SPE-114168-MS-P - SPE 114168 The Characteristic Flow...

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Unformatted text preview: SPE 114168 The Characteristic Flow Behavior of Low-Permeability Reservoir Systems T.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., 10–12 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 been reviewed 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, its officers, 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 to reproduce 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 we focus 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) permeability reservoirs, 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 the relatively 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 permeability reservoirs, and we apply both analytical and numerical solutions to a typical field case to illustrate the validity of the elliptical flow regime. Literature General/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, such understanding 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- 2 SPE 114168 layer) reservoir system — i.e., that a heterogeneous system quite often exhibits the character/behavior of a homogeneous 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 integrated 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 resistivity. 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 accurate for 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 the basis for a popular correlation that is tuned using local data to provide a mechanism for estimating permeability from well logderived 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 of permeability, and the inter-relationship of these estimates. In simple terms, there may often be no correlation. The interrelation of permeability estimates is, as Ahmed et al suggest, 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 Fancher et 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 by Comiti 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 (β) with permeability (k) as a mechanism to estimate β without a laboratory measurement. Geertsma (1974), Firoozabadi and Katz (1979), and Jones (1987) all provide SPE 114168 3 such correlations, with different bases (and data), as well as some discrepancies in how the original estimates of β 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 (β) with "pore structure." 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 diffusion in 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 overpressured gas 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 et al (1981) who studied the geology, petrophysical properties, and reservoir production behavior of the Lewis sands in Wyoming. Brown et al show 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 for clays 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 worth noting 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 recently proposed, 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 intervention 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. Tight Gas Reservoir Behavior: As we move to consider reservoir performance as a component of the reservoir characterization process, we must realize that the 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. 4 SPE 114168 For the purpose of modeling elliptical flow behavior, we consider the work of Riley (1991) for the infinite-acting reservoir case (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. Discussion In 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 fundamentally unchanged over the years and the correlation of log(k) versus φ (Fig. 1b) [which presumes a correlation model of the form: k=aexp(bφ)]. While Fig. 1b cannot be "proved" rigorously, this plot is probably the most widely used porosity-permeability 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=α/φβ, α and β 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 in Fig. 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 Paper et al correlation varies for individual cases, but for a given case (or combination of cases) the "fractal" (multi-power law) function appears to model some cases extremely 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 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 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 al attempt 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 kd2 versus φ 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 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 kd2 and φ data for these cases — the off-trend points (2 or 3 of the Morrow et al data in the vicinity of φ ≈ 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 φ has some underlying 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-φ 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 SPE 114168 5 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 coefficients c1, 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 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 use of dimensionless variables, this work clearly shows that the data can be overlain (i.e., correlated) provided the proper x and yaxis 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 superimposed (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" (velocitysquared) 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 Forchheimer 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 industry for 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 