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SPE 114168 The Characteristic Flow Behavior o f Low-Perme

T.A. Blasingame Texas A&M Univ

The Characteristic Flow BehaLow-Permeability Reservoir Sy

SPE 114168

T.A. Blasingame, Texas A&M UniveDepartment of Petroleum Enginee

Texas A&M UniversityCollege Station, TX 77843-3116+1.979.845.2292 t-blasingame@tam

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Presentation Outline

OrientationProperties of Reservoir Rocks: Petrophysics Primer (review of Archie work). Power Law Models for Permeability (low permeabilit

Non-Darcy Flow Behavior: Historical Perspectives. Current Perspectives.

Characteristics of Low Permeability Reservoi

Effect of Clay Minerals. Issues Related to Flow in Low Permeability Reservo

Hydraulic Flow Units: Data Integration Work-Flows. Reservoir Scaling.

Tight Gas Reservoir Behavior:

Concept/Schematic of Elliptical Flow Behavior. Performance of Fractured Wells in Low Permeability

Conclusions and Recommendations

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Properties of Reservoir Ro

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Archie " Map" of Inter-relations ofPetrophysical Properties (1950!)

b. Crossplot of permeability to

trends) used to imply tha

meability have some type of

ship. Obviously, this remai

derable discussion.

[From: Archie, G.E.: "Introduction to Petrophysics of Reservoir Rocks," Bull., AAPG (1950) 34, 943-961.]

a. Systematic "mapping" of the inter-relation of petro-

physical properties. Note that Archie observed that

permeability was "connected" to saturation, poro-

sity, and electrical properties but the relationship

was vague, as it remains today.

Petrophysics: Petrophysical Properties M

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b. Crossplot of formation (resis

permeability (F =A/kB).

a. Crossplot of formation (resistivity) factor versus

permeability (F = a/m).

==

mw

o a

R

RF

Porosity Model: Permeabili ty Model:

==

Bw

o

k

A

R

RF

Equating the models: Solving for k:

Bmk

Aa=

/1

=

=

Bm

a

Ak

This exercise suggests that permeability and porosityare related by a power law relation this observation

is only t rue for uniform pore systems.

[From: Archie, G.E.: "Introduction to Petrophysics of Reservoir Rocks," Bull., AAPG (1950) 34, 943-961.]

Petrophysics:Archie k--F Relations

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Legend: Thin Sections (photomicrographs)A. Upper shoreface ( = 0.207, k = 46.5 md) Vinton Cty, OH.B. Lower shoreface ( = 0.085, k = 3.43 md) Hocking Cty, OH.C. Tidal channel ( = 0.066, k = 0.0178 md) Carroll Cty, OH.D. Tidal flat ( = 0.053, k = 0.0011 md) Portage Cty, OH.E. Fluvial ( = 0.087, k = 15.3 md) Kanawha Cty, WV.F. Estuarine ( = 0.068, k = 0.0048 md) Preston Cty, WV.

b. Appalachian samples pemated as a power law funct

a. Thin sections of Lower Silurian Sandstones, Appa-lachian Basin (US).

c. Attempt to correlate Morrowtion similar to Appalachi

[From: Castle, J.W. and Byrnes, A.P.: "Petrophysics of Lower Silurian Sandstones and Integration with The Tectonic-Stratigraphic Framework, Appalachian Basin, United States," B

Petrophysics: Power Law Permeability Re

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a. Pape concept model plot based on a fractal poredistribution. Some concern regarding the additivestructure of the model (this seems to be a sim-plistic reduction of the fractal concept).

b. Legend for the Pape concepthat there are several quite dshown, yet the "structure" oappears consistent.

[From: Pape, H., Clauser, C., Iffland, J.: "Permeability Prediction Based on Fractal Pore-Space Geometry," Geophysics (1999) Vol. 64, (September-October 1999), 14471460.]

221 aak +=

Pape et al Fractal Model for


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a. Data from Beard and Weyl, and Morrow et al.These are unconsolidated sand samples.

b. Log-log plot ofk/d2 versus agreement given data qualit

Beard and Weyl Data:

Morrow Data: (selected)

[From: Beard, D.C. and Weyl, P.K.: "Influence of Texture on Porosity and Permeability of Unconsolidated Sand," Bull., AAPG (1973) 57, 349-369.Morrow, N.M, Huppler, J.D., and Simmons III, A.B: "Porosity and Permeability of Unconsolidated, Upper Miocene Sands From Grain-Size Analysis," J. Sed. Pet. (1969) Vol. 39, N


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East Texas Tight Gas Sand

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1

.E-04

1

.E-03

1

.E-02

1

.E-01

1.E

+00

Measured Permeability (md)

CalculatedPermeability(md)

Correlation Line

k_EOS Model

]exp[

8)()(

321max

cw

c

b

Sccc

bcak

=

+=

[From: Siddiqui and Blasingame (2008) Work in Progress.]

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E

-02

1.E

-01

1.E

+00

Porosity (fraction)

Permea

bility

(md)

Permea

13140

13160

13180

13200

13220

13240

1.E

-04

Pe

Dep

th(ft)

a. Correlation plot of calculated versusmeasured permeability. East Texas(US) tight gas example.

b. Log-log correlation plot ofkversus . The correlationfunction yields an envelope.

c. Correversuappea

Correlation relation for this case.k=f(,Sw)


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Non-Darcy Flow Behavio

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a. Fancheret al this was the first systematicattempt to validate Darcy's law, and considerextensions for high-velocity flow.

c. Cornell and Katz this workfied" solution for high-velociForchheimer relation.

[From: Fancher, G.H., Lewis, J.A., and Barnes, K.B.: "Some Physical Characteristics of Oil Sands," Pa. State College, Min. Ind. Exp. Sta. Bull. 12 (1933), 65-171.Cornell, D., and Katz, D.L. "Flow of Gases Through Consolidated Porous Media" Ind. Eng. Chem. (1953) 45, 2145-2152.Firoozabadi, A. and Katz, D.L.: "An Analysis of High Velocity Gas Flow Through Porous Media," JPT (Feb. 1979) 211-216.]

b. Firoozabadi and Katz Schehigh velocity flow regimes (fo

Non-Darcy Flow: Historical Perspectives

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[From: Barree, R.D. and Conway, M.W.: "Beyond Beta Factors: A Complete Model for Darcy, Forchheimer, and Trans-Forchheimer Flow in Porous Media," Paper SPE 89325 at the SPEExhibition, Houston, TX, U.S.A., 26-29 September 2004.Huang, H. and Ayoub, J.: "Applicability of the Forchheimer Equation for Non-Darcy Flow in Porous Media," Paper SPE 102715 presented at the 2006 SPE Annual Technical ConU.S.A., 24-27 September 2006.]

Questions: (Huang and Ayoub)1. What is the applicable range of the

Forchheimer equation for describingnon-Darcy flow?

2. What are the flow regimes andbehaviors beyond the Forchheimerregime?

3. Are these flow regimes relevant?

Issues: The Darcy and Forchheimer equations

were developed empirically and vali-dated using fluid mechanics. Will itever be possible to characterize aporous media uniquely, at the micro- ornano-scale levels?

Is the Forchheimer regime a limitation?(probably not, but more work is war-ranted)

Proposal: (Barree and Co The "Logistic Dose"

posed to model the "meability (kapp) variab

The "Logistic Dose" cally tuned to data.

app kk(

min +=

Where:kd = Darcy permeabkapp = Apparent permkmin = Minimum permRE = Reynolds numbE = Empirical consF = Empirical cons

Non-Darcy Flow: Current Perspectives

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Characteristics of

Low Permeability Reservo

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A B

C D

Legend: SEM Micrographs

A. (240X) Grains with clay overgrowths.

B. (2000X) Microporosity formed by illite clay filaments.

C. (600X) Microporosity and clay filling.

D. (1400X) Rosettes of chlorite (note illite deposition).

c. Note the poor producti

(well) Hay Reservoir Unhas been recompleted/

completion lasted less

[From: Brown, C.A., Erbe, C.B. and Crafton, J.W.: "A Comprehensive Reservoir Model of the Low Permeability Lewis Sands in the Hay Reservoir Area, Sweetwater County, Wyoming," pSPE Annual Technical Conference and Exhibition, San Antonio, TX, 5-7 October 1981]

a. Severe influence of clay minerals in this

reservoir system production shown to beuniquely tied to reservoir quality and

effectiveness of well stimulation.

b. Geology concept mode

Low k Reservoirs: Influence of Clay Miner

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Three general types of dispersed clay in

sandstone reservoir rock

b. Crossplot of air permea

1000 psig. Note correla

[From: Neasham, J.W.: "The Morphology of Dispersed Clay in Sandstone Reservoirs and Its Effect on Sand-stone Shaliness, Pore Space and Fluid Flow Properties," Paper SPE 6858 preTechnical Conference and Exhibition, Denver, CO, U.S.A., 9-12 October 1977.]

a. Schematic diagrams of clay minerals occurring

in "tight gas" reservoirs.


