Neuquén, Argentina

10-12 June 2014

Dynamic Characterization of

Unconventional Gas Reservoirs: Field Cases

SPE Exploration and Development of Unconventional

Reservoirs Conference

Jorge Arévalo, Francisco Castellanos, Jose Pacheco, PEMEX E&P,

Nestor Martínez, CNH, and Francisco Pumar, CBM

Contents

• Introduction and background

• Conceptual model for unconventional gas

reservoirs

• Model modification to consider desorbed gas

• Analyses of field cases

• Final remarks

Shale Total Recoverable Resources (TRR)

In June 2013 the U.S EIA estimated TRR of shale gas at 6,634 tcf across 137

formations in 41 countries.

TRR of shale gas is nearly ten times the 665 tcf estimated for the U.S.

The international some countries in the Middle East, which still have significant

conventional natural gas reserves still in place.

Shale test wells have already been fracture-stimulated in Argentina, Australia,

the United Kingdom, Poland, China, and Mexico.

Some plays like Eagle Ford and Woodford have

transborder continuity

Other plays like Bakken and

Haynesville in the U.S. are

analogous to some Mexican

plays.

NiobraraMarcellus

HeneysvilleBarnet

Antrim

Monterey

Woodford

Bakken

Contents

• Introduction and background

• Conceptual model for unconventional gas

reservoirs

• Model modification to consider desorbed gas

• Analyses of field cases

• Final remarks

The Mexican shale basins are conterminous with

those in the U.S.

In Mexico, five oil provinces with

potential shale oil/gas plays have

been identified: Chihuahua,

Sabinas-Burro Picachos, Burgos,

Tampico-Misantla, and Veracruz.

Haynesville

EUA

Golfo de Mexico

Océano

Pacífico

Sierra Marathon

Ouachita

México

Eagle Ford

Área de Lutitas del Cretácico Superior

Área de Lutitas del Jurásico Superior0 200 400100

KmsEsc.: 1:9,000,000

Chihuahua

Sabinas

Tampico -

Misantla

Burgos

Mz

Veracruz

Burro-

Picachos

Mexico began exploring its shale basins in 2011

0 400 800 Kilómetros200

Chihuahua

Sabinas

Burro-Picachos

Burgos MZ

Tampico-

Misantla

Veracruz

Gas seco

Gas y condensado

Aceite

República Mexicana

Gas y aceite en

estudioIn study

0 400 800 Kilómetros200

Chihuahua

Sabinas

Burro-Picachos

Burgos MZ

Tampico-

Misantla

Veracruz

Gas seco

Gas y condensado

Aceite

República Mexicana

Gas y aceite en

estudio

In study

Some important shale

hydrocarbon basins have

been identified such as La

Pimienta-La Casita and

Eagle Ford formations in

which 545 tcf of TRR were

estimated.

This represents 27% of

North American shale gas

reserves and 7.5% of shale

gas reserves worldwide.

The geological formations of these basins range from low k (< less than 0.1

md) to extremely low k (nano-darcies).

It is necessary to drill horizontal wells with multiple fracking stages to improve

the fluid transmissibility in the formations.

Contents

• Introduction and background

• Conceptual model for unconventional gas

reservoirs

• Model modification to consider desorbed gas

• Analyses of field cases

• Final remarks

Geomechanic

properties

Micro- y nanoporosity

Thermal maturity

Adsorbed gas

adsorbido

COT > 2

9

Conceptual model for unconventional gas reservoirs

Organic material content (OMC) and

adsorbed gas are the governing factors that

have a major influence on the behavior of

unconventional gas reservoirs with low

permeability.

This behavior can be represented through

conceptual models taking the following

concepts into consideration:

1) storage mechanisms

2) transport

3) physical gas adsorption and desorption

effects

Triple porosity storage model for UGRs

Main types of gas storage in UGRs:

a) free gas in the matrix pores

b) adsorbed gas in the matrix surface

A triple-porosity model includes:

free gas and adsorbed gas (it

considers all of the gas that is stored

in formations that contain organic

material)

a combination of double-porosity,

matrix fractures and adsorbed gas in

which free gas is stored in the double-

porosity

Porosity 1 = matrix micro-pores

Porosity 2 = natural fractures

Porosity 3 = gas adsorbed (a “virtual

porosity” in the surface of the formation

particles in the matrix)

Transport mechanism with adsorption process

A diffusion process is present in the primary porosity that can be categorized into three

different mechanisms:

Rock matrix diffusion (molecule-molecule interactions dominate)

Knudsen diffusion (molecule-surface interactions dominate)

Surface diffusion from the adsorbed gas layer

In the primary porosity (rich in

OMC) there are large surface

areas for gas adsorption that

allow for the storage of large

amounts of gas.

