Copyright 2004, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in Houston, Texas, U.S.A., 26–29 September 2004. This paper was selected for presentation by an SPE Program Committee following review of information contained in a proposal submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to a proposal of not more than 300 words; illustrations may not be copied. The proposal must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435. Abstract Petrophysical cut-offs are commonly applied so as to discard non-producing pay, yet, several aspects must be balanced one against the other in the process. On one hand, considering present hardware and grid size limitations, one of the main benefit of cut-offs is that the relationships between petrophysical parameters are better preserved at the upscaled model grid scale. Otherwise, some bias between porosity, permeability and water saturation distributions may result from the upscaling process, due to the non-linear dependences between those parameters. Conversely, applying cut-offs may tend to downgrade volumetrics and reservoir connectivity, and alter the actual reservoirs dynamics. The overall process must therefore aim at defining an optimized set of cut-offs providing the simplest yet accurate upscaled model. This set must be basically adapted to both rock-type and recovery mechanism. Some case studies are shown to illustrate how cut-offs can limit upscaling bias. The benefits of both "total" and "effective" porosity – saturation approaches are briefly reviewed. We illustrate how "rock-types" characteristics differ in effective and total domains, and how cut-offs must therefore be tuned in each case. Impacts of cut-offs on static volumetrics must be quantified. This can be conveniently achieved by visualizing the whole cumulative curve of "net hydrocarbon volume" vs. cut-offs values for each rock-type. We present a handy way of testing and visualizing multiple combinations of nested cut-offs, which allows to distinguish critical from redundant or secondary cut-offs. Introduction Worthington & Cosentino 1 have made an exhaustive review of basic terminology and traditional methodologies in use in the industry, to conclude that there is still no established or unambiguous methodology for defining cut-offs for incorporation within integrated reservoir studies, partly because of the different perceptions – geological or engineering – of what Net Pay is. In this paper, we briefly review the benefits of applying cut-offs in reservoir models. We then present a method to distinguish potentially discriminative cut-offs from irrelevant or redundant cut-offs. Benefits of cut-offs Benefits are mainly hardware efficiency and reduced upscaling bias. Hardware efficiency. This is one of the main justifications of cut-offs, considering present hardware and grid size limitations : discarded gross-pay is treated as one unique non- reservoir class, which renders the model much easier and faster to handle. 3D reservoir connectivity must not be degraded in the process. Reduced upscaling bias. Relationships between porosity PHI, permeability K and water saturation Sw are basically non-linear, which induces a bias between raw and upscaled petrophysical distributions. This bias is illustrated on Fig. 1, with the example of water saturation Sw : the blue curve on Fig.1b is for instance the one derived from capillary pressure Pc, with a classic hyperbolae shape Sw = f (PHI) or (K) for a given height above FWL. For clarity, we consider a model grid made of equal proportions of poor (porosity PHI 1 ) and good (porosity PHI 2 ) petrophysics facies (Fig. 1a) ; even if both facies pertain to the same blue curve, it is apparent (Fig. 1b) that - the average Sw being the average of both Sw (weighted by porosity PHI) - the upscaled grid Sw is not anymore on-trend on the blue curve but systematically higher than the one derived from the raw Sw = f (PHI) equation applied to the average grid porosity PHI (and the more heterogeneous the grid is, the higher the bias). This is a classic upscaling bias, which is handled through the use of upscaled "pseudos" equations. a practical way to limit this upscaling bias (apart from the upscaled "pseudos" curves) is to apply some cut-off by discarding the low PHI – high Sw vertical portion of the hyperbolae (contributes less to the volumes, by definition), as on Fig. 2c : this renders the grid much more petrophysically homogeneous (portion PHI2 – PHI3 closer to linear section), hence reducing the upscaling bias. SPE 91040 Impacts of Petrophysical Cut-Offs in Reservoir Models Bruno JP. Lalanne, Gérard J. Massonnat, SPE, TOTAL
Transcript
Copyright 2004, Society of Petroleum Engineers Inc. This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in Houston, Texas, U.S.A., 26–29 September 2004. This paper was selected for presentation by an SPE Program Committee following review of information contained in a proposal submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to a proposal of not more than 300 words; illustrations may not be copied. The proposal must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.
Abstract Petrophysical cut-offs are commonly applied so as to discard non-producing pay, yet, several aspects must be balanced one against the other in the process. On one hand, considering present hardware and grid size limitations, one of the main benefit of cut-offs is that the relationships between petrophysical parameters are better preserved at the upscaled model grid scale. Otherwise, some bias between porosity, permeability and water saturation distributions may result from the upscaling process, due to the non-linear dependences between those parameters. Conversely, applying cut-offs may tend to downgrade volumetrics and reservoir connectivity, and alter the actual reservoirs dynamics.
