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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.

AbstractThis 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). Generallyspeaking, we focus on the single-phase gas flow case as this is most relevant and we avoid concerns related to multiphaseflow.

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 conductorsof 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 atthis point is that the reservoir permeability and the reservoir heterogeneity are fixed constants that we can not change. Whiletrue, we can change our mechanism for accessing the reservoir (i.e. , the well) and we can change our development strategy toensure 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 wellwill 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 theelliptical 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


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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 almostcertainly yield a "dual system" response ( i.e. , either dual porosity or dual permeability behavior). On the other hand, a lowcontrast ( i.e. , near uniform permeability system) will almost always behave as a homogeneous system. The "scaling" issuemay 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 thesedata 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). Suchcorrelations of porosity and permeability are local at best ( i.e. , are calibrated to a particular data set, most likely for a singledepositional 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 the

basis 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) andWorthington (1997) both provide methodologies to achieve such correlations. Our efforts to use the formation factor as acorrelating variable have led to concerns about the quality of the measurements, but generally speaking, our experience withsuch correlations has been successful.

The estimation of shale permeability remains difficult, particularly with regard to the interpretation of the results of commonflow 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 isuseful 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 shalevolume. 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 of permeability, 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 al suggest, dependent on "measurement scale, environment, and physics." Ifa 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 usingdifferent 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 andcurrent 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"-typevariables for flow in porous media (cores, bead packs, etc.) this work was systematic and thorough, and confirmed the

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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 (ifnot 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 olderconcept based on an apparent permeability, where this permeability changes with the flow conditions. Both sets of workacknowledge 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 aredirectly 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 hisconcept 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 inWyoming. Brown et al show that clay diagenesis can have a negative, if not debilitating effect on reservoir performance. As amechanism 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 clayminerals on permeability. Wilson extended the permeability-porosity correlation plot into a schematic plot (with additionaldata) 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) andAmaefule et al (1988). The technique originally relied on identification of "rock types" using data functions segmented bycertain defined parameters (most often the reverse-calculated pore throat sizes). There are several application cases worth

noting are: Abbaszadeh et al (1996); Porras et al (1999); Al-Ajmi and Holditch (2000); and Perez et al (2005). In addition tothe methodologies provided by Amaefule et al (1986) and Amaefule et al (1988), other techniques have been recently proposed, in particular Aguilera and Aguilera (2002) and Civan (2003). These newer techniques utilize an alternative basis tothe Carman-Kozeny relation, where we note that most flow unit schemes are based upon the Carman-Kozeny relation. Todate, 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 thereservoir 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 whichemphasize the characterization of tight gas/shale gas reservoirs. In addition, the Rushing and Newsham process extendsdirectly to incorporate well test data, production data, and reservoir simulation results.

Tight Gas Reservoir Behavior :

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 significantlystimulated. Roberts (1981) and Thompson (1981) separately considered the issue of the flow behavior for a fractured well in atight gas (low permeability) reservoir Roberts worked from the perspective of fracture optimization (optimal placement/


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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 ofArchie'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 theform: 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 notethat 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 itsuggests that formation factor and permeability are uniquely correlated (which is only true for certain, very simplifiedconditions). We also provide the proof on Fig. 2 that if Fig. 2b is valid ( i.e. , F=A/k B), then permeability and porosity areuniquely 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 modeland 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 wasgiven to the derivation of the "fractal" permeability-porosity correlation model, Pape et al provide a final form that is simplythe 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 Paper et al correlation varies for individualcases, 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 numerouscases to the original Pape et al plot 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 al work is given in Fig. 4b . It is worth noting that this work iscontinued 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 mannersimilar to, but independent of the work of Berg (1970). Morrow et al attempt to derive a statistical average grain size ( d ) for agive 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 2 versus on a log-log scale. Applying the Berg "transform" to the data ofMorrow et al , we obtain Fig. 5 . The data from a study by Beard and Weyl (1973) for very highly sorted sands is presentedalong 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 al data and all of the Beard and Weyl data are shown in Fig. 5b .