The rock pores are extremely

small, which causes the

system permeability of this

primary porosity to be

substantially small, resulting

in no gas or water flow.

𝑞𝑔 =−𝐷𝐴 𝑧𝑠𝑐𝑅𝑇𝑠𝑐𝑝𝑠𝑐

𝑑𝐶

𝑑𝑥

Physical gas adsorption and desorption in UGRs

In UGRs that present OMC, a storage mechanism that is different from conventional gas

reservoirs is the additional phenomenon of adsorption of the gas molecules

to the organic rock walls (adsorption or physisorption, a process in which the adsorbed

molecules conserve their chemical nature)

The Langmuir model

describes the gas

adsorption phenomenon in

solids, which considers that

a gas molecule is adsorbed

in a single place and

doesn’t affect neighboring

molecules.

𝑉𝑎 =𝑉𝐿𝑝

𝑝𝐿 + 𝑝

Langmuir isotherm of a saturated gas reservoir with

adsorbed gas

Desorption or saturation pressure is equal to the undersaturated initial reservoir pressure,

which can be graphically represented by an initial gas content that is on the isotherm curve.

Langmuir isotherms describe the

maximum gas amount in UGRs that

can be stored under certain

conditions with OMC, p and T.

There are different factors that can

decrease the maximum adsorption

capacity of reservoir gas such as

OMC, p, and T.

Langmuir isotherm of an unsaturated gas reservoir

with adsorbed gas

In this case, the desorption or saturation pressure is less than the undersaturated initial

reservoir pressure, represented by an initial gas content that is below the isotherm.

Behavior of the adsorption isotherm upon changing

the Langmuir pressure

Other main parameters to consider during the exploitation of unconventional gas reservoirs

include the Langmuir parameter values since they determine the type of isotherm and in

consequence the desorption pressure, the gas storage volume, and the desorbed gas that

can be produced during exploitation.

Contents

• Introduction and background

• Conceptual model for unconventional gas

reservoirs

• Model modification to consider desorbed gas

• Analyses of field cases

• Final remarks

Model modification to consider desorbed gas

The model for conventional and unconventional reservoirs takes the desorption process

into account as a modified function of pseudotime.

The desorption phenomenon can be taken into consideration in the solutions for the

dry gas diffusion equation, using gas m(p) and modified total system compressibility

(ct*)

𝑚 𝑝 = 2 𝑝

𝜇𝑧𝑑𝑝

𝑝

𝑝0

𝑐𝑡∗ = 𝑐𝑔 1 − 𝑆𝑤 + 𝑐𝑤𝑆𝑤 + 𝑐𝑓 + 𝑐𝑑

𝑐𝑑 =𝑝𝑠𝑐𝑇𝑉𝐿𝑝𝐿𝑧

𝑇𝑠𝑐𝜙𝑝 𝑝 + 𝑝𝐿2=𝜌𝑔𝑠𝑐𝑉𝐿𝑝𝐿

𝜙𝜌 𝑔 𝑝 + 𝑝𝐿2

where

Model modification to consider desorbed gas

To eliminate the nonlinearity of the diffusion equation, the Fraim and Wattenbarger

pseudotime function is used.

Fraim and Wattenbarger studied flow regimes from a production data analysis through

the derivative function for normalized rate.

They defined the term “time match function” to take into account the definition of

modified apparent pseudotime that considers gas desorption effects using (𝑐𝑡∗).

𝑡𝑎∗ 𝑝 = 𝜇𝑖𝑐𝑡

∗𝑖

𝑑𝑡

𝜇𝑐𝑡∗𝑝

𝑡

0

These variables consider instantaneous desorption (assumption for long-term gas

production in some low-permeability, shale, and coalbed methane reservoirs).

Flow regime identification using the derivative

function for normalized gas rate and pseudotime

The modified pseudotime function can be included in the multi-fractured horizontal

well models.

The desorbed gas effect can be considered in the pseudotime function to resolve the

modified diffusion equation for adsorbed gas.