The overall process must therefore aim at defining an optimized set of cut-offs providing the simplest yet accurate upscaled model. This set must be basically adapted to both rock-type and recovery mechanism.
Some case studies are shown to illustrate how cut-offs can limit upscaling bias.
The benefits of both "total" and "effective" porosity – saturation approaches are briefly reviewed. We illustrate how "rock-types" characteristics differ in effective and total domains, and how cut-offs must therefore be tuned in each case.
Impacts of cut-offs on static volumetrics must be quantified. This can be conveniently achieved by visualizing the whole cumulative curve of "net hydrocarbon volume" vs. cut-offs values for each rock-type. We present a handy way of testing and visualizing multiple combinations of nested cut-offs, which allows to distinguish critical from redundant or secondary cut-offs.
Introduction Worthington & Cosentino1 have made an exhaustive review of basic terminology and traditional methodologies in use in the
industry, to conclude that there is still no established or unambiguous methodology for defining cut-offs for incorporation within integrated reservoir studies, partly because of the different perceptions – geological or engineering – of what Net Pay is.
In this paper, we briefly review the benefits of applying cut-offs in reservoir models. We then present a method to distinguish potentially discriminative cut-offs from irrelevant or redundant cut-offs.
Benefits of cut-offs Benefits are mainly hardware efficiency and reduced upscaling bias. Hardware efficiency. This is one of the main justifications of cut-offs, considering present hardware and grid size limitations : discarded gross-pay is treated as one unique non-reservoir class, which renders the model much easier and faster to handle. 3D reservoir connectivity must not be degraded in the process. Reduced upscaling bias. Relationships between porosity PHI, permeability K and water saturation Sw are basically non-linear, which induces a bias between raw and upscaled petrophysical distributions.
This bias is illustrated on Fig. 1, with the example of water saturation Sw : the blue curve on Fig.1b is for instance the one derived from capillary pressure Pc, with a classic hyperbolae shape Sw = f (PHI) or (K) for a given height above FWL. For clarity, we consider a model grid made of equal proportions of poor (porosity PHI1) and good (porosity PHI2) petrophysics facies (Fig. 1a) ; even if both facies pertain to the same blue curve, it is apparent (Fig. 1b) that - the average Sw being the average of both Sw (weighted by porosity PHI) - the upscaled grid Sw is not anymore on-trend on the blue curve but systematically higher than the one derived from the raw Sw = f (PHI) equation applied to the average grid porosity PHI (and the more heterogeneous the grid is, the higher the bias). This is a classic upscaling bias, which is handled through the use of upscaled "pseudos" equations.
a practical way to limit this upscaling bias (apart from the upscaled "pseudos" curves) is to apply some cut-off by discarding the low PHI – high Sw vertical portion of the hyperbolae (contributes less to the volumes, by definition), as on Fig. 2c : this renders the grid much more petrophysically homogeneous (portion PHI2 – PHI3 closer to linear section), hence reducing the upscaling bias.
SPE 91040
Impacts of Petrophysical Cut-Offs in Reservoir Models Bruno JP. Lalanne, Gérard J. Massonnat, SPE, TOTAL
2 SPE 91040
A compromise must be found between limiting as much as possible the upscaling bias and not downgrading too much volumes in producing pay ; cumulated curves of "H * PHI * Shc" net volumes versus cut-offs (Fig. 2a) can be very useful in this process.
Finally, with present hardware and grid size limitations,
benefits of cut-offs can be seen as a way to decrease upscaling bias and render the 3D model easier to handle (future hardware improved efficiency and fine-grid models may limit the benefit of cut-offs, as the actual reservoir productivity would be then correctly handled by the model).
Conversely, applying cut-offs may tend to downgrade volumetrics and reservoir connectivity, and alter the actual reservoirs dynamics.
The overall process must therefore aim at defining an optimized set of cut-offs providing the simplest yet accurate upscaled model. This set must be basically adapted to both rock-type and recovery mechanism.
A practical way to look for discriminative cut-offs : the cumulated plots of net volume per well pay zone Whatever the type of cut-off retained (Vclay, PHI, K / µ,..), it must be robust enough to be insensitive to small calculation errors. Robustness criterion can be derived from cumulated plots of "net H * PHI * Shc" volumes.
Presentation. Plots of cumulated "Net H * PHI * Shc" such as the ones on Fig. 3 can be quickly produced for whatever cut-off on X-axis (Vclay, PHI, ..), the Y-axis being normalized to 100% to obtain the respective contributions for distinct classes of cut-offs values.
