.0

Covariance of Ln K

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00

0.0

5.0

10.0

15.0

20.0

25.0

Lag(m)

SGS Realization

(GAUSS1)

x y

z

SGS Realization(largest connected body)

(GAUSS1)

x y

z

TProGS vs. SGS

TProGS SGS

RF Discrete(e.g. facies unit) Continuous

SpatialProcess Markovian Gaussian

VariabilityMeasure Transition Probability Covariance

Advantage- Asymmetry- Juxtapositional tendency- Sharp contact

- Easy application- Simple and fast algorithm

Disadvantage- Relatively more uncertain in x, y than z direction

- Poor Connectivity of extreme values (Maximum entropy)

Geologic Model Development in Aneth site

- Data Acquisition

- Petrophysical Properties Estimation

Estimation of porosity

Porosity & Permeability Relationship

- Geologic Model Development

Data Acquisition

- Core plug analyses

(porosity, density, and permeability)

- Geophysical well log images

- Stratigraphic formation tops data

- Well information

- Injection/production history

Navajo

Kayenta

Wingate

Chinle

Dechelly

Organ Rock

Hermosa

Ismay

Gothic

Desert Creek

Entrada

Petrophysical Properties Estimation

FormationNo. of

Samples

Porosity () Permeability (mD)

Mean MedianStd. Dev.

Mean Median Std. Dev.

Ismay 10 0.05 0.02 0.06 0.47 0.04 0.78

Gothic Shale 1 0.009 0.009 0 0.012 0.012 0

Desert Creek 81 0.09 0.1 0.07 5.12 0.31 18.92

Texaco Aneth H-117

5380

5400

5420

5440

5460

5480

5500

5520

5540

0 5 10 15 20 25 30

Porosity (%)

Dep

th (

ft)

Ambient Porosity vs. Neutron-Density Porosity

Upscaled Porosity Logs

Porosity Field(n=9,170,238; dx=dy=100m, dz=1m; nz=1,644)

Upscaled Porosity Field(n=227,950; dx=dy=100m; nz=41)

y = 0.0253e0.2824x

R2 = 0.6626

y = 0.0504e0.1655x

R2 = 0.3485

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

0 5 10 15 20 25 30 35

porosity (%)

k (m

D)

Desert Creek

Gothic

Ismay

Expon. (Desert Creek)

Expon. (Ismay)

Porosity vs. Permeability

Permeability Field(n=227,950; dx=dy=100m; nz=41)

Questions ?