Flow regime Log-Log diagnostic Derivative function slope Type of plot

Bilinear flow

Radial derivative m = 1/4 𝑚 𝑝𝑖 −𝑚 𝑝𝑤𝑓

𝑞𝑔 𝑣𝑠. 𝑙𝑜𝑔 𝑡∗

(1.1)

Bilinear derivative m = 0 𝑚 𝑝𝑖 −𝑚 𝑝𝑤𝑓

𝑞𝑔 𝑣𝑠. 𝑡∗

4

(1.2)

Linear flow

Radial derivative m = 1/2 𝑚 𝑝𝑖 −𝑚 𝑝𝑤𝑓

𝑞𝑔 𝑣𝑠. 𝑙𝑜𝑔 𝑡∗

(1.3)

Linear derivative m = 0 𝑚 𝑝𝑖 −𝑚 𝑝𝑤𝑓

𝑞𝑔 𝑣𝑠. 𝑡∗

(1.4)

Radial flow Radial derivative m = 0 𝑚 𝑝𝑖 −𝑚 𝑝𝑤𝑓

𝑞𝑔 𝑣𝑠. 𝑙𝑜𝑔 𝑡∗

(1.5)

PSS flow.

Radial derivative m = 1 𝑚 𝑝𝑖 −𝑚 𝑝𝑤𝑓

𝑞𝑔 𝑣𝑠. 𝑙𝑜𝑔 𝑡∗

(1.6)

Derivative functions for normalized gas rate for

vertical wells (gas adsorption using pseudotime)

Flow

regime Specialized plot Interpretation equation

Lineara 𝑞𝑔𝑗 − 𝑞𝑞𝑗−1

𝑞𝑔𝑛𝑡𝑎𝑛∗ − 𝑡𝑎(𝑛−1)

∗

𝑛

𝑗=𝑖

𝑣𝑠.𝑚 𝑝𝑖 −𝑚 𝑝𝑤𝑓

𝑞𝑔 𝑘𝑚𝑓𝐴𝑐 =

𝛼 𝑇

𝜇𝑔𝑖 𝜙𝑉𝑐𝑡 𝑓𝑖 + 𝜙𝑉𝑐𝑡 𝑚𝑖

1

𝑚𝐿𝑃𝐶

(2.1)

Bilinearb 𝑞𝑔𝑗 − 𝑞𝑞(𝑗−1)

𝑞𝑔𝑛𝑡𝑛∗ − 𝑡𝑛−1

∗4

𝑛

𝑗=𝑖

𝑣𝑠.𝑚 𝑝𝑖 −𝑚 𝑝𝑤𝑓

𝑞𝑔

𝑘𝑚𝑓

34 𝑤

=984 𝐴𝑐

4 𝑇

𝜇𝑔𝑖 𝜙𝑉𝑐𝑡 𝑓𝑖 + 𝜙𝑉𝑐𝑡 𝑚𝑖4

1

𝑚𝐿𝑃𝐶

(2.2)

Radialc 𝑞𝑔𝑗 − 𝑞𝑞(𝑗−1)

𝑞𝑔𝑛𝑙𝑜𝑔 𝑡𝑎𝑛

∗ − 𝑡𝑎(𝑛−1)∗

𝑛

𝑗=𝑖

𝑣𝑠.𝑚 𝑝𝑖 −𝑚 𝑝𝑤𝑓

𝑞𝑔 𝑘ℎ 𝑚𝑓 =

1640𝑇

𝑚𝐶𝑃𝑅𝑃𝐶

(2.3)

Sphericalb 𝑞𝑔𝑗 − 𝑞𝑞(𝑗−1)

𝑞𝑔𝑛

1

𝑡𝑎𝑛∗ − 𝑡𝑎(𝑛−1)

∗

𝑛

𝑗=𝑖

𝑣𝑠.𝑚 𝑝𝑖 −𝑚 𝑝𝑤𝑓

𝑞𝑔

𝑘𝑓

= 𝜇𝑔𝑖 𝜙𝑉𝑐𝑡 𝑓𝑖 + 𝜙𝑉𝑐𝑡 𝑚𝑖10098

𝑚𝐶𝑅𝑆𝐷𝑃

23

(2.4)

Boundary

dominated

effectsb

𝑞𝑔𝑗 − 𝑞𝑞(𝑗−1)

𝑞𝑔𝑛𝑡𝑎𝑛∗ − 𝑡𝑎(𝑛−1)

∗

𝑛

𝑗=𝑖

𝑣𝑠.𝑚 𝑝𝑖 −𝑚 𝑝𝑤𝑓

𝑞𝑔 𝑘ℎ 𝑓 =

712𝑇

𝑏𝑆𝑆𝑃𝐷𝑃𝑙𝑛2.2458 𝐴

𝐶𝐴𝑟𝑤2+ 2𝑆

(2.5)