Figure 5b shows a remarkable (if not incredible) correlation of the kd 2 and data for these cases the off-trend points (2 or 3of the Morrow et al data in the vicinity of 0.3) are most likely due to incomplete sorting of the sample. It is relevant tonote that the exponent of porosity for the trend shown in Fig. 5b is approximately 8, which may have some basis in theory [perthe work of Pape et al (1999)]. Simply put, the data in Fig. 5b strongly suggest that the correlation of kd 2 and has someunderlying theoretical basis possibly along the lines of theories proposed by Berg (1970) and Pape et al (1999). We have

presented 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


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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 Fancher et al work was "unsuccessful" in that a single trend for all cases was not achieved by their useof 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 flow

behavior 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 otherdisciplines, 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, wedo 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 mechanisticmodels 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, Huangand 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 andConway 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 ofnon-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 ofBrown et al which shows the influence of clay materials on the pore space using SEM micrographs ( Fig. 9a ), as well as thegeologic model ( Fig. 9b ) which can produce the clay alteration, transport, and deposition which yields the images shown inFig. 9a . We also provide an example given by Brown et al of 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 thatcan degrade quickly.

Continuing the discussion of clays we provide the work of Neasham (1977) in Fig. 10 and the work of Wilson (1982) inFig. 11 , where the premise is that clay alteration to Kaolinite, Chlorite, and Illite can be visualized and somewhat quantifiedusing permeability-porosity data sorted by clay type. In Fig. 10a we present the schematic diagrams of Neasham whichillustrate Kaolinite ("discrete particle" clay), Chlorite ("pore-lining" clay), and Illite ("pore-bridging" clay) where theseschematics are useful for illustrative purposes. Correlations of permeability and porosity serve as more tangible mechanism toassess the influence of authigenic clays as shown in Fig. 10b [Neasham (1977)] and Fig. 11a [Wilson (1982)]. Figure 11a is 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 aguidepost of tangible (and practical) correlations for at least qualifying the influence of authigenic clays. Fig. 11b illustratesthe 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 certain


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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 beingcurrently used for the exploitation of tight gas reservoirs. This significant differences at present compared to the mid-1980sare the advances in reservoir description/characterization processes, improved well stimulation practices, and a willingness ofoperators 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 tohave 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 sandswhich are generally more normal-pressured. In Fig. 14b we show a map of the U.S. in terms of basin-centered gas systems asgiven by Law we note that virtually the entire nation has the potential for basin-centered gas systems, and one can suspectthat 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 0.01md, often in the range of 0.0001 md. Such reservoirs will be difficult (read expensive) to develop, and well-targeting and wellstimulation 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 theenhanced process model given by Rushing and Newsham (2001b) which focuses more on tight gas/shale gas types ofreservoirs and also incorporates reservoir performance and reservoir modeling directly into the reservoirdescription/characterization procedure. The procedures given by Gunter et al and Rushing and Newsham seek to relatedifferent scales of data and to incorporate as many data types as possible. The challenges for the application of proceduressuch as these are access to sufficient data (especially petrophysical and reservoir performance data) and software necessaryto 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 willsignificantly affect the reservoir description/characterization. For this purpose we review the work of Haldorsen (1986) asshown 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 wewill 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 tointegrate information across each scale.

In Fig. 17b we observe the so-called "volume of investigation" schematic, which is particularly useful for explaining thedifference 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" ofreservoir ( i.e. , the engineering mode) often serves quite well as a surrogate for the geological description. We believe thatwhen the "block" (or cylinder) model works well in the reservoir description, that the reservoir is either essentiallyhomogeneous, or so heterogeneous that a volume average represents bulk behavior. Our perspective is something of acontradiction, 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 highlyfractured). Our goal in discussing Fig. 17b is to orient the engineer and geologist to communicate their perception of whatfeature(s) or issue(s) will dominate reservoir performance behavior. Put simply, the reservoir scale and reservoir model issueswill 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 permeabilityreservoir. As shown in Fig. 18 , Thompson ( Fig. 18a ) suggested that linear, elliptical, and pseudoradial flow regimes exist inpractice (although for permeabilities less than 0 001 md ( i e the modern definition of tight gas reservoirs) pseudoradial flow


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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 thesummary, 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 reservoir

systems. Workflows should provide mechanisms which attempt to correlate and/or scale small-scale reservoir properties into large-scale ( i.e. , volume) rock "flow units." It is critical that scale comparisons be achieved (or at leastestimated) 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 lowpermeability reservoir systems. This work emphasizes the relatively simple case of a fractured well producing in aclosed 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, dimensionlessk = Absolute permeability, mdk r = 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 Fractal

Pore 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 ofRock 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


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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 September2006.