Cut-off on type-1 shape is to avoid, as there is too much sensitivity (e.g. to an error on the E-log being the support of the selected cut-off on X-axis). Type-2 plot is less sensitive, but displays a continuum which makes it difficult to objectively decide where to put a cut-off if no dynamic data is available. Type-3 plot shape gives some valuable clues on where to select a potential cut-off, as it spontaneously splits the pay zone in distinct classes. Type-4 corresponds to discrete cut-off variable (e.g. geological facies, petrophysical groups, rock-types…) which requires that the discrete groups identified on the core by the geologist or the petrophysicist be propagated to the un-cored well section through "log-typing" (a permeability modeling though neural network or equivalent being ideally associated in the process). Plots of cumulated net volumes vs. classical cut-off (Vclay, K…) can in turn be produced for each of these discrete groups which allows to fine-tune the cut-off per rock-type.
Classic cut-off types derived from the quantitative interpretation of the E-logs. Once the E-logs interpretation is completed, a minimal set of cumulated Net H * PHI * Shc curves can be plotted vs. depth plus the CPI outputs Vclay (or Vshale), PHI and Sw as cut-offs on X-axis (Fig. 4).
Depth on X-axis. This plot (Fig. 4a) is useful for displaying the distribution of volumes along the whole well pay zone. Specific cumulated plots vs. Vclay, PHI, K,.. can in turn be produced on selected well pay sections (e.g. the most prolific ones).
Sw on X-axis. The Sw cut-off (Fig. 4d) should be used with caution. The reason is that some reservoirs are known to present high to very high irreducible Swirr. which may be discarded through inappropriate Sw cut-off ; this may happen in chloritic sands for instance, known to present in extreme cases some Swirr. up to 50% - 70% in even good reservoirs with perms up to 50 – 100 mD (DST tests showing anhydrous hydrocarbons production at Swirr. = 50 – 70%). Sw cut-off can be used for "cosmetic" purposes (e.g. remove some residual hydrocarbons below the FWL in the model volumetrics).
Vclay (or Vshale) on X-axis. The Vclay cut-off (Fig. 4b) can be appropriate provided the E-logs derived Vclay is itself calibrated with numerous Vclay lab measurements (XRD).
Unfortunately, unlike conventional coreplugs PHI – K data, Vclay lab data are often very scarce which makes that absolute error on the E-logs derived Vclay is often at the best ~ 10% (Vclay units). When no lab Vclay data is available, only a qualitative Vshale indicator can be computed from E-logs. Several field examples worldwide have shown that the discrepancy Vclay – Vshale can be then up to 100% ! Exhaustive Vclay lab data are then compulsory, particularly in cases like the one on Fig. 4b where the slope of the cumulated plot is very steep, and a small error on Vclay has a significant impact on the volumes after cut-off.
PHI on X-axis. Plots of cumulated net HC vs. PHI cut-off often present the shape on Fig. 4c, i.e. a continuum without clear slope break, which can make it difficult to objectively pick distinct PHI classes.
Benefit of the permeability cut-off compared to previous classic E-logs derived indicators. Permeability is the logic cut-off one would look for as it can be tied to dynamic, but this requires modeling (through neuronal network or equivalent) as permeability cannot be directly derived from E-logs.
As a shortcut, equivalent PHI and / or Vclay cut-offs may be assigned to a given K cut-off from K – PHI and K – Vclay coreplugs plots as on Fig. 5, the issue being that the uncertainty range resulting from the Fig.5 plots dispersion may be critical enough to practically prohibit such shortcut : with this field case example, a (for instance) 0.01 mD K cut-off spans some [PHI1, PHI2] and [Vclay1, Vclay2] ranges. These PHI – Vclay cut-off ranges are posted on Fig. 6 cumulated plots, from which it is apparent that they are unacceptable as they induces a close-to 50% uncertainty on the volumes after cut-off (Fig. 6b and 6c). The steep slope derivatives are such that a 1 P.U. PHI or 2 % Vclay absolute variation is enough to generate a 10% impact on the volumes, which is too much sensitive (from experience, a 5 to 10% absolute error on Vclay is not unusual !).
On the other hand, the 0.01 mD K cut-off which discards 6% of the in-place volumes (Fig. 6d) is much more robust to errors, with a slope close-to 10% impact on volumes per K decade variation. A permeability modeling may be then justified in such similar cases.
Even in cases where there is a straightforward correlation
between air permeability Kair and porosity PHI at ambient conditions (Fig. 7a), there is a benefit in picking cut-off on
SPE 91040 3
permeability rather than on porosity : the cumulated plot of net volume is identical vs. porosity or ambient Kair (red and blue curves on Fig. 7b, with compatible PHI and K X-axis as per Fig. 7a), but the plot becomes more discriminative vs. Overburden and Klinkenberg corrected KlOVBD permeability (green curve on Fig. 7b). This results from the non-linear character of both Klinkenberg and overburden permeability corrections such as the ones posted on Fig. 8a and 8b. This explains what has been observed on the previous Fig. 6 example, that the slope of Fig. 6d plot (KlOVBD) is less steep than the one on Fig. 6c (PHI).