Solution:

a. 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑝𝑤𝑓 , 𝛼 = 201 and constant 𝑞𝑔 , 𝛼 = 128

a. For constant 𝑞𝑔

a. For 𝑝𝑤𝑓 and constant 𝑞𝑔

Derivative functions for normalized gas rate for

horizontal wells (gas adsorption using pseudotime)

Flow regime Derivative

function plot Type of plot Interpretation equation

Early linear flow m = 1/2 𝑚 𝑝𝑖 −𝑚 𝑝𝑤𝑓

𝑞𝑔 𝑣𝑠. 𝑡𝑎

∗ 𝑘𝑓𝐴𝑐𝑤 =1262𝑇

𝜔 𝜙𝜇𝑐𝑡 𝑓+𝑚

1

𝑚1 (3.1)

Bilinear flow m = 1/4 𝑚 𝑝𝑖 −𝑚 𝑝𝑤𝑓

𝑞𝑔 𝑣𝑠. 𝑡𝑎

∗4 𝑘𝑓𝐴𝑐𝑤 =4064𝑇

𝜎𝑘𝑚 𝜙𝜇𝑐𝑡 𝑓+𝑚0.25

1

𝑚2 (3.2)

Linear flow

m = 1/2 𝑚 𝑝𝑖 −𝑚 𝑝𝑤𝑓

𝑞𝑔 𝑣𝑠. 𝑡𝑎

∗ 𝑘𝐴𝑐𝑤 =1262𝑇

𝜙𝜇𝑐𝑡 𝑓+𝑚

1

𝑚3 (3.3)

Transitory linear

flow in the matrix m = 1/2 𝑚 𝑝𝑖 −𝑚 𝑝𝑤𝑓

𝑞𝑔 𝑣𝑠. 𝑡𝑎

∗ 𝑘𝑚𝐴𝑐𝑤 =1262𝑇

𝜙𝜇𝑐𝑡 𝑚

1

𝑚4 (3.4)

Contents

• Introduction and background

• Conceptual model for unconventional gas

reservoirs

• Model modification to consider desorbed gas

• Analyses of field cases

• Final remarks

Extension of the Eagle Ford formation in southern

Texas

Data from a well located in the Eagle Ford shale

formation in southern Texas

Depth, ft. 2,500 - 14,000

Net thickness, ft. 50 - 300

Pressure gradient, psia/ft. 0.4 - 0.8

TOC, % 2 - 9

Gas saturation, %: 83 – 85

Permeability, nd 1 - 800

Data from well A in the Eagle Ford formation in

southern Texas

Well radius, ft. 0.33

Lateral length, ft. 4,000

Thickness, ft. 283

Depth, TVD, ft. 10875

Hydrocarbon porosity (%) (φhc = φef (1-Sw)) 5.76

Reservoir pressure, psia 8,350

Temperature, °R 745

Gas compressibility, 10-5 psia-1 6

Gas viscosity, cp 0.03334

Number of effective fractures 20

Stimulated Reservoir Volume (SRV), MMft3 169

Gas rate, cumulative production and pwf history for

well A

Diagnostic plots of normalized Δm(p)/qg vs. t and

Δm(p)/qg vs. ta for well A

Specialized plots to characterize bilinear flow:

Δm(p)/qg vs. t1/4 and Δm(p)/qg vs. ta1/4

Specialized plots to characterize linear flow of

Δm(p)/qg vs. t1/2 and Δm(p)/qg vs. ta1/2

Adsorbed gas values of shale formations in the

U.S. (Andrews, 2013)

Rock parameters to estimate gas desorption in

well A (Xu, 2012)

VL = 720 scf/ton ρr = 2.5 gr/cm3

PL = 550 SRV = 17 MM ft.

T = 285 °F mr = 12 MM tons

φ = 0.0576

Matrix and fracture permeabilities for well A both

without and with gas desorption

Permeability Without gas

desorption

With gas

desorption

matrix (𝑘𝑚): 2.15 × 10−4 𝑚𝑑 1.28 × 10−5 𝑚𝑑

fracture (𝑘𝑓): 1.61 × 10−2 𝑚𝑑 2.62 × 10−2 𝑚𝑑

𝑶𝑮𝑰𝑷 =𝟐𝟎𝟎. 𝟔 𝑻 𝑺𝒈𝒊

𝝁𝒄𝒕𝑩𝒈 𝒊

∙𝒕𝒍𝒓𝒎𝟑+𝒑𝒊𝑽𝑳𝒑𝒊 + 𝒑𝑳

𝒎𝒓

OGIP = 3.15 Bscf (without gas adsorption) OGIP = 4.06 Bscf (with gas adsorption)