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

May 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 theHay 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., andMast, 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 atthe 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


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Tight Gas Reservoir Behavior :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 HydraulicFracturing 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," PaperSPE/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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2008 SPE Unconventional Reservoirs ConferenceKeystone, CO, U.S.A. 1012 February 2008

SPE 114168 The Characteristic Flow Behavior of Low-Permeability Reservoir SystemsT.A. Blasingame Texas A&M University (11 February 2008)

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The Characteristic Flow Behavior of

Low-Permeability Reservoir Systems

SPE 114168

T.A. Blasingame, Texas A&M UniversityDepartment of Petroleum Engineering

Texas A&M UniversityCollege Station, TX 77843-3116

+1.979.845.2292 [email protected]

Presentation Outline )


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Orientation

Properties of Reservoir Rocks:Petrophysics Primer (review of Archie work).Power Law Models for Permeability (low permeability systems).

Non-Darcy Flow Behavior:

Historical Perspectives.Current Perspectives.Characteristics of Low Permeability Reservoirs:

Effect of Clay Minerals.

Issues Related to Flow in Low Permeability Reservoirs.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 Systems.

Conclusions and Recommendations

( P r e s e n t a t

i o n O u t

l i n e )


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Low-Permeability Reservoir SystemsProperties of Reservoir Rocks

SPE 114168




Petrophysics: Petrophysical Properties Map


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

b. Crossplot of permeability to porosity (averagetrends) used to imply that porosity and per-meability have some type of functional relation-ship. Obviously, this remains a topic of consi-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 thatpermeability was "connected" to saturation, poro-sity, and electrical properties but the relationshipwas vague, as it remains today.

p y p y p p

( P e t r o p h y s

i c s )

Petrophysics: Archie k-

-F Relations


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b. Crossplot of formation (resistivity) factor versuspermeability ( F = A/k B).

a. Crossplot of formation (resistivity) factor versuspermeability ( F = a/ m ).

mwo

a R R

F

Porosity Model : Permeability Model :

Bwo

k

A R R

F

Equating the models : Solving for k :

Bm k

Aa

/1 B

m

a

Ak

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

is only true for uniform pore systems.

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

( P e t r o p h y s

i c s )

Petrophysics: Power Law Permeability 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 permeability is approxi-mated as a power law function of porosity.

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

c. Attempt to correlate Morrow samples by deposi-tion similar to Appalachian samples.

[From: 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. ]

( P e t r o p h y s

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

b. Log-log plot of k/d 2 versus extraordinaryagreement given data quality (note slope 8).

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, No. 1, 312-321.]

( P e t r o p h y s

i c s )



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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 - 0

4

1 . E - 0

3

1 . E - 0

2

1 . E - 0

1

1 . E + 0 0

Measured Permeability (md)

C a l c u

l a t e d P e r m e a

b i l i t y

( m d )

Correlation Linek_EOS Model

]exp[ 8)( )(

321max

cw

c

b

S cccbcak

[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 - 0

2

1 . E - 0

1

1 . E + 0 0

Porosity (fraction)

P e r m e a

b i l i t y

( m d )

Permeability Correlation13140

13160

13180

13200

13220

13240

1 . E - 0

4

1 . E - 0

3

1 . E - 0

2

1 . E - 0

1

Permeability (md)

D e p

t h ( f t )

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

b. Log-log correlation plot of k versus . The correlationfunction yields an envelope.

c. Correlation plot of depthversus log( k ). Correlationappears to be excellent.

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

( P e t r o p h y s

i c s )

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Low-Permeability Reservoir SystemsNon-Darcy Flow Behavior

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Non-Darcy Flow: Historical Perspectives)


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

c. Cornell and Katz this work provided a "uni-fied" solution for high-velocity by employing theForchheimer 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 Schematic of low andhigh velocity flow regimes (for visualization).