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 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 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 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) of clays 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 conditions which they call a "permeability jail." The permeability jail concept is illustrated using relative permeability and 6 SPE 114168 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, where today (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 would (as expected) include the same areas as shown on Fig. 13b, as well as many more. In Fig. 13c we present the comparison 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 concepts 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 the modern 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 socalled 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 of Thompson (1981) and Roberts (1981) regarding the reservoir flow behavior near a fractured well in a low permeability SPE 114168 7 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 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 Conclusions Summary: 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 φ plot, petrophysics maps. — Modern assessment: Use of thin sections, power law correlations of porosity and permeability data, etc. Application of a modified power law correlation to low permeability data. — k-φ correlations: ● 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, φ) 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 al process 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: Presumed elliptical flow geometry somewhat validated using historical data. — Analysis of Performance: 8 SPE 114168 ■ Riley infinite-acting elliptical flow solution. ■ Amini, et al finite-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 of performance 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 the optimal development of a low permeability reservoir system. The geological character must be assessed — including the effects of clays (shales) on the reservoir production potential. Specialized analyses (capillary pressure and relative 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 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 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 lowpermeability 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 β = d F k kr pc = = = = = φ = Forchheimer inertial flow coefficient, 1/ft Average grain size diameter, mm Formation factor, dimensionless Absolute permeability, md Relative permeability, fraction 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. and Carroll Jr., H.B., Editors, 1986. Reservoir Characterization, Academic Press, Orlando, FL, 293–340. Properties of Reservoir Rocks: 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), 1447–1460. 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, 603–619. PPR-1. SPE 114168 9 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, P–T 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), 651–662. 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 November 2007. 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., 26-29 September 2004. 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," Chem. 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) 445450. 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, β, to Characterize Heterogeneity in Reservoir Rock," Paper SPE 16949 presented at the 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., 18-19 May 1987. Characteristics of Low Permeability Reservoirs: LPR-1. LPR-2. LPR-3. LPR-4. LPR-5. LPR-6. LPR-7. LPR-8. 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 Technical Conference and Exhibition, San Antonio, TX, 5-7 October 1981. 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), 69–85. Law, B.E.: "Basin-Centered Gas Systems," Bull., AAPG (2002) 86, 1891-1919. 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. 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. 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 Development, and Risk Analysis," Bull., AAPG (2004) 88, 1083–1121. Spencer, C.W.: "Review of Characteristics of Low-Permeability Gas Reservoirs in Western United States," Bull., AAPG (1989) 73, 613-629. 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), 263–271. 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 at the 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 Log Data 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. 10 SPE 114168 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 an Integrated 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 Petrophysical Based Reservoir Descriptions," paper SPE 38748 presented at the 1997 SPE Annual Technical Conference and Exhibition, 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 Technical Conference 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 Conference and Exhibition, New Orleans, LA, Sept. 30-Oct. 3, 2001b. Tight Gas Reservoir Behavior: TGR-1. TGR-2. TGR-3. TGR-4. 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. Riley, M.F.: Finite Conductivity Fractures in Elliptical Coordinates, Ph.D. Dissertation, Stanford U., Stanford, CA, 1991. 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. 