the hugoton geomodel: a hybrid stochastic-deterministic approach

The Hugoton Geomodel: A Hybrid Stochastic-Deterministic Approach

Geoffrey C Bohling

Martin K Dubois

Alan P Byrnes

Long Beach, 2 April 2007

Bohling, Dubois, Byrnes 2

Study Area and History Largest gas field in North America.

EUR 75 TCF (2.1 trillion m3) 12,000 wells, 6200 mi2 (16,000 km2).

2.8 BCF per well. Spacing: 2-3 wells per 640 acres Discovered 1922, developed 1940-

50s. Maximum continuous gas column: 500

ft (165 m). Shallow: Top 2100-2800 ft deep (640-

850 m). Initial wellhead SIP 437 psi (3013 kPa) Dry gas, pressure depletion reservoir,

stratigraphic trap

Miles

Kilometers

10 0 10 20 30 40 50

0 20 6040 10020 80

COLORADO

KANSAS

OKLAHOMA

TEXAS

N

-500

0

0

500

500

500

1000

1500

1500

1000

1000

500

500

500

0

- 500

0

-1500

-1000

-500

0

1000

1000

500 0

-1000-500

Amarillo

Wichita

Uplift

Byerly

Bradshaw

Panoma

KansasHugoton

GuymonHugoton

TexasHugoton

WestPanhandle

EastPanhandle

38°

102°103°

35°

37°

36°

Legend

Oil productive area

Major faults

Gas productive areas

STUDYAREA

Study AreaPermian

(Wolfcampian) gas and oil fields

Wolfcamp Structure (CI=500’)(modified after Pippin, 1970, and Sorenson, 2005)



Stratigraphy Herington Limestone

Krider Limestone

Odell Shale

Winfield Limestone

Gage Shale

Towanda Limestone

Holmesville Shale

Ft Riley Limestone

Matfield Shale

Wreford Limestone

Speiser Shale

Funston Limestone

Blue Rapids Shale

Crouse Limestone

Easly Creek Shale

Middleburg Limestone

Hooser Shale

Grenola Limestone

Eskridge Shale

Cottonwood Limestone

Eiss Limestone Stearns Shale Morrill Limestone Florena Shale

Formation or Member

Ch

ase

Gro

up

Co

un

c il G

rove

Gr o

up

10

Lith

ofa

cie

s C

od

e

9

8

7

6

5

4

3

2

1

0

C_LM

A1_SH

A1_LM

B1_SH

B1_LM

B2_SH

B2_LM

B3_SH

B3_LM

B4_LM

B4_SH

B5_SH

B5_LM

C_SH

DE

PT

H (

ft)

Ss

Dol, mxln

Grnst

Pkst

Dol, fxln

Wkst

Mdst

Silt/sh

Fn Silt

Crs Silt

Ss

( fro

m c

or e

)C

on

tine

nta

l L

0,

L1

, L

2

Ma

rin

e

L3

- L

10

Flower A-1,Stevens Co., KS

Logged interval = 520 ft (160 m)

SYSTEM SERIES GROUPKansas fields

Oklahoma field

Leo

nard

ian

Sumner

Chase

Admire

Wabaunsee

Shawnee

Guymon- Hugoton

Greenwood

Per

mia

n

Wo

lfc

amp

ian

Pe

nn

syl-

van

ian

Virg

ilian

Council Grove

Hugoton-Panoma Byerly

Bradshaw

(compiled from Zeller, 1968; Pippin, 1970; Barrs et al., 1994; Merriam, 2006)

Production from 13 fourth order marine-continental cycles.

Shoaling upward carbonate cycles (reservoir) separated by redbed siltstones of poor reservoir quality.



Basic Problem

Inability to compute saturations from logs due to deep filtrate invasion

Significant differences in permeability-porosity and capillary pressure relationships between facies

Prompts development of geomodel of entire field for property-based evaluations of volumetrics and flow

Supported by consortium of 10 companies



Hugoton Geomodel 108-million cell

Petrel model Cells 660 ft x 660

ft (200 m x 200m) and ~3 ft (1 m) thick on average

11 lithofacies Six submodels

(stratigraphically)



Basic Workflow

Neural network(s) trained on log-lithofacies relationships in 27 cored wells (15 Chase, 16 Council Grove)

Lithofacies predicted in ~1600 logged wells Sequential indicator simulation of lithofacies,

sequential Gaussian simulation of porosity Permeability, capillary pressure, water

saturation from lithofacies-specific functions of porosity and height above free water level



Neural Network Structure



Neural Network Parameter SelectionLooking for optimal

values of network size and damping parameter

Each cored well removed in turn from training set

Neural net trained on remaining wells; predictions compared to core in withheld well

Five trials per well and parameter combination

Sundry measures of prediction accuracy computed



Variation of Crossvalidation ResultsDifferent symbol style

for each (withheld) well; 5 trials per well; 14 wells (Upper Chase)

Line is median, shown on previous slide

Variability among wells larger than variability among parameter sets

On the other hand, accuracy of predictions not hugely sensitive to choice of parameters



Variability of Neural Net PredictionsFive realizations

of neural net – different initial weights

Predicting on a cored well withheld from training set

Some variability, but big picture is the same

This source of variation not pursued further; one network used



Lithofacies Variograms

Variogram fitting problematic due to volume of data, number of facies (11) and intervals (23), trends and/or zonal anisotropy

Upscaled data at wells exported from Petrel to R for automated analysis

Exponential variograms with zero nugget imposed by fiat; ranges estimated for each facies and stratigraphic submodel (six of them)