( N o n - D a r c y F

l o w

)

Non-Darcy Flow: Current 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 SPE Annual Technical Conference andExhibition, 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 Conference and Exhibition, San Antonio, TX,U.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 equationswere 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 Conway)The "Logistic Dose" equation is pro-posed to model the "apparent" per-meability ( k app ) variable.The "Logistic Dose" relation is empiri-cally tuned to data.

E F e

d app

R

k k k k

)1(

)( minmin

Where:k d = Darcy permeability.k app = Apparent permeability.k min = Minimum permeability.R E = Reynolds number.E = Empirical constant.F = Empirical constant.

( N o n - D a r c y F

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Low k Reservoirs: Influence of Clay Minerals


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A B

C DLegend: SEM MicrographsA. (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 production behavior of the(well) Hay Reservoir Unit No. 2. This wellhas been recompleted/re-stimulated, initialcompletion lasted less than 4 years.

[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," paper SPE 10193 presented at the 1981SPE Annual Technical Conference and Exhibition, San Antonio, TX, 5-7 October 1981]

a. Severe influence of clay minerals in thisreservoir system production shown to beuniquely tied to reservoir quality andeffectiveness of well stimulation.

b. Geology concept model for Hay Reservoir.

( I n f

l u e n c e o f

C l a y

M i n e r a

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Three general types of dispersed clay insandstone reservoir rock

b. Crossplot of air permeability to porosity at1000 psig. Note correlation with clay types.

[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 presented at the 1977 SPE AnnualTechnical Conference and Exhibition, Denver, CO, U.S.A., 9-12 October 1977.]

a. Schematic diagrams of clay minerals occurringin "tight gas" reservoirs.

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l u e n c e o f

C l a y

M i n e r a

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c. Schematic illustration of clay diagenesis asa function of burial depth.

a. Schematic/semi-quantitative extension of Neashamwork showing permeability-porosity relationship forclay-bearing sandstones. Should be extended formodern cases of very low porosity/micro-Darcypermeability.

b. Schematic illustrating distributions of de-trital clays.

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

? ( I n f

l u e n c e o f

C l a y

M i n e r a

l s )

Low k Reservoirs: Tight Gas Basins (circa 1980s)])


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Comparison of Properties for Conventional and Tight Gas Reservoirs

c. Schematic of "blanket" and "lenticular" sands,including gas and water distributions. Reservoirquality controlled by deposition and diagenesis.

[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 "indirect" basin-centered gas accumulations note that the gasis 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 gasaccumulation, the overpressure zone is mappedand correlated with the depth-pressure chart.

b. Known and potential basin-centered gasaccumulations in the United States (circa 2000).

( T i g h t G a s

/ S h a l e G a s

B a s

i n s [ U S ] )

Low k Reservoirs: Performance Impedimentsa s

)


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"Permeability Jail" Concept (attempt to explain water-blocked gas production )

b. Illustrative example of "permeability jail" con-cept for a stratigraphic trap with high capillarypressure 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 Assessment, Prospect Develop-ment, andRisk Analysis," Bull. , AAPG (2004) 88, 10831121.]

a. Comparison of concept models for "traditional"and low permeability reservoir rock. Impliesthat gas flow in low permeability systems isdominated by capillary pressure effects .

( F l o w

I m p e

d i m e n

t s

T i g h t G a s

/ S h a l e

G a

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Low-Permeability Reservoir SystemsHydraulic Flow Units

(Integration of Reservoir Scales)

SPE 114168




Integration Work-Flows: Gunter et al PIPM (1997)s )


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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 presented at the 1997 SPEAnnual Technical Conference and Exhibition, San Antonio, TX, 5-8 October 1997b.]

Petrophysical Integration Process Model

( I n t e g r a t

i o n

W o r

k - F l o w s)

Integration Work-Flows: Rushing et al RIPM (2001)s )


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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," paper SPE 71352 presented atthe 2001 SPE Annual Technical Conference and Exhibition, New Orleans, LA, Sept. 30-Oct. 3, 2001b.]

Reservoir Integration Process Model

Reservoir Integration Process ModelEnhanced over previous process in terms ofdata integration and connection withreservoir modeling.Emphasizes multiple analyses and overlap-ing data types to confirm flow capability.