In case several "rock-types" are present (Fig. 9), sets of
cumulated plots must be produced for each rock-type. A rock-type modeling has then to be conducted through log-typing so as to propagate the rock-types described on the cores to the uncored well sections. To note that the overburden correction may be itself "rock-type" dependant (Fig. 10), which reinforces the need to distinguish specific cut-offs for each rock-type.
"Total" and "Effective" petrophysical properties : need to tune cut-offs accordingly Effective porosity PHIeff. is defined as Total porosity PHItot. minus clay contribution Vclay * PHIclay. Effective water saturation Sweff. is lower than Total Swtot., as the hydrocarbon volume must be identical in both "effective" and "total" domains. The benefit from shifting from "total" to "effective" domains is that this may sharpen the K – PHI, Sw – PHI and PHI – Vclay relationships (e.g. Fig. 11), particularly when clay and clean reservoir porosities are similar (case of some undercompacted and unconsolidated settings). It is clear from Fig. 11 that cut-offs must be tuned accordingly, depending on whether the 3D model is build in "total" or "effective" properties. It is then convenient to produce the plots of cumulated net HC in both "total" and "effective" domains, as on Fig. 12. Independent and redundant cut-offs It is possible to simultaneously assess the impacts of 2 nested cut-offs on plots of cumulated Net volumes through the graphical display on Fig. 13. In addition, this is a quick way of identifying redundant cut-offs : for instance, effective PHIeff. and Vclay cut-offs are practically redundant in this field case (Fig. 13a or 13b) contrarily to total PHItot. and Vclay cut-offs (Fig. 13c), which is logic, as effective PHIeff. integrates effects of both total PHItot. and Vclay. More generally, Fig. 14a and Fig. 14b shapes are characteristic of redundant and independent cut-offs, respectively. Dependencies of average petrophysical parameters resulting from cut-off application So far, only plots of cumulated "Net H * PHI * Shc" have been discussed (Fig. 15a). It is possible to similarly produce plots of cumulated "Net H * PHI" and cumulated "Net H". By combining these 3 curves (ratio), one can derive the plots of Net-to-Gross ratio N / G, average porosity PHI and average
water saturation Sw, as deriving from the base definitions of N / G, average PHI and Sw posted on Fig. 15b. Such plots on Fig. 15c may be useful to detect critical cut-offs values beyond which the average petrophysical parameters variations become unstable (meaning the mapping of these parameters may become unstable as well). Conclusions The review of potential cut-off indicators has shown that classic E-log derived cut-offs may be too sensitive in many instances, particularly Vshale which is too often poorly constrained by lab Vclay measurements. Permeability cut-off looks the most robust, but a dedicated modeling is needed. K modeling can be coupled with rock-type modeling in a final attempt to reconcile static and dynamic data, by fine-tuning the K cut-off to each rock-type (dynamic data, PLT, wireline testing, DST, .., must be selective enough to test a given rock-type with a given permeability range). Plots of cumulated Net HC vs. cut-off can be helpful in assessing cut-off robustness and redundant or independent cut-offs. By-products of cumulated net HC curves are the plots of "average petrophysical parameters", which can be useful as well to assess the parameters stability (impact on mapping). Acknowledgements The authors wish to thank TOTAL for permission to publish this paper. References 1. Worthington, P.F. & Cosentino, L., "The Role of Cut-Offs in
Integrated Reservoir Studies", SPE paper 84387 (2003) 2. Hamon, G., "Two-Phase flow Rock-Typing : Another
Perspective", SPE paper 84035 (2003) Nomenclature FWL : free water level H : thickness HC (or hc) : hydrocarbons K : permeability Ka : air permeability (not Klinkenberg corrected) Kl : Klinkenberg corrected permeability KOVBD : overburden corrected permeability N / G : Net-to-Gross thickness ratio OVBD : overburden Pc : capillary pressure PHI : porosity PHIclay : clay porosity PHIeff. : effective porosity PHItot. : total porosity Sw : water saturation Sweff. : effective water saturation Swirr. : irreducible water saturation Swtot. : total water saturation Vclay : clay fraction volume Vshale : shale fraction volume
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Fig. 2 less upscaling bias on water saturation Sw when cut-off applied
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SPE 91040 5
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SPE 91040 7
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8 SPE 91040
Fig. 7 benefit of K cut-off compared to PHI cut-off (field B)