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c. Schematic illustration of cl

a function of burial depth.

a. Schematic/semi-quantitative extension of Neasham

work showing permeability-porosity relationship for

clay-bearing sandstones. Should be extended for

modern cases of very low porosity/micro-Darcy

permeability.

b. Schematic illustrating distr

trital clays.

[From: Wilson, M.D.: "Origins of Clays Controlling Permeability in Tight Gas Sands," JPT (December 1982), 2871-2876.]

?


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Comparison of Properties for Conventionaland Tight Gas Reservoirs

c. Schematic of "blanket" and including gas and water dis

quality controlled by deposi

[From: Spencer, C.W.: "Review of Characteristics of Low-Permeability Gas Reservoirs in Western United States," Bull., AAPG (1989) 73, 613-629.]

a. Comparative data for conventional and tight gasreservoirs in the U.S. (circa 1980's). Note that

"tight" is defined as k

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Basin-Centered Gas Systems

c. Schematic of "direct" and "i

centered gas accumulations

is trapped below the water.

[From: Law, B.E.: "Basin-Centered Gas Systems," Bull., AAPG (2002) 86, 1891-1919.]

a. Schematic diagram of a basin-centered gas

accumulation, the overpressure zone is mapped

and correlated with the depth-pressure chart.

b. Known and potential basin-

accumulations in the United

Low k Reservoirs: Basin-Centered Gas (c

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"Permeability Jail"(attempt to explain water-bloc

b. Illustrative example of "perme

cept for a stratigraphic trap w

pressure behavior.

[From: Shanley, K.W., Cluff, R.M., and Robinson, J.W.: "Factors Controlling Prolific Gas Production From Low-Permeability Sandstone Reservoirs: Implications for Resource AssessmeRisk Analysis," Bull., AAPG (2004) 88, 10831121.]

a. Comparison of concept models for "traditional"

and low permeability reservoir rock. Implies

that gas flow in low permeability systems is

dominated by capillary pressure effects.

Low k Reservoirs: Performance Impedime

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Hydraulic Flow Units

(Integration of Reservoir Sca

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[From: Gunter, G.W., Pinch, J.J., Finneran, J.M., and Bryant, W.T.: "Overview of an Integrated Process Model to Develop Petrophysical Based Reservoir Descriptions," paper SPE 38748 Annual Technical Conference and Exhibition, San Antonio, TX, 5-8 October 1997b.]

Petrophysical Integration Process Model

ntegration Work-Flows: Gunter et al PIPM

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[From: Rushing, J.A. and Newsham, K.E.: "An Integrated Work-Flow Process to Characterize Unconven-tional Gas Resources: Part II Formation Evaluation and Reservoir Modeling,"the 2001 SPE Annual Technical Conference and Exhibition, New Orleans, LA, Sept. 30-Oct. 3, 2001b.]

Reservoir Integration P

Reservoir Integration Proces Enhanced over previous

data integration and conreservoir modeling. Emphasizes multiple ana

ing data types to confirm

Remaining Technical Challe Need for to create functi

workflow/computer modbe performed sequentially.

Need to resolve reservoi

example, petrophysical mthe results of well test an

Other Pitfalls: This is not an inexpensiv

data must be acquired ecularly production data.

Can not avoid expenditudata (core, logs, etc.) geted, but not eliminated

ntegration Work-Flows: Rushing et al RIP

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Reservoir Scaling Issues

b. (Haldorsen) Volume of inves

sure build-up test and cross

large-scale internal heterog

[From: Haldorsen, H.H.: "Simulator Parameter Assignment and the Problem of Scale in Reservoir Engineer-ing," Lake, L.W. and Carroll Jr., H.B., Editors, 1986. Reservoir Characterizati293340.]

a. (Haldorsen) Four conceptual scales associated

with porous media averages.

NANO or ATTO

?

Reservoir Scale Issues: Halderson Schem

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Tight Gas Reservoir Behav

(Elliptical Flow Behavior

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Linear Flow (Early to Intermediate Times)

Elliptical Flow (Intermediate to Late Times)

Pseudoradial Flow (Late Times)

b. (Roberts) The concept of sinwell elliptical drainage patte

and assumption for tight ga

[From: Thompson, J.K.: "Use of Constant Pressure, Finite Capacity Type Curves for Performance Prediction of Fractured Wells in Low Permeability Reservoirs," Paper SPE/DOE 9839 pPermeability Reservoirs Symposium, Denver, CO, U.S.A. 27-29 May 1981.Roberts, C.N.: "Fracture Optimization in a Tight Gas Play: Muddy "J" Formation, Wattenberg Field, Colorado," Paper SPE/DOE 9851 presented at the 1981 Low Permeability ReseU.S.A. 27-29 May 1981.]

a. (Thompson) At the micro-Darcy permeability scale,it is VERY unlikely that pseudoradial flow will ever

exist. The elliptical pattern is more likely.

Single-Well Elliptical Dra

Multi-Well Elliptical Drain

Elliptical Flow: Elliptical Flow (circa 1980)

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[From: Riley, M.F.: Finite Conductivity Fractures in Elliptical Coordinates, Ph.D. Dissertation, Stanford U., Stanford, CA, 1991.]Amini, S., Ilk, D., and Blasingame, T.A.: "Evaluation of the Elliptical Flow Period for Hydraulically-Fractured Wells in Tight Gas Sands Theoretical Aspects and Practical Considpresented at the 2007 SPE Hydraulic Fracturing Technology Conference held in College Station, TX, 29-31 January 2007.]

b. Riley solution for compared to conventionalsolution for finite conductivity fracture case.

a. Fracture modeled as an ellipse Riley solution(infinite-acting reservoir).

"Riley" Elliptical Flow Model(Infinite-Acting Reservoir Case)

Extension of "Riley" Elliptical Finite-Acting Reservoi

[Amini, et al (2007)]

c. Elliptical boundary configuraductivity fracture case [Amin

Elliptical Flow: Elliptical Flow Models (Ba

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d. Match of production data fuGas Well) elliptical flow ty

[From: Amini, S., Ilk, D., and Blasingame, T.A.: "Evaluation of the Elliptical Flow Period for Hydraulically-Fractured Wells in Tight Gas Sands Theoretical Aspects and Practical Considpresented at the 2007 SPE Hydraulic Fracturing Technology Conference held in College Station, TX, 29-31 January 2007.]

b. Elliptical flow type curve solution high fractureconductivity case.

Single-Well Elliptical Drai(Extension of Riley So

a. Elliptical flow type curve solution low fractureconductivity case.

c. Schematic of the elliptical bsingle well.

Elliptical Flow: Production Decline Type C

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[From: Ecrin Product Suite, Kappa Engineering, Sophia Antipolis, France (2008).]

a. Pressure profile at 0 year (0 hr).

b. Pressure profile at 1 year (8768 hr).

c. Pressure profile at 5.59 years (49,010 hr).

d. Pressure profile at 9.26 ye

e. Pressure profile at 18.44 y

f. Pressure profile at 44.10 y

Elliptical Flow: Numerical Solution

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Summary, Conclusions, a

Recommendations

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Conclusions and Recommendations

Petrophysical data are critical elements ofservoir description for a low permeability s

Non-Darcy flow models are largely empiricmay also be sufficient for application purpThe effect of clay in a low permeability gas

voir should never be ignored/neglected.Tight gas/shale gas basins are well-known

America), but are (historically) slow to devIntegrated reservoir descriptions are nece

for the exploitation of low permeability gasvoirs tie geology and reservoir performFractured wells in low permeability reserv

produce elliptical flow patterns for the (ess

ly) the productive life of the well.We need to improve our understanding of

effects" in low permeability reservoirs (geo

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End of Presentation

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SPE 114168

The Characteristic Flow Behavior of Low-Permeability Reservoir SystemsT.A. Blasingame, SPE, Texas A&M University

Copyright 2008, Society of Petroleum Engineers

This paper was prepared for presentation at the 2008 SPE Unconventional Reservoirs Conference held in Keystone, Colorado, U.S.A., 1012 February 2008.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not beenreviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, itsofficers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission toreproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract

This paper considers the mechanisms and characteristic flow patterns of low permeability reservoir systems. In this paper wefocus on the issue of low permeability in conjunction with reservoir heterogeneity (as these often go hand in hand). Generally

speaking, we focus on the single-phase gas flow case as this is most relevant and we avoid concerns related to multiphase

flow.

Low permeability reservoir systems exhibit unique flow behavior for the following reasons:

Low permeability (which yields poor utilization of reservoir pressure), this is caused in part by:

Depositional issues: very small grains, mixed with detrital muds (clays).