Remaining Technical Challenges:Need for to create functional computationalworkflow/computer module so that tasks canbe performed sequentially and simultaneous-ly.Need to resolve reservoir scales forexample, petrophysical measurements andthe results of well test analyses.

Other Pitfalls:This is not an inexpensive proposition data must be acquired early and often, parti-cularly production data.Can not avoid expenditure on petrophysicaldata (core, logs, etc.) tasks can be tar-geted, but not eliminated.

( I n t e g r a t

i o n

W o r

k - F l o w s

Reservoir Scaling Issues

Reservoir Scale Issues: Halderson Schematicsti c

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Reservoir Scaling Issues

b. (Haldorsen) Volume of investigation of a pres-sure build-up test and cross section indicatinglarge-scale internal heterogeneities.

[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 Characterization , Academic Press, Orlando, FL,293340.]

a. (Haldorsen) Four conceptual scales associatedwith porous media averages.

NANO or ATTO

?

( R s e r v

i o r S c a l e

S c h e m

a t i

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The Characteristic Flow Behavior ofLow-Permeability Reservoir Systems

Tight Gas Reservoir Behavior (Elliptical Flow Behavior )

SPE 114168




Elliptical Flow: Elliptical Flow (circa 1980)


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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 single and multiplewell elliptical drainage patterns has long beenand assumption for tight gas development.

[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 presented at the 1981 LowPermeability 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 Reservoirs Symposium, Denver, CO,U.S.A. 27-29 May 1981.]

a. (Thompson) At the micro-Darcy permeability scale,it is VERY unlikely that pseudoradial flow will everexist. The elliptical pattern is more likely.

Single-Well Elliptical Drainage Pattern

Multi-Well Elliptical Drainage Pattern ( E l l i p t

i c a l

F l o w )

"Ril " Elli i l Fl M d l

Elliptical Flow: Elliptical Flow Models (Basics )


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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 Considerations," paper SPE 106308presented at the 200 7 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 Flow Model Finite-Acting Reservoir Case

[Amini, et al (2007)]

c. Elliptical boundary configurations (finite con-ductivity fracture case [Amini, et al (2007)].

( E l l i p t

i c a l

F l o w

)

Single-Well Elliptical Drainage Model (Extension of Riley Solution )

Elliptical Flow: Production Decline Type Curves


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d. Match of production data functions ("Mexico"Gas Well) elliptical flow type curve solution.

[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 Considerations," paper SPE 106308presented at the 200 7 SPE Hydraulic Fracturing Technology Conference held in College Station, TX, 29-31 January 2007.]

b. Elliptical flow type curve solution high fractureconductivity case.

a. Elliptical flow type curve solution low fractureconductivity case.

c. Schematic of the elliptical boundary model for asingle well.

( E l l i p t

i c a l

F l o w

)

Elliptical Flow: Numerical Solution


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[From: Ecrin Product Suite, Kappa Engineering, Sophia Antipolis, France (20 08).]

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 years (81,200 hr).

e. Pressure profile at 18.44 years (161,700 hr).

f. Pressure profile at 44.10 years (386,600 hr).

( E l l i p t

i c a l

F l o w

)

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Summary, Conclusions, andRecommendations

SPE 114168




Conclusions and RecommendationsPetrophysical data are critical elements of a re- io

n s )


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p yservoir description for a low permeability system.Non-Darcy flow models are largely empirical, butmay also be sufficient for application purposes.The effect of clay in a low permeability gas reser-

voir should never be ignored/neglected.Tight gas/shale gas basins are well-known (NorthAmerica), but are (historically) slow to develop.Integrated reservoir descriptions are necessaryfor the exploitation of low permeability gas reser-voirs tie geology and reservoir performance.Fractured wells in low permeability reservoirs willproduce elliptical flow patterns for the (essential-ly) the productive life of the well.We need to improve our understanding of "scaleeffects" in low permeability reservoirs (geology?).

( C o n c l u s i o n s a n

d R e c o m m e n d a t

i o

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End of Presentation




(example) [p631 2014a] spe paper y pres in pdf (spe 114168) (pdf)

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