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 Low Permeability Reservoirs Symposium, Denver, CO, U.S.A. 27-29 May 1981. SPE 114168 11 Fig. 1 — Introduction to petrophysics. (a.) Archie petrophysical properties map (note the inter-relation of rock and rock-fluid properties — and that often such relationships are poorly defined. (b.) Archie also presented one of the first permeabilityporosity correlations — in this case the "logarithmic" model commonly accepted for the correlation of permeability and porosity data (i.e., the k = a exp(bφ ) correlation model). 12 SPE 114168 Fig. 2 — Introduction to electrical properties. (a.) Archie formation factor-porosity correlation — basis for modern well log analysis. (b.) Archie formation factor-permeability correlation — arguably one of the most interesting correlations in petrophysics. 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 porosity which exists for unconsolidated, high-sorted intergranular systems (clastics). SPE 114168 Fig. 3 — Examples of attempts to use power law relationships for permeability and porosity. (a.) Thin sections indicate fair to good sorting and some relatively uniform grain samples. There are also cases (D and F) which are less well-sorted and have significant components of clay. (b.) Logarithm of permeability versus porosity plot with power law models superimposed (Appalachian Silurian samples) — fairly good correlation with depositional sequence type. (c.) Similar format plot of permeability and porosity for Morrow samples also illustrates correlation with deposition. 13 14 SPE 114168 Fig. 4 — Pape, et al work regarding the "fractal" nature of permeability-porosity transforms (resulting in a "multi-term" power law model). (a.) Pape, et al "global" correlation plot showing numerous, distinct data sets — the "curve" is achieved by adding 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. SPE 114168 15 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 (φ) and the 2 2 permeability multiplied by the average grain size squared (kd ). (b.) The log(kd ) versus log(φ) validates the "power law" 8 correlation and indicates at slope of approximately 8 (i.e., φ ) — 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. 16 SPE 114168 Fig. 6 — Correlation attempt by Siddiqui and Blasingame [2008, (unpublished)] using a modified power law permeability-porosity correlation for a tight gas sandstone case. This is an "intuitive" correlation with a "correction" factor used to capture the non-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 "equation of state" for permeability — however; it is possible that the work may best serve as a permeability correlator. SPE 114168 17 Fig. 7 — Summary of historical work regarding the issue of non-laminar (or non-Darcy) flow in porous media. (a.) The work of Fancher, et al shows clear non-linear behavior of their "friction factor" versus their "Reynolds number" — but no universal 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 correlation of behavior. Very recent work has sought to utilize more generalized flow concepts (not the Forchheimer relation). 18 SPE 114168 Fig. 8 — Examples of very recent work on non-laminar/non-Darcy flow in porous media. Barree and Conway suggest that an "apparent permeability" concept is preferred — where the apparent permeability is correlated as a modified power law relation. Huang and Ayoub suggest that there should be a more rigorous concept than the Forchheimer relation — and cite recent work in other disciplines to support the need for a more universal theory/model for non-laminar/non-Darcy flow in porous media. SPE 114168 Fig. 9 — Historical case (late 1970s) case of a tight gas reservoir where production behavior was significantly affected by clay diagenesis (cited because it was one of the first cases to attempt to document such behavior). (a.) Scanning electron microscope (SEM) examples clay materials deposited in low permeability sandstones (Hay Reservoir Field, WY). (b.) .Geologic model proposed for how clays deposit with depth. (c.) Example of a "poor" performing well in the Hay Reservoir Field, clay diagenesis is believed to be the primary cause of this poor performance. 19 20 SPE 114168 Fig. 10 — Schematic behavior of clay diagnosis/deposition (circa late 1970s), and samples of the effect of "clay types" on permeability. (a.) Schematic diagrams shown for Kaolinite, Chlorite, and Illite as proposed by Neasham. (b.) Logarithm of permeability versus porosity plot for sample cases of clay diagnosis/deposition — as prescribed by Neasham, the "porebridging" Illite has the most significant (negative) effect on permeability. SPE 114168 21 Fig. 11 — Further attempts to qualify the effect of clay diagnosis/deposition on tight gas sandstones (circa 1982). (a.) Schematic plot (logarithm of permeability versus porosity) which illustrates conceptually the effect of "clay types" on permeability — this work should be revised to consider low porosity, very low permeability samples currently encountered in practice. (b.) Schematic of depositional sequences where clays are commonly found. (c.) Schematic of clay diagenesis/conversion with burial depth — Illite is always most prevalent at deep burial conditions. 