Diagenetic issues: clay precipitation, massive cementation, pressure compaction, etc.

Reservoir heterogeneity dictated by deposition and post-deposition (diagenetic) events, including:

Vertical heterogeneity: layering, laminae, etc.

Lateral heterogeneity: medium to large scale geologic features (e.g., turbidite deposition, faults, etc.).

Differential diagenesis, including hydrocarbon generation and migration.

These characteristics lead us to the relatively simple observation that low permeability reservoirs are simply poor conductors

of fluids. As a matter of background, this work discusses the issues relevant to the origin of low (and ultra-low) permeabilityreservoirs, but our primary focus is flow at macro- and mega-scales (as would be observed at a well). An obvious comment at

this point is that the reservoir permeability and the reservoir heterogeneity are fixed constants that we can not change. While

true, we can change our mechanism for accessing the reservoir (i.e., the well) and we can change our development strategy to

ensure optimal performance and recovery of a particular reservoir.

As for changing our access to the reservoir, we can utilize hydraulic fracture stimulation techniques to create a conductive

pathway into the reservoir from the well. This is and will be implicit in the continued development of low and ultra-low

permeability reservoirs regardless of the well type (vertical or horizontal). In this work, our emphasis is to consider therelatively simple case of a single vertical well with a hydraulic fracture and the resulting flow behavior that this type of well

will experience. It is our contention that the elliptical flow regime dominates reservoir performance in low/ultra-low per-

meability reservoirs, and we apply both analytical and numerical solutions to a typical field case to illustrate the validity of the

elliptical flow regime.

LiteratureGeneral/Reservoir Engineering:

As a general reference on reservoir engineering, the reader is directed to Dake (2001). In this reference Dake is prone to mix

reservoir engineering with philosophy. In a typical scenario, Dake challenges the reservoir engineer to consider that the ability

to model the reservoir system should not imply that the engineer truly understands the processes in the reservoir. Rather, suchunderstanding is achieved through the interpretation of well/reservoir performance and material balance. This reference is

particularly useful in terms of such fundamental flow behavior, but it is not a specialized text for well performance or

geology/petrophysics.

In a similar context, Haldorsen (1986) focuses on the various scales of data which exist in a reservoir. Haldorsen does not

offer a solution (other than averaging formulae and statistical methods), but he does challenge the reader in terms of how data

for each scale can (or should) be integrated. Haldorsen also offers insight into the "homogeneity" of a heterogeneous (multi-layer) reservoir system i.e., that a heterogeneous system quite often exhibits the character/behavior of a homogeneous

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2 T.A. Blasingame SPE 114168

reservoir system. The key to this "homogeneity" is the permeability contrast e.g., a high permeability contrast will almost

certainly yield a "dual system" response (i.e., either dual porosity or dual permeability behavior). On the other hand, a low

contrast (i.e., near uniform permeability system) will almost always behave as a homogeneous system. The "scaling" issue

may never be quantified, but Haldorsen does try to provide insight as to how small-scale flow features affect reservoir-scale

flow behavior.

For this work we have used the Ecrin Product Suite from Kappa Engineering (ref. GRE-3), where we note that Ecrin has inte-

grated modules for pressure transient analysis, production data analysis, and high-precision numerical simulation.

Properties of Reservoir Rocks:

No discussion of rock properties (or "petrophysics") would ever be complete without reference to the work of Archie [Archie(1942, 1950)]. As the "father" of well log analysis, Archie developed relations for porosity and water saturation with resistiv-

ity. Archie also attempted correlation of permeability with resistivity measurements, but any correlation on the part of these

data imply a direct (power law) correlation of permeability and porosity. Archie also provide an early "map" of petrophysical

properties specifically, how petrophysical properties are inter-related. To his credit, Archie recognized that any correlation

of permeability with other common petrophysical data is tenuous.

Numerous authors have attempted correlation of the permeability of sandstone rocks with average grain size values [Morrow,

et al (1969); Berg (1970); and Beard and Weyl (1973)]. These studies all yield correlations that would (if valid) be accuratefor unconsolidated (or slightly consolidated) reservoir rocks. Other attempts to correlate (or generalize) the relationship of

permeability with porosity include Nelson (1994); Pape et al (1999); Pape et al (2000); Pape et al (2005). Such

correlations of porosity and permeability are local at best (i.e., are calibrated to a particular data set, most likely for a single

depositional sequence). Castle and Byrnes (2005) provide some insight into the case of Silurian sandstones (Appalachia, U.S.)using fine scale images (thin sections) and correlations of permeability with porosity via a power law transform. Timur (1968)

extends the use of a generalized power law transform of permeability and porosity to include water saturation forming thebasis for a popular correlation that is tuned using local data to provide a mechanism for estimating permeability from well log-

derived porosity and saturation data.

Another approach could be to correlate permeability, porosity, and the Archie formation factor (F) Ehrlich, et al(1991) and

Worthington (1997) both provide methodologies to achieve such correlations. Our efforts to use the formation factor as a

correlating variable have led to concerns about the quality of the measurements, but generally speaking, our experience with

such correlations has been successful.

The estimation of shale permeability remains difficult, particularly with regard to the interpretation of the results of common

flow measurements (e.g., steady-state permeability measurements). Neuzil (1994) focuses less on specific values of shale

permeability and more on the "regions" shown on a plot of porosity versus logarithm of permeability. This perspective is

useful in understanding that shales/clays have high porosity and low permeability, and some predictability in terms of trends.Revel and Cathles (1999) utilize a power-law model for estimating permeability in shaly-sands using porosity and shale

volume. This exercise is somewhat similar to that of Timur, in that ultimately a power law (or in some cases, a modified

power law) relation is obtained.

The final reference cited is that of Ahmed et al (1991), where this work considers laboratory and field estimates ofpermeability, and the inter-relationship of these estimates. In simple terms, there may often be no correlation. The inter-

relation of permeability estimates is, as Ahmed et alsuggest, dependent on "measurement scale, environment, and physics." If

a correlation of permeabilities estimated using different methods is attempted, then " Integration of available information

pertaining to these factors enhances correlation" In short, one should not necessarily expect permeabilities estimated using

different techniques and at different scales to correlate unless significant effort has been made to assess all aspects of a

particular measurement technique.

Non Darcy Flow Behavior:The discussion of non-laminar/non-Darcy flow in this work is limited to informational issues seminal references and

current issues related to this phenomenon. Historically, the work of Fancher et al (1933) was possibly the most impressive

(and exhaustive), given the technology of the day. Fancher et al fashioned "friction factor" and "Reynolds Number"-type

variables for flow in porous media (cores, bead packs, etc.) this work was systematic and thorough, and confirmed the

concept of high-velocity flow not being represented by Darcy's law. Fancher et al did not define the dimensionless variables

in a manner that consolidated the trends, but the concept was valid. Cornell and Katz (1953) "recast" the work of Fancheret al

using the Forchheimer flow equation to define the requisite dimensionless variables and achieved a single data trend valid for

both "Darcy" flow and "non-Darcy" flow. The work of Cornell and Katz has also been recast several times; recent work byComiti et al(2000) appears to be the latest manifestation of such a correlation.

There have also been numerous attempts to correlate the inertial flow coefficient () with permeability (k) as a mechanism to

estimate without a laboratory measurement. Geertsma (1974), Firoozabadi and Katz (1979), and Jones (1987) all provide

such correlations, with different bases (and data), as well as some discrepancies in how the original estimates of

were made.In fairness, each of these correlations has some legitimacy, as well as supporters. Noman and Archer (1987) provide another

study, which (like the work of Jones [Jones (1987)]) attempted to relate the inertial flow coefficient ( ) with "pore structure."

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SPE 114168 The Characteristic Flow Behavior of Low-Permeability Reservoir Systems 3

Most recently, Balhoff and Wheeler (2007) have developed an analytical model of a porous media that can reproduce most (if

not all) of the non-Darcy behavior observed in rock samples. This work may lead to other models for non-Darcy flow.

The most recent work on this topic [Huang and Ayoub (2006); Barree and Conway (2004)] discuss mechanisms for moving

past the Forchheimer flow model. In particular, Huang and Ayoub propose that there are a variety of fluid mechanics models

that can be utilized to represent high-velocity flow in porous media. Barree and Conway provide an enhancement of an older

concept based on an apparent permeability, where this permeability changes with the flow conditions. Both sets of work

acknowledge that the Forchheimer is probably sufficient for current needs.

Characteristics of Low Permeability Reservoirs:

To begin a discussion on the characteristics of low permeability reservoirs, it is probably best to address the issue of diffusionin porous media as proposed by Pandey et al(1974) where this work illustrated that the diffusion term and permeability are

directly proportional. We do not address the issue of diffusive flux in this work, only note that this term may be non-trivial in

practice for low permeability gas reservoirs.