Vertical fits mostly OK, horizontal fits . . . well, a little iffy



Porosity Variograms

Porosity variograms generally rattier than facies variograms

Automatically estimated ranges for all variograms (facies and porosity) then generalized/adjusted to reduced set of range values (by facies, one set for Chase, another for Council Grove); ranges ~20-40 kft

SIS for facies, SGS for porosity – only one realization for full model



Submodel for Uncertainty AssessmentStratigraphically continuous model for 2200 mi2 (5700 km2) east-west “laydown” across middle of field; ~24 million cells

Assembled by Manny Valle, Oxy

200 realizations of entire workflow – facies SIS, porosity SGS, property and OGIP computations – saving only OGIP

10 realizations saving all intermediate properties

OGIP evaluated for whole model and low-, medium-, and high-data density regions

Properties examined at a synthetic well in each of three regions



Varying Well Density RegionsEach region is one township in size (36 mi2, 93 km2)

Low density: 2 wells, both Chase and Council Grove

Medium density: 9-14 Chase, 7-8 Council Grove

High density: 20-25 Chase, 20-22 Council Grove

Evaluation of data density effects will be obscured somewhat by variations in geological setting



Facies Variation at Synthetic Wells



Porosity Variation at Synthetic Wells



Perm, Sw, OGIPPermeability (k), Sw, and OGIP for each cell computed as functions of lithofacies and porosity ()

k – (Lith, )

Sw = f(Lith, , FWL)

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000

0 2 4 6 8 10 12 14 16 18 20 22 24 26

In situ Porosity (% )

Insi

tuK

lin

ken

ber

gP

erm

eab

ilit

y(m

d)

9 -crs sucros ic D o l3 -fn sucros ic D o lcrs sucros ic D o lfn sucros ic D o l

0.00001

0.0001

0.001

0.01

0.1

1

10

100

0 2 4 6 8 10 12 14 16 18 20 22 24 26In situ Porosity (% )

Insi

tuK

lin

ken

ber

gP

erm

eab

ilit

y(m

d)

0-N M vf sandstone1-N M crs s ilts tone2-N M vf-m ed s ilts tonevf S andstonecrs S ilts tonevf-m S ilts toneS ilts tones U nd if.

0.00001

0.0001

0.001

0.01

0.1

1

10

100

0 2 4 6 8 10 12 14 16 18 20 22 24 26In situ Porosity (% )

Insi

tuK

lin

ken

ber

gP

erm

eab

ilit

y(m

d)

8-gra in-/bafflestone7-pack/pack-gra instone5-wacke/wacke-packstone4-m ud/m ud-w ackestonebafflestonegrainstonepack-gra instonepackstonewacke-packstonewackestonem ud-wackestonem udstone

A

B

C

Mdst

Wkst

Pkst

fn-med sltstn

crs sltstn

vfn Ss

vfxln Dol

mxlnmoldic

Dol.

Grnst

k- relationships

Capillary Pressure Curves by Facies(Porosity = 10%)

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Water Saturation (%)

Ga

s-B

rin

e H

eig

ht

Ab

ov

e F

ree

Wa

ter

(ft)

1-NM Silt&Sand

2-NM Shaly Silt

3-Marine Sh & Silt

4-Mdst/Mdst-Wkst

5-Wkst/Wkst-Pkst

6-Sucrosic Dol

7-Pkst/Pkst-Grnst

8-Grnst/Grnst-PhAlg Baff

Capillary Pressure Curves Pkst/Pkst-Grainstone(Porosity = 4-18%)

10

100

1000

0 10 20 30 40 50 60 70 80 90 100

Water Saturation (%)

Ga

s-B

rin

e H

eig

ht

Ab

ov

e F

ree

Wa

ter

(ft)

Porosity=4%

Porosity=6%

Porosity=8%

Porosity=10%

Porosity=12%

Porosity=14%

Porosity=16%

Porosity=18%



Stabilization of OGIP Distribution



Overall Pore Volume, OGIP Variation



OGIP Variation by Data Density Area



Conclusions Study illustrates development of a lithofacies-based matrix properties model for

a giant gas field The 108-million cell, 169-layer geomodel was developed by:

Defining lithofacies in 1600 wells with neural network models trained on core lithofacies-to-log correlations

Modeling between wells using sequential indicator simulation (SIS) for lithofacies and sequential gaussian simulation (SGS) for porosity

Calculating permeability, capillary pressure, and relative permeability for each unique lithofacies-porosity combination using empirical transforms

Calculating water saturation using the lithofacies/porosity-specific capillary pressure and a location-specific height-above-free-water level

Because horizontal ranges for estimated variograms (20-40 kft) are > than node well spacing (~1-3 kft), expected multiple realizations from stochastic simulations to be nearly deterministic; perhaps approaching that where well density is high

Variations in OGIP estimates quite small, at least in areas of moderate to high data density

The Hugoton geomodel illustrates the continuum between stochastic and deterministic modeling and the dependence of the methodology used for each property on the available data, the scale of prediction, and the order (predictability) of the system relative to the property being modeled



AcknowledgementsWe thank our industry partners for their support of the Hugoton Asset Management Project and their permission to share results of the study.

Anadarko Petroleum CorporationBP America Production Company

Cimarex Energy Co.ConocoPhillips Company

E.O.G. Resources Inc.ExxonMobil Production Company El Paso Exploration & Production

Osborn Heirs CompanyOXY USA, Inc.

Pioneer Natural Resources USA, Inc.

and Schlumberger for providing software

the hugoton geomodel: a hybrid stochastic-deterministic approach

Documents

cored wells

wells larger

remaining wells predictions

wells upper chaseline

kpadry gas

network usedbohling

historylargest gas field

pressure depletion reservoir