22 SPE 114168 Fig. 12 — An approximately 20-year "look back" at the definitions and concepts of "tight gas" reservoirs in the late 1980s. (a.) Table of conditions/properties that describe/define low permeability/"tight gas" reservoir systems — note that the "definition" for "tight gas" was cases where permeability is less than 0.1 md. (b.) Map of tight gas basins circa 1989. (c.) Schematic of lenticular and blanket sands circa 1989 — this model has been shown to be uniquely accurate for recent developments in the western U.S., and including the "water on top of gas" concept recently defined as "basin-centered" gas systems. SPE 114168 23 Fig. 13 — Conceptual definitions of "basin-centered" gas systems — defined uniquely by the "water on top of gas" proposed by Law (and others). (a.) Schematic of a "basin-centered" gas system — including the evolution of abnormal pressure. (b.) Map of know/potential "basin-centered" gas systems in the U.S. (shale gas and tight gas sands fit this definition) — interesting that this map includes essentially every recent shale gas play. (c.) Schematic of the stratigraphic conditions required for a "basin-centered" gas system to form. 24 SPE 114168 Fig. 14 — Recent work (circa 2004) regarding the influence of capillarity on gas production in tight gas reservoirs. (a.) Schematics of "traditional" (high) permeability and "low" permeability capillary pressure and relative permeability data are used to illustrate "capillary dominance" or a "permeability jail" where no fluids move at certain saturation conditions. (b.) Illustrative (conceptual) example of how the capillary dominance/permeability jail concept could affect gas and water performance. This work is cited to as another concept to explain poor gas flow behavior in "tight gas" reservoir systems. SPE 114168 Fig. 15 — The Petrophysical Integration Process Model (PIPM) as proposed by Gunter, et al for reservoir characterization. All elements of a reservoir study are included — geophysical data, geological data, petrophysical data, engineering data — as well as interpretations/results, modeling, and statistical correlations. 25 26 SPE 114168 Fig. 16 — Rushing and Newsham provide a modified process to the PIPM proposed by Gunter, et al. The workflow Rushing and Newsham emphasizes the integration of data at each scale, with multiple data types to support the analyses/conclusions at each step of the process. The Reservoir Integration Process Model (RIPM) process as proposed by Rushing and Newsham also tends to incorporate more "reservoir-scale" engineering analyses/results — thereby providing a better interpretation of reservoir-scale flow. SPE 114168 27 Fig. 17 — Reservoir scaling and heterogeneity concepts as introduced by Haldorsen (circa 1986). (a.) The four "conventional" reservoir scales are shown, and the nano/atto scale added for current interest — i.e., to recognize the recent emphasis on very small scale reservoir characterization (petrophysical data, geomechanical data/concepts, etc.). (b.) The concept of a homogeneous "control volume" given at the reservoir-scale is provided to illustrate the complexity of the actual reservoir system — and the simplified "homogeneous" reservoir concepts most often used for modeling. 28 SPE 114168 Fig. 18 — The concepts of linear and elliptical flow as proposed heuristically (and separately) by Thompson and Roberts (circa 1981). (a.) Thompson schematic diagrams for linear, elliptical, and pseudoradial flow behavior in tight gas systems. Thompson employed these models for estimation of reservoir properties from production performance. (b.) Roberts specifically considered the issue of an elliptical drainage pattern — primarily to describe the properties that control production character from wells in a low permeability gas reservoir. SPE 114168 29 Fig. 19 — Riley solution approach for an infinite-acting elliptical flow system and the Amini, et al modification of Riley's work for an elliptically-shaped reservoir boundary. (a.) Riley concept of an elliptical "fracture," shown with flux trends and a control volume in the fracture. (b.) Results of Riley's solution and that of the standard solution for a fractured well confirm the accuracy of Riley's reservoir model. (c.) Schematic diagrams of various elliptical boundary configurations used by Amini, et al — these represent certain common elliptical cases (as a model the Amini, et al solution is completely general). 30 SPE 114168 Fig. 20 — Amini, et al model for a fractured well in an elliptical flow drainage system. (a.) Dimensionless production type curve for a low fracture conductivity case. (b.) Dimensionless production type curve for a high fracture conductivity case. (c.) Completely general schematic of the reservoir system modeled by the Amini, et al solution. (d.) Production data for the "Mexico" gas well imposed on the elliptical flow type curve. The "Mexico" gas well has more than 40 years of continuous production from a reservoir of permeability that is on the order of 0.001 md. SPE 114168 Fig. 21 — Computed reservoir pressure profiles at various producing times for the "Mexico" gas well — profiles are generated using a commercial reservoir simulation package. (a.) Pressure profile at time 0 (years). (b.) Pressure profile at 1 year. (c.) Pressure profile at 5.59 years. (d.) Pressure profile at 9.26 years. (e.) Pressure profile at 18.44 years. (f.) Pressure profile at 44.10 years (i.e., end of available production history). The most interesting feature of this numerical study is that the numerically generated pressure profiles confirm the elliptical flow concept — throughout the well's history. 31 ...
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