From the standpoint of the morphology and structure of low permeability gas reservoirs, several studies provide insight.

Finley (1986) and Spencer (1989) somewhat define the status of low permeability (or tight gas) reservoirs in North America,

with emphasis on reservoir and production properties common to low permeability gas reservoirs. Law (2002) presents his

concept of a "basin-centered gas system" and emphasizes the "inverted" nature of wet zones being underlain by overpressuredgas zones. Shanley et al (2004) provide a provocative study with regard to their concept of capillarity controlled production

the so-called "permeability jail" concept where there may conditions of capillary pressure dominance where no fluids flow.

As for the practical effects of clays/shales on the production performance of a low permeability reservoir, we can cite Brown etal (1981) who studied the geology, petrophysical properties, and reservoir production behavior of the Lewis sands in

Wyoming. Brown et alshow that clay diagenesis can have a negative, if not debilitating effect on reservoir performance. As a

mechanism to "quantify" the influence of clay minerals on the pore space (both porosity and permeability), Neasham (1977)

and later Wilson (1982) provide schematic and petrophysical data to show the influence of clay minerals kaolinite, chlorite,

and illite. Neasham presents schematic diagrams of the clay minerals deposited in the pore space to illustrate the potential forclays to alter the pore space. Neasham also presents a permeability-porosity correlation plot to illustrate the effect of clay

minerals on permeability. Wilson extended the permeability-porosity correlation plot into a schematic plot (with additional

data) which illustrates the "regions" of influence for the kaolinite, chlorite, and illite minerals.

Hydraulic Flow Units:

The popular use of petrophysical data (core and well log data) arose in the mid-1980s with work of Amaefule et al(1986) and

Amaefule et al (1988). The technique originally relied on identification of "rock types" using data functions segmented by

certain defined parameters (most often the reverse-calculated pore throat sizes). There are several application cases worthnoting are: Abbaszadeh et al (1996); Porras et al(1999); Al-Ajmi and Holditch (2000); and Perez et al(2005). In addition to

the methodologies provided by Amaefule et al (1986) and Amaefule et al (1988), other techniques have been recentlyproposed, in particular Aguilera and Aguilera (2002) and Civan (2003). These newer techniques utilize an alternative basis to

the Carman-Kozeny relation, where we note that most flow unit schemes are based upon the Carman-Kozeny relation. To

date, there is no "automated" data segregation mechanism for flow unit definition nor should there be human interven-

tion is critical in defining the "flow unit" criteria.

As part of the "flow unit" discussion, we consider the process models proposed by Gunter et al (1997a) and Gunter et al

(1997b), where these techniques focus primarily on the utilization and integration of petrophysical data to describe the

reservoir model. There are extensions to other data types (e.g., well test data and reservoir simulation). Rushing and

Newsham (2001a, 2001b) propose enhancements to the Gunter et al (1997a) and Gunter et al (1997b) processes which

emphasize the characterization of tight gas/shale gas reservoirs. In addition, the Rushing and Newsham process extends

directly to incorporate well test data, production data, and reservoir simulation results.


As we move to consider reservoir performance as a component of the reservoir characterization process, we must realize thatthe flow behavior in low and ultra-low permeability reservoirs yields very poor recovery unless the reservoir is significantly

stimulated. Roberts (1981) and Thompson (1981) separately considered the issue of the flow behavior for a fractured well in a

tight gas (low permeability) reservoir. Roberts worked from the perspective of fracture optimization (optimal placement/

production), and Thompson worked from the perspective of analyzing production performance data. Both Roberts and

Thompson concluded separately and independently that elliptical flow plays a major role in the performance of fractured tight

gas wells.

For the purpose of modeling elliptical flow behavior, we consider the work of Riley (1991) for the infinite-acting reservoircase (i.e., no boundary effects). Amini et al (2007) extended the solution proposed by Riley for the case of a fractured well

with a closed elliptical boundary. The importance of recognizing the dominant flow profile cannot be overstated for design

of the optimal drainage patterns and for stimulation treatment design.

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DiscussionIn this section we discuss the elements of our perspectives on the characteristic flow behavior of low-permeability (tight gas)

reservoir systems. Our approach consists of the following components:

Petrophysical Description:

Non-Laminar/Non-Darcy Flow Behavior:

Effect of Clays (Shale) on Flow Behavior:

Geologic Character of Tight Gas/Shale Gas Reservoirs: (focus on North America)

Integrated Reservoir Description Processes for Low Permeability Reservoir Systems: Reservoir Performance: Elliptical Flow Behavior

Petrophysical Description: We begin with the work of Archie (1950) as presented in Figs. 1 and 2. In Fig. 1 we find 2 of

Archie's major contributions to petrophysics the map of petrophysical properties (Fig. 1a) which has remained fundamen-

tally unchanged over the years and the correlation of log(k) versus (Fig. 1b) [which presumes a correlation model of the

form: k=aexp(b)]. While Fig. 1b cannot be "proved" rigorously, this plot is probably the most widely used porosity-per-

meability transform plot in petrophysics. In Fig. 2a we present Archie's formation factor-porosity correlation and we note

that this correlation is considered generally valid for "clean" and "slightly shaly" sands (the data trend is still linear for "shaly"

sands, but the intercept coefficient is altered). Alternatively, Fig. 2b is one of the most contentious plots in petrophysics as it

suggests that formation factor and permeability are uniquely correlated (which is only true for certain, very simplified

conditions). We also provide the proof on Fig. 2 that if Fig. 2b is valid (i.e., F=A/kB

), then permeability and porosity are

uniquely defined by a power law function [i.e., k=/, and are arbitrary (correlation) constants].

In Fig. 3 we present the work of Castle and Byrnes (2005) where Silurian sandstones are analyzed to establish a petrophysical(power law) model permeability-porosity model based on depositional sequence. The thin section micrographs are shown inFig. 3a, and the Silurian core data are presented in Fig. 3b (we note very good correlation of the proposed power law model

and the Silurian core data given for this case). Castle and Byrnes also present additional core data (Morrow sandstone) for

comparison to the Silurian data as shown in Fig. 3c.

Pape et al(1999) presented a "fractal" model for permeability-porosity data as shown in Fig. 4. While considerable effort was

given to the derivation of the "fractal" permeability-porosity correlation model, Pape et al provide a final form that is simply

the addition of 3 power law functions (y = ax1

+ bx3

+ cx10

where the exponents 1, 3, and 10 are different "fractal"

dimensions thought to be valid for different ranges of data). As seen in Fig. 4a, the Paperet alcorrelation varies for individual

cases, but for a given case (or combination of cases) the "fractal" (multi-power law) function appears to model some casesextremely well. This observed behavior may be due to judicious selection of data for comparison, as we have added numerous

cases to the original Pape et alplot as shown in Fig. 4a, and while many of these "new" data do follow some of the Pape et al

data "families," some data do not. The legend for the Pape et alwork is given in Fig. 4b. It is worth noting that this work is

continued and to some degree expanded to other cases and other materials in Pape et al(2000) and Pape et al(2005).

Morrow et al(1969) attempted to correlate the permeability, grain size, and porosity of unconsolidated sandstones in a manner

similar to, but independent of the work of Berg (1970). Morrow et alattempt to derive a statistical average grain size (d) for a

give set of data and correlate this average value with permeability and porosity. Shortly after the work of Morrow et al(1969),Berg (1970)presented a correlation of the form kd

2versus on a log-log scale. Applying the Berg "transform" to the data of

Morrow et al, we obtain Fig. 5. The data from a study by Beard and Weyl (1973) for very highly sorted sands is presented

along with selected cases from the Morrow et al (1969) study in Fig. 5a. While only a portion of the Morrow et al data are

presented in Fig. 5a, all of the Morrow et aldata and all of the Beard and Weyl data are shown in Fig. 5b.

Figure 5b shows a remarkable (if not incredible) correlation of the kd2

and data for these cases the off-trend points (2 or 3

of the Morrow et al data in the vicinity of 0.3) are most likely due to incomplete sorting of the sample. It is relevant to

note that the exponent of porosity for the trend shown in Fig. 5b is approximately 8, which may have some basis in theory [per

the work of Pape et al (1999)]. Simply put, the data in Fig. 5b strongly suggest that the correlation of kd2

and has some

underlying theoretical basis possibly along the lines of theories proposed by Berg (1970) and Pape et al (1999). We havepresented this work to illustrate that it may be possible to extend the power law-type of models to lower permeability data sets,

as a mechanism to infer permeability from porosity (and other measurements) for tight gas sands. This remains a work in

progress.