Mechanical state of well B

Data from well B in the Eagle Ford formation in

northern Mexico

Well radius, ft. 0.375

Lateral length, ft. 1837

Thickness, ft. 492

Depth, TVD, ft. 2530

Hydrocarbon porosity (%) (φhc = φef (1-Sw)) 6.0

Reservoir pressure, psia 5,100

Temperature, °R 667

Gas compressibility, 10-4 psia-1 1.3

Gas viscosity, cp 0.0239

Number of effective fractures 8

Stimulated Reservoir Volume (SRV) (MMft3) 445

3936 ft

646 ft

Drainage volume of well B

𝑳 =𝑯𝒐𝒓𝒊𝒛𝒐𝒏𝒕𝒂𝒍 𝒘𝒆𝒍𝒍 𝒍𝒆𝒏𝒈𝒕𝒉

𝑬𝒇𝒇𝒆𝒄𝒕𝒊𝒗𝒆 𝒇𝒓𝒂𝒄𝒕𝒖𝒓𝒆𝒔=𝟏𝟖𝟑𝟕

𝟖= 𝟐𝟑𝟎 𝒇𝒕

Cross-sectional area to flow is:

Acw = 2xeh = 2 x 1837 x 492 = 1,807,411 ft2

The matrix–natural fracture area between the blocks formed by the hydraulic fractures is

Acm = 2 x 2yehL = 2 x 2 x 246 x 1837 x 492 x 8 = 3,873,024 ft2

t (days)

Pressure and gas rate history of well B

Diagnostic plots of Δm(p)/qg vs. ta for well B

Specialized plots to characterize linear flow of

Δm(p)/qg vs. ta1/2

Parameters calculation for well B

𝒄𝒕∗ = 𝒄𝒈 𝟏 − 𝑺𝒘 + 𝒄𝒘𝑺𝒘 + 𝒄𝒇 + 𝒄𝒅

𝒄𝒅 =𝒑𝒔𝒄𝑻𝑽𝑳𝒑𝑳𝒛

𝑻𝒔𝒄𝝓𝒑 𝒑 + 𝒑𝑳𝟐 =

𝝆𝒈𝒔𝒄𝑽𝑳𝒑𝑳

𝝓𝝆 𝒈 𝒑 + 𝒑𝑳𝟐

where

Using the m3 slope equation, matrix permeability (km) was estimated,

assuming that the fracture porosity is negligible compared with matrix

porosity,

𝝓𝝁𝒄𝒕 𝒇+𝒎 = 𝝓𝝁𝒄𝒕 𝒎

The reservoir is saturated in its desorption pressure (the desorption began

with reservoir pressure)

and Rock compressibility (cf) is negligible in comparison with gas

compressibility

𝒄𝒕∗ = cg + cd

History matches of qg vs. ta1/2 and Δm(p)/qg vs. ta

1/2

for linear flow

Rock parameters to estimate gas desorption in

well B (Xu, 2012)

VL = 60 scf/ton ρr = 2.8 gr/cm3

PL = 250 SRV = 446 MM ft.3

T = 207 °F mr = 35 MM tons

φ = 0.06

km = 3.85x10-6 md

OGIP = 1.7 Bscf (without gas adsorption)

Final remarks

In UGRs with high OMC, it is important to consider the gas that is

adsorbed in the formation since this can significantly alter the OGIP and

the estimated parameters such as primary and secondary

permeabilities.

Applying Langmuir’s isotherm model, it is possible to take into

consideration and predict the behavior of adsorbed and desorbed gas in

UGRs that contain organic material. This is significant since, once gas

desorption pressure is reached, there is an additional production

mechanism in the reservoir.

Pseudotime developed for the characterization of conventional gas

reservoirs can be effectively applied to UGRs, taking into account

instantaneous gas desorption in the total compressibility of the system

and depending on the average reservoir pressure.

Final remarks

Through the well data analysis, it was possible to confirm the

applicability of the modified models to analyze production and

characterization data from UGRs, taking into consideration the

phenomenon of adsorption using Langmuir’s isotherm and modified

pseudotime at any moment during well production.

For the characterization models used in this work, the assumption was

made that the desorbed gas is instantaneous, obtaining good results.

However, it is important to bear in mind that desorption is not

instantaneous in all reservoirs. As such, it is recommended to adjust the

models taking into account real gas desorption time.

Langmuir isotherms only consider the monocomponent fluid, methane

gas. For multicomponent blends, it is recommendable to utilize the

multicomponent Langmuir isotherm or to study how to adjust a cubic

state equation, allowing us to better characterize the desorption

phenomenon.

THANKS

QUESTIONS?