In Fig. 6 we present a correlation of tight gas sand data using a modification of the traditional power law k- correlation

where our correlation includes a "correction" for low porosity (and low permeability) samples. Recall from the discussion

given above that, for high porosity-high permeability, well-sorted clastics, we should expect a power law correlation (of some

form) for permeability and porosity [Berg (1970); Pape et al(1999); Pape et al(2000); and Pape et al (2005)]. In Fig. 6a we

present the "correlation" plot of estimated versus measured permeability on a log-log scale, including the 45-degree "perfect

correlation" trend. The data are somewhat well-correlated by our proposed model, and we do note that part the correlation

model was fitted by hand (a, b, and cmax were determined graphically using Fig. 6b), and the coefficients c1, c2, and c3 were

optimized by hand and using regression methods. For reference, the measured and estimated permeability values are also

plotted in a "well log" format in Fig. 6c for a practical perspective view. As a comment, the final estimates of the coefficientsc1, c2, and c3 were adjusted by hand to reflect a "best fit" across all plots (Figs. 6a, 6b, and 6c). As noted, this is a work in

progress, and we hope to demonstrate a simple and consistent approach for applying the proposed correlation to a wide variety

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of cases but we also recognize that we will require at least 1 additional variable in addition to porosity and permeability

in this particular example case water saturation data were available.

In addition to the estimation of permeability, we also consider the influence of non-laminar or non-Darcy flow in this work

in particular, we want to understand the visualization of non-Darcy flow behavior as shown in Fig. 7. In Fig. 7a we present

the classic view of a pseudo-"friction factor" versus a pseudo-"Reynolds number" as presented in 1933 by Fancher et al

(1933). Although the Fancheret alwork was "unsuccessful" in that a single trend for all cases was not achieved by their use

of dimensionless variables, this work clearly shows that the data can be overlain ( i.e., correlated) provided the proper x and y-

axis transforms are achieved. In Fig. 7b we present the schematics given by Firoozabadi and Katz (1979) to illustrate flowbehavior within the pore space.

In Fig. 7c we present the pseudo-"friction factor" versus pseudo-"Reynolds number" as proposed by Cornell and Katz (1953)

for various porous media, and we note a very strong correlation as indicated by a single data trend with Darcy's law super-

imposed (i.e., the straight-line shown on Fig. 7c). The work of Cornell and Katz has been extended by researchers in other

disciplines, but until recently, essentially all such correlations were based (all or in part) on the "Forchheimer" (velocity-

squared) model. The "take-away" from Fig. 7 is that we can have confidence that for high-velocity flow in porous media, we

do have some fundamental understanding (and correlations) which can be used to model this behavior. As noted in the

Literature section, recent advances in the modeling of high-velocity flow in porous media are tending towards mechanistic

models based on fundamental laws of fluid dynamics as opposed to empirical relations such as Darcy's law and the Forch-

heimer equation (also referred to as Forchheimer's law).

To continue the discussion of the "modern" aspects of high-velocity flow behavior, we present a summary of 2 recent

publications in Fig. 8. The most recent work [Huang and Ayoub (2006)] attempts to link the needs of the petroleum industryfor the case of high velocity flow in porous media with recent work performed in other disciplines and in doing so, Huang

and Ayoub propose questions regarding the continued use of the empirical flow laws given by Darcy and Forchheimer.

Essentially, Huang and Ayoub provide a discussion of what is (or what should be) available for modeling high-velocity flow.

In a different fashion, but also attempting to move beyond the use of the Darcy and Forchheimer relations, Barree and Conway

(2004) propose an "apparent permeability" correlation which has the form of a bounded power law relation. Barree and

Conway note that this result is not new, but it may provide more consistent performance than the Forchheimer relation.

Our discussion now moves away from trying to correlate flow behavior at the macro-scale to understanding the influence of

non-idealities in the porous media system (at both the micro- and the macro-scales). Specifically, we seek to understand the(primarily) post-depositional influence of clays/shales on the internal structure of the rock. In Fig. 9 we provide the work of

Brown et al which shows the influence of clay materials on the pore space using SEM micrographs ( Fig. 9a), as well as the

geologic model (Fig. 9b) which can produce the clay alteration, transport, and deposition which yields the images shown in

Fig. 9a. We also provide an example given by Brown et alof a typical production-time plot for a well in a reservoir thought to

be affected (severely) by clay diagenesis (Fig. 9c). While it is difficult to "quantify" directly the influence of clays on well

productivity, we know that such reservoirs are water sensitive, are difficult to stimulate, and have production performance that

can degrade quickly.

Continuing the discussion of clays we provide the work of Neasham (1977) in Fig. 10 and the work of Wilson (1982) in

Fig. 11, where the premise is that clay alteration to Kaolinite, Chlorite, and Illite can be visualized and somewhat quantified

using permeability-porosity data sorted by clay type. In Fig. 10a we present the schematic diagrams of Neasham which

illustrate Kaolinite ("discrete particle" clay), Chlorite ("pore-lining" clay), and Illite ("pore-bridging" clay) where these

schematics are useful for illustrative purposes. Correlations of permeability and porosity serve as more tangible mechanism to

assess the influence of authigenic clays as shown in Fig. 10b [Neasham (1977)] and Fig. 11a [Wilson (1982)]. Figure 11ais perhaps more useful than Fig. 10b as a diagnostic, and we have noted on Fig. 11a that this work needs to be extended to

include more samples of lower porosity and permeability. Our rationale in presenting Fig. 11a (and Fig. 10b) is to provide a

guidepost of tangible (and practical) correlations for at least qualifying the influence of authigenic clays. Fig. 11b illustrates

the distribution of clays in a typical depositional system and Fig. 11c provides orientation as to the alteration (diagenesis) ofclays as a function of burial depth.

The next portion of our discussion addresses the geologic aspects of tight gas/shale gas reservoirs as understood at present.

The work by Shanley, et al(2004) shown in Fig. 12 proposes that there are conditions where capillary effects (or capillarity)

completely dominates the flow behavior in the reservoir and there may be little (if any) gas (or water) production under certainconditions which they call a "permeability jail." The permeability jail concept is illustrated using relative permeability and

capillary pressure plots in Fig. 12a, and as a schematic of a gas-water reservoir affected by the permeability jail concept in

Fig. 12b. The reality of poor well performance is explained in principle by the concept of permeability jail, but there are other

specific factors influencing flow at the reservoir scale (e.g., stimulation, well placement, etc.) and these factors must also be

considered.

Performing a "look-back" to the 1980s for the case of "tight gas" reservoir systems we consider the work of Spencer (1989) as

summarized in Fig. 13. Spencer provides a table of reservoir properties/conditions for tight gas reservoirs in Fig. 13a

where one should note that "tight gas" reservoirs are defined as those systems having permeabilities less than 0.1 md, wheretoday (2008) we consider "tight gas" reservoirs as those having permeabilities less than 0.001 md. In Fig. 13b we provide

Spencer's map of the western U.S. illustrating tight gas basins/areas as known in the mid-1980s interestingly, a modern map

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would (as expected) include the same areas as shown on Fig. 13b, as well as many more. In Fig. 13c we present the compari-

son given by Spencer for "blanket" and "lenticular" sands which, ironically, is an exploration/exploitation model being

currently used for the exploitation of tight gas reservoirs. This significant differences at present compared to the mid-1980s

are the advances in reservoir description/characterization processes, improved well stimulation practices, and a willingness of

operators to regularly produce multi-zone "stacked-pay" reservoirs. In addition, there are improvements in geological con-

cepts and practices that enable development of tight gas/shale gas reservoirs that, 20 years ago, would have been considered to

have too much risk and/or operations issues to produce economically.

Continuing with our discussion of geological characterization/definition of tight gas/shale gas reservoirs we now consider themodern exploration model of the "basin-centered gas system" as prescribed by Law (2002) and shown in Fig. 14. In Fig. 14a

we present the "typical" basin-centered gas system as a zone of overpressured gas reservoirs overlain by water bearing sands

which are generally more normal-pressured. In Fig. 14b we show a map of the U.S. in terms of basin-centered gas systems as

given by Law we note that virtually the entire nation has the potential for basin-centered gas systems, and one can suspect

that in 20 years time we may find that the entire U.S. has active basin-centered gas plays. The schematic of "water-over-gas"

described by Law (200) is shown in Fig. 14c this phenomenon is relevant for exploration. We must recognize that most so-

called basin-centered gas systems are large to very large packages of sediments, often hundreds if not thousands of feet thick

and these are typically low quality "reservoirs" very shaly sands or (at best) sandy shales of permeabilities less than 0.01

md, often in the range of 0.0001 md. Such reservoirs will be difficult (read expensive) to develop, and well-targeting and well

stimulation will be the primary mechanisms for optimal production/recovery.

Changing our tact, we now consider processes to describe/characterize tight gas/shale gas reservoirs. The original

"Petrophysical Integration Process Model" (or PIPM procedure) given by Gunter et al (1997b) is shown in Fig. 15. This

procedure documents a petrophysics-based approach to develop an integrated reservoir description. In Fig. 16 we present the

enhanced process model given by Rushing and Newsham (2001b) which focuses more on tight gas/shale gas types of

reservoirs and also incorporates reservoir performance and reservoir modeling directly into the reservoir

description/characterization procedure. The procedures given by Gunter et al and Rushing and Newsham seek to relate

different scales of data and to incorporate as many data types as possible. The challenges for the application of procedures

such as these are access to sufficient data (especially petrophysical and reservoir performance data) and software necessary

to facilitate sequential and simultaneous workflows that can quickly and effectively integrate different data types.

The issue of reservoir scales is critical for the characterization of the performance of low-permeability reservoirs however;

the most effective mechanism to assess reservoir scales remains to be the geologist, the skill and determination of which will

significantly affect the reservoir description/characterization. For this purpose we review the work of Haldorsen (1986) as

shown in Fig. 17 specifically Haldorsen's "reservoir scales" schematic (Fig. 17a) and his "volume of investigation"

schematic for reservoir heterogeneity (Fig. 17b). In Fig. 17a we have added the atto/nano-scale feature to illustrate that we

will soon have to consider near-atomic scale features especially for the case of ultra-low permeability shale gas reservoirs.The other scales shown on Fig. 17a are meant to demonstrate the need for expertise in assessing each scale, as well as need to

integrate information across each scale.

In Fig. 17b we observe the so-called "volume of investigation" schematic, which is particularly useful for explaining the

difference in perspective between classical reservoir engineers and geologists. The upper cylinder of rock (engineering model)

is meant to somehow represent the lower geological description of the reservoir structure. Surprisingly, the "block" of

reservoir (i.e., the engineering mode) often serves quite well as a surrogate for the geological description. We believe that

when the "block" (or cylinder) model works well in the reservoir description, that the reservoir is either essentially

homogeneous, or so heterogeneous that a volume average represents bulk behavior. Our perspective is something of a

contradiction, but we also believe that the "block" model fails due to the contrast in reservoir properties ( e.g., a very high

permeability layer dominates performance, or a major geological feature exists (fault or channel), or the reservoir is highly

fractured). Our goal in discussing Fig. 17b is to orient the engineer and geologist to communicate their perception of what

feature(s) or issue(s) will dominate reservoir performance behavior. Put simply, the reservoir scale and reservoir model issues

will become more and more important as we develop lower permeability reservoir systems.

We now begin our discussion of reservoir performance issues for low permeability reservoir systems with the work ofThompson (1981) and Roberts (1981) regarding the reservoir flow behavior near a fractured well in a low permeability

reservoir. As shown in Fig. 18, Thompson (Fig. 18a) suggested that linear, elliptical, and pseudoradial flow regimes exist in

practice (although for permeabilities less than 0.001 md (i.e., the modern definition of tight gas reservoirs), pseudoradial flow

will never occur in practice). Similarly Roberts (Fig. 18b) suggests that elliptical drainage patterns evolve in tight gas

reservoirs and that the recovery of gas is wholly dependent on the converge of the well spacing with the elliptical drainage

patterns (see the multiwell representation in Fig. 18b). These perspectives and observations lead us to conclude that an

elliptical flow model is the most representative case for fractured wells in tight gas reservoir systems.

In Fig. 19 we provide orientation for the Riley (1991) elliptical flow solution for the case of an infinite-acting reservoir (Figs.

19a and 19b). Amini et al (2007) extended the work of Riley to include a closed elliptical boundary as shown schematically

in Fig. 19c. The Amini et al(2007) closed elliptical boundary solution was used to generate production decline "type curves"

as shown in Figs. 20a and 20b and the well/reservoir schematic for this solution is shown in Fig. 20c. In Fig. 20d, Amini

et al (2007) present the match of the "Mexico" gas well on the elliptical flow type curve for the case of a vertical well with a

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high-conductivity vertical fracture. The match shown in Fig. 20d is excellent and provided estimates of reservoir properties as

well as contacted gas volume. The permeability estimated from this type curve match is on the order of 0.001 md, and the

well had (at that time) a production history in excess of 44 years.

In Fig. 21 we employ the results of the analysis given by Amini et al(2007) for the case of the "Mexico" gas well to generate

pressure distributions using a commercial reservoir simulation program [Ercin (2008)] for the purpose of visualizing the

evolution of the elliptical drainage boundary. In Figs. 21a-21f we provide the pressure distributions at 0, 1, 5.59, 9.26, 18.44,

and 44.10 years, respectively. The evolution of the elliptical drainage pattern is confirmed from the results shown in Figs.

21a-21f, and we should make certain to incorporate such observations into our analyses and our development planning.

Summary and ConclusionsSummary: In this work we attempt, more than anything else, to document the progression of technology for the evaluation and

characterization of low permeability reservoir systems specifically, the description of the reservoir in terms of geology and

petrophysics, and the characterization of the reservoir in terms of well/reservoir performance. These tasks (reservoir

description and reservoir characterization) are somewhat unrelated particularly when we consider the scale of data related

to each task, as well as the state of the technology for each task. For example, we can obtain micro- to nano-scale images of

rock structure, but "scaling up" those data is an essentially impossible task. Further, we can invert production performance

(rates and pressures) to estimate reservoir properties (permeability, fracture half-length, fracture conductivity, reservoir

volume, etc.), but these are "gross averages" of the properties which exist in-situ.

As such, we have considered the evolution of technologies that can be applied to describe/characterize low permeability gas

reservoirs, especially those "fundamental" technologies geology, petrophysics, and reservoir engineering. We provide an

overview, as well as several paths that converge to the evaluation of well/reservoir performance behavior where production

is the only "tangible" evidence of successful exploitation. As such, we provide the following components as a workflow to

characterize low permeability reservoir behavior:

Petrophysical Description:

Classical relationships: Archie relations, log(k) versus plot, petrophysics maps. Modern assessment: Use of thin sections, power law correlations of porosity and permeability data, etc. k-correlations: Application of a modified power law correlation to low permeability data.

Non-Laminar/Non-Darcy Flow Behavior:

Traditional Approach: Utilize the (essentially empirical) Forchheimer relation for high velocity flow. Recent Work: Modern fluid mechanics provides general results, as opposed to the Forchheimer model.

Effect of Clays (Shale) on Flow Behavior:

Historical issues: Origin, distribution, and diagenesis of clay materials.

Attempts to correlate clay type with rock properties (k, ) and rock fluid properties (pc, kr).

Influence on production: Clay type and distribution can be correlated (poor) with production performance.

Geologic Character of Tight Gas/Shale Gas Reservoirs: (focus on North America)

Tight Gas Reservoirs: Concept model used for last 30 years has been repeatedly validated (water over gas). Shale Gas Reservoirs: Basin-centered gas reservoirs high temperatures and pressures, heterogeneous. Capillarity Influence: Modern proposal is that capillarity can dominate fluid flow behavior in-situ.

Integrated Reservoir Description Processes for Low Permeability Reservoir Systems:

Petrophysics Focus: Gunter, et alprocess emphasizes geological and petrophysical data. Characterization Focus: Rushing and Newsham process adds emphasis on reservoir performance and modeling. Reservoir Scale Effects: Atto-nano-micro-macro-mega-giga-scale comparisons, and average volume modeling.

Reservoir Performance: Elliptical Flow Behavior

Field Observations: Presumedelliptical flow geometry somewhat validated using historical data. Analysis of Performance:

Riley infinite-acting elliptical flow solution.

Amini, et alfinite-acting elliptical flow solution (closed elliptical reservoir).

Production type curves and analysis of reservoir performance (analytical and numerical solutions).

Reservoir pressure distributions for a bounded elliptical reservoir (numerical solution).

Conclusions:

1. Low permeability reservoirs require programs of data acquisition which evolve as the reservoir is developed. For

example at an early stage core data may not be a priority, but as reservoir performance does not meet expectations,

more geological and petrophysical data should be taken. However, one set of data which should be considered

compulsory is that of continuously measured rates and pressures such data provide an on-demand assessment ofperformance relative to expectations, and also provide continuous calibration of the well/reservoir model.

2. Petrophysical data derived from core, well logs, image tools, and formation sampling tools are a necessity for theoptimal development of a low permeability reservoir system. The geological character must be assessed including

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the effects of clays (shales) on the reservoir production potential. Specialized analyses (capillary pressure and rela-

tive permeability) are also essential for understanding the true flow potential of the system as noted in the

summary, some low permeability reservoir systems are presumed to be dominated by capillarity effects.

3. The development of an integrated reservoir description is particularly important for low permeability gas reservoirsystems. Workflows should provide mechanisms which attempt to correlate and/or scale small-scale reservoir pro-

perties into large-scale (i.e., volume) rock "flow units." It is critical that scale comparisons be achieved (or at least

estimated) whether by a specific workflow (as mentioned above), or using reservoir simulation to test up-scaling.

4. The characterization of well/reservoir performance is the critical link in understanding the flow behavior of low-permeability reservoir systems. This work emphasizes the relatively simple case of a fractured well producing in a

closed drainage pattern (our preference it to represent the drainage pattern as a closed ellipse).

Nomenclature

= Forchheimer inertial flow coefficient, 1/ft

d = Average grain size diameter, mm

F = Formation factor, dimensionless

k = Absolute permeability, md

kr = Relative permeability, fraction

pc = Capillary pressure, psia

= Porosity, fraction

References

General/Reservoir Engineering:

GRE-1. Dake, L. P.: The Practice of Reservoir Engineering, Elsevier (2001).

GRE-2. Ecrin Product Suite, Kappa Engineering, Sophia Antipolis, France (2008).

GRE-3. Haldorsen, H.H.: "Simulator Parameter Assignment and the Problem of Scale in Reservoir Engineering," Lake, L.W. andCarroll Jr., H.B., Editors, 1986. Reservoir Characterization, Academic Press, Orlando, FL, 293340.

Properties of Reservoir Rocks:

PPR-1. Ahmed, U., Crary, S.F., and Coates, G.R.: "Permeability Estimation: The Various Sources and Their Interrelationships," JPT

(May 1991), 578-587.

PPR-2. Archie, G.E.: "Electrical Resistivity Log as an Aid in Determining Some Reservoir Characteristics," Trans. AIME (1942) 146,54-62.

PPR-3. Archie, G.E.: "Introduction to Petrophysics of Reservoir Rocks," Bull., AAPG (1950) 34, 943-961.

PPR-4. Beard, D.C. and Weyl, P.K.: "Influence of Texture on Porosity and Permeability of Unconsolidated Sand," Bull., AAPG (1973)57, 349-369.

PPR-5. Berg, R.R.: "Method for Determining Permeability from Reservoir Rock Properties," GCAGS Trans. (1970) Vol. 20, 303-317.PPR-6. Castle, J.W. and Byrnes, A.P.: "Petrophysics of Lower Silurian Sandstones and Integration with The Tectonic-Stratigraphic

Framework, Appalachian Basin, United States," Bull., AAPG (2005) 89, 41-60.PPR-7. Ehrlich, R., Etris, E.L., Brumfield, D., Yuan, P., and Crabtree, S.J.: "Petrography and Reservoir Physics III: Physical Models for

Permeability and Formation Factor," Bull., AAPG (1991) 75, 1579-1592.

PPR-8. Morrow, N.M, Huppler, J.D., and Simmons III, A.B: "Porosity and Permeability of Unconsolidated, Upper Miocene Sands

From Grain-Size Analysis," J. Sed. Pet. (1969) Vol. 39, No. 1, 312-321.PPR-9. Nelson, P.H.: "Permeability-Porosity Relationships in Porous Rocks," The Log Analyst(May-June 1994), 38-62.PPR-10. Neuzil, C.E.: "How Permeable are Clays and Shales?" Water Resources Research, Vol. 30 (February 1994), 145-150.PPR-11. Pape, H., Clauser, C., Iffland, J.: "Permeability Prediction Based on Fractal Pore-Space Geometry," Geophysics (1999) Vol. 64,

(September-October 1999), 14471460.

PPR-12. Pape, H., Clauser, C., Iffland, J.: "Variation of Permeability with Porosity in Sandstone Diagenesis Interpreted with a FractalPore Space Model," Pure Appl. Geophys. (2000) Vol. 157, 603619.

PPR-13. Pape, H., Clauser, C., Iffland, J., Krug, R., and Wagner, R.: "Anhydrite Cementation and Compaction in Geothermal Reservoirs:Interaction of Pore-Space Structure with Flow, Transport, PT Conditions, and Chemical Reactions," International Journal of

Rock Mechanics and Mining Sciences, Vol. 42, (October-December 2005), 1056-1069.PPR-14. Revil, A. and Cathles III, L. M.: "Permeability of Shaly Sands" Water Resources Research, Vol. 35 (March 1999), 651662.PPR-15. Timur, A.: "An Investigation of Permeability, Porosity, and Residual Water Saturation Relationships for Sandstone Reservoirs,"

The Log Analyst (July-August 1968), 8-17.

PPR-16. Worthington, P.F.: "Petrophysical Estimation of Permeability as a Function of Scale," Geol. Soc., London, Special Publications,

1997, Vol. 122, 159-168.

Non Darcy Flow Behavior:

NDF-1. Balhoff, M.T. and Wheeler, M.F.: "A Predictive Pore-Scale Model for Non-Darcy Flow in an isotropic Porous Media," paper

SPE 110838 presented at the 2007 SPE Annual Technical Conference and Exhibition, Anaheim, CA, U.S.A., 11-14 November2007.

NDF-2. Barree, R.D. and Conway, M.W.: "Beyond Beta Factors: A Complete Model for Darcy, Forchheimer, and Trans-Forchheimer

Flow in Porous Media," Paper SPE 89325 at the SPE Annual Technical Conference and Exhibition, Houston, TX, U.S.A., 26-29September 2004.

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NDF-3. Comiti, J., Sabiri, N.E., and Montillet, A.: "Experimental Characterization of Flow Regimes in Various Porous Media - III:

Limit of Darcy's or Creeping Flow Regime for Newtonian and Purely Viscous Non-Newtonian Fluids," C hem. Engng Sci.(2000) 55, 3057-3061.

NDF-4. Cornell, D., and Katz, D.L. "Flow of Gases Through Consolidated Porous Media" Ind. Eng. Chem. (1953) 45, 2145-2152.NDF-5. Fancher, G.H., Lewis, J.A., and Barnes, K.B.: "Some Physical Characteristics of Oil Sands," Pa. State College, Min. Ind. Exp.

Sta. Bull. 12 (1933), 65-171.

NDF-6. Firoozabadi, A. and Katz, D.L.: "An Analysis of High Velocity Gas Flow Through Porous Media," JPT(Feb. 1979) 211-216.

NDF-7. Geertsma, J.: "Estimating the Coefficient of Inertial Resistance in Fluid Flow Through Porous Media," SPEJ (Oct. 1974) 445-

450.NDF-8. Huang, H. and Ayoub, J.: "Applicability of the Forchheimer Equation for Non-Darcy Flow in Porous Media," Paper SPE

102715 presented at the 2006 SPE Annual Technical Conference and Exhibition, San Antonio, TX, U.S.A., 24-27 September

2006.

NDF-9. Jones, S.C.: "Using the Inertial Coefficient, , to Characterize Heterogeneity in Reservoir Rock," Paper SPE 16949 presented atthe 1987 SPE Annual Technical Conference and Exhibition, Dallas, TX, 27-30 September 1987.

NDF-10. Noman, R., and Archer, J.S.: "The Effect of Pore Structure on Non-Darcy Gas Flow in some Low Permeability Reservoir

Rocks," Paper SPE 16400 presented at the SPE/DOE Low Permeability Reservoirs Symposium, Denver, CO, U.S.A., 18-19May 1987.

Characteristics of Low Permeability Reservoirs:

LPR-1. Brown, C.A., Erbe, C.B. and Crafton, J.W.: "A Comprehensive Reservoir Model of the Low Permeability Lewis Sands in the

Hay Reservoir Area, Sweetwater County, Wyoming," paper SPE 10193 presented at the 1981 SPE Annual TechnicalConference and Exhibition, San Antonio, TX, 5-7 October 1981.

LPR-2. Finley, R.J.: "An Overview of Selected Blanket-Geometry, Low Permeability Gas Sandstones in Texas," in Spencer, C.W., and

Mast, R.F., eds., Geology of Tight Gas Reservoirs: AAPG Studies in Geology, No. 24 (1986), 6985.LPR-3. Law, B.E.: "Basin-Centered Gas Systems," Bull., AAPG (2002) 86, 1891-1919.LPR-4. Neasham, J.W.: "The Morphology of Dispersed Clay in Sandstone Reservoirs and its Effect on Sandstone Shaliness, Pore Space

and Fluid Flow Properties," Paper SPE 6858 presented at the 1977 SPE Annual Technical Conference and Exhibition, Denver,CO, U.S.A., 9-12 October 1977.

LPR-5. Pandey, G.N., Tek, M.R., and Katz, D.L: "Diffusion of Fluids through Porous Media with Implications in Petroleum Geology,"Bull., AAPG (1974) 58, 291-303.

LPR-6. Shanley, K.W., Cluff, R.M., and Robinson, J.W.: "Factors Controlling Prolific Gas Production From Low-Permeability Sand-stone Reservoirs: Implications for Resource Assessment, Prospect Development, and Risk Analysis," Bull., AAPG (2004) 88,

10831121.

LPR-7. Spencer, C.W.: "Review of Characteristics of Low-Permeability Gas Reservoirs in Western United States," Bull., AAPG (1989)73, 613-629.

LPR-8. Wilson, M.D.: "Origins of Clays Controlling Permeability in Tight Gas Sands," JPT(December 1982), 2871-2876.

Hydraulic Flow Units:

HFU-1. Abbaszadeh, M. Fujii, H. and Fujimoto, F.: "Permeability prediction by Hydraulic Flow Units Theory and Applications,"

SPEFE. (December 1996), 263271.HFU-2. Aguilera, R. and Aguilera, M.S.: "The Integration of Capillary Pressures and Pickett Plots for Determination of Flow Units and

Reservoir Containers," SPEREE(December 2002), 465-471.HFU-3. Al-Ajmi, F., Holditch, S.A.: "Permeability Estimation Using Hydraulic Flow Units in a Central Arabia Reservoir," paper SPE

63254 prepared for presentation at the 2000 SPE Annual Technical Conference and Exhibition, Dallas, TX, 1-4 October, 2000.

HFU-4. Amaefule, J.O., Kersey, D.G., Marschall, D.M., Powell, J.D., Valencia, L.E., and Keelan, D.K.: "Reservoir Description: A

Practical Synergistic Engineering and Geological Approach Based on Analysis of Core Data, " Paper SPE 18167 presented atthe 1988 SPE Annual Technical Conference and Exhibition, Houston, TX, 2-5 October 1988.

HFU-5. Amaefule, J.O., Altunbay, M., Tiab, D., Kersey, D.G., and Keelan, D.K.: Enhanced Reservoir Description: Using Core and LogData to Identify Hydraulic (Flow) Units and Predict Permeability in Uncored Intervals/Wells," Paper SPE 26436 presented at

the 1993 SPE Annual Technical Conference and Exhibition, Houston, TX, 3-6 October 1988.

HFU-6. Civan, F.: "Leaky-Tube Permeability Model for Identification, Characterization, and Calibration of Reservoir Flow Units,"Paper SPE 84603 presented at the 2003 SPE Annual Technical Conference and Exhibition, Denver, CO, 5-8 October 2003.

HFU-8. Gunter, G.W., Finneran, J.M., Hartmann, D.J., and Miller, J.D.: "Early Determination of Reservoir Flow Units Using anIntegrated Petrophysical Method," paper SPE 38679 presented at the 1997 SPE Annual Technical Conference and Exhibition,

San Antonio, TX, 5-8 October 1997a.HFU-7. Gunter, G.W., Pinch, J.J., Finneran, J.M., and Bryant, W.T.: "Overview of an Integrated Process Model to Develop Petro-

physical Based Reservoir Descriptions," paper SPE 38748 presented at the 1997 SPE Annual Technical Conference andExhibition, San Antonio, TX, 5-8 October 1997b.

HFU-9. Perez, H.H., Datta-Gupta, A., and Mishra, S.: "The Role of Electrofacies, Lithofacies, and Hydraulic Flow Units in

Permeability Predictions from Well Logs: A Comparative Analysis Using Classification Trees," SPEREE(April 2005) 143-155.HFU-10. Porras, J.C., Barbato, R., and Khazen, L.: "Reservoir Flow Units: A Comparison Between Three Different Models in the Santa

Barbara and Pirital Fields, North Monagas Area, Eastern Venezuela Basin," paper SPE 53671 presented at the 1999 SPE Latin

American and Caribbean Petroleum Engineering Conference, Caracas, Venezuela, April 21-23, 1999.HFU-11. Rushing, J.A. and Newsham, K.E.: "An Integrated Work-Flow Process to Characterize Unconventional Gas Resources: Part I

Geological Assessment and Petrophysical Characterization," paper SPE 71352 presented at the 2001 SPE Annual TechnicalConference and Exhibition, New Orleans, LA, Sept. 30-Oct. 3, 2001a.

HFU-12. Rushing, J.A. and Newsham, K.E.: "An Integrated Work-Flow Process to Characterize Unconventional Gas Resources: Part II Formation Evaluation and Reservoir Modeling," paper SPE 71352 presented at the 2001 SPE Annual Technical Conferenceand Exhibition, New Orleans, LA, Sept. 30-Oct. 3, 2001b.

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TGR-1. Amini, S., Ilk, D., and Blasingame, T.A.: "Evaluation of the Elliptical Flow Period for Hydraulically-Fractured Wells in Tight

Gas Sands Theoretical Aspects and Practical Considerations," paper SPE 106308 presented at the 2007 SPE Hydraulic

Fracturing Technology Conference held in College Station, TX, 29-31 January 2007.TGR-2. Riley, M.F.: Finite Conductivity Fractures in Elliptical Coordinates, Ph.D. Dissertation, Stanford U., Stanford, CA, 1991.TGR-3. Roberts, C.N.: "Fracture Optimization in a Tight Gas Play: Muddy "J" Formation, Wattenberg Field, Colorado," Paper

SPE/DOE 9851 presented at the 1981 Low Permeability Reservoirs Symposium, Denver, CO, U.S.A. 27-29 May 1981.

TGR-4. Thompson, J.K.: "Use of Constant Pressure, Finite Capacity Type Curves for Performance Prediction of Fractured Wells in LowPermeability Reservoirs," Paper SPE/DOE 9839 presented at the 1981 Low Permeability Reservoirs Symposium, Denver, CO,U.S.A. 27-29 May 1981.

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Fig. 1 Introduction to petrophysics. (a.) Archie petrophysical properties map (note the inter-relation of rock and rock-fluidproperties and that often such relationships are poorly defined. (b.) Archie also presented one of the first permeability-porosity correlations in this case the "logarithmic" model commonly accepted for the correlation of permeability and

porosity data (i.e., the )exp( bak

correlation model).

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Fig. 2 Introduction to electrical properties. (a.) Archie formation factor-porosity correlation basis for modern well loganalysis. (b.) Archie formation factor-permeability correlation arguably one of the most interesting correlations inpetrophysics. However, permeability is a flow property and porosity is a volumetric property the correlation of

formation factor and permeability is actually an artifact of the (power law) relationship between permeability and porositywhich exists for unconsolidated, high-sorted intergranular systems (clastics).

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Fig. 3 Examples of attempts to use power law relationships for permeability and porosity. (a.) Thin sections indicate fair togood sorting and some relatively uniform grain samples. There are also cases (D and F) which are less well-sorted andhave significant components of clay. (b.) Logarithm of permeability versus porosity plot with power law models super-

imposed (Appalachian Silurian samples) fairly good correlation with depositional sequence type. (c.) Similar formatplot of permeability and porosity for Morrow samples also illustrates correlation with deposition.

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Fig. 4 Pape, et al work regarding the "fractal" nature of permeability-porosity transforms (resulting in a "multi-term" power lawmodel). (a.) Pape, et al "global" correlation plot showing numerous, distinct data sets the "curve" is achieved byadding different power law relations. (b.) Legend provides orientation to models (lines) and data (points) used by Pape, et

al. Note that no single, unique trend can be fitted to the entire database, but individual models are plotted for separate(and in some cases, paired) data sets.

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Fig. 5 Data of Beard and Weyl and Morrow, et al used to define a power law relationship of permeability and (average) grain size

as a function of porosity. (a.) Beard and Weyl and Morrow, et al note the "correlation" data are porosity () and thepermeability multiplied by the average grain size squared (k d

2). (b.) The log(k d

2) versus log() validates the "power law"

correlation and indicates at slope of approximately 8 (i.e., 8) Pape, et al suggest a slope of 10 for the "high"permeability portion of their correlation, so these data validate that a power correlation with porosity is possible.

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Fig. 6 Correlation attempt by Siddiqui and Blasingame [2008, (unpublished)] using a modified power law permeability-porositycorrelation for a tight gas sandstone case. This is an "intuitive" correlation with a "correction" factor used to capture thenon-linear (i. e., non-power law) portion of the data. This correlation approach has been used for clastics and carbonates,

and performs reasonably well for cases of good data quality. The ultimate goal of this work is to establish an "equationof state" for permeability however; it is possible that the work may best serve as a permeability correlator.

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Fig. 7 Summary of historical work regarding the issue of non-laminar (or non-Darcy) flow in porous media. (a.) The work ofFancher, et al shows clear non-linear behavior of their "friction factor" versus their "Reynolds number" but no univer-sal relation is observed. (b.) Concept of high-velocity flow in pore throats (Firoozabadi and Katz). (c.) The work by

Cornell and Katz (based on the Forchheimer quadratic velocity relation) appears to have achieved a universal correlationof behavior. Very recent work has sought to utilize more generalized flow concepts (not the Forchheimer relation).

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Fig. 8 Examples of very recent work on non-laminar/non-Darcy flow in porous media. Barree and Conway suggest that an

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