p. spe-144590-pa-p petrophysics of triple-porosity tight gas reservoirs with a link to gas...

566 October 2011 SPE Reservoir Evaluation & Engineering

Petrophysics of Triple-Porosity Tight Gas Reservoirs With a Link to Gas Productivity

Hui Deng, SPE, Javier Leguizamon, SPE, and Roberto Aguilera, SPE, Schulich School of Engineering/University of Calgary

SummaryPetrographic work on thin sections from rock samples collected in tight gas sandstones of the western Canada sedimentary basin (WCSB) shows that the sandstones are composed of intergranular, microfracture and slot, and isolated noneffective porosities. The petrographic observations of these triple-porosity rocks have led to a petrophysical interpretation with the use of a triple-porosity model.

Tight gas reservoirs are very complex heterogeneous systems that have been evaluated in the past mostly with single-porosity models. We propose that these types of reservoirs can be repre-sented better by triple-porosity models for more rigorous quan-titative petrophysical characterization. The triple-porosity model discussed in this paper fits the petrographic observations very well, leading to a more rigorous characterization of effective and noneffective porosity.

The petrographic and core-calibrated triple-porosity model is then used for well-log interpretation of those wells when these data are not available. The result is a reasonable quantitative charac-terization of the tight gas reservoir that can be used for improving hydraulic-fracturing design, flow-units determination, reservoir engineering, and simulation studies. The data can be determined at room conditions and simulated conditions of net stress.

It is concluded that honoring with a triple-porosity model the different types of porosities observed in thin sections and cores leads to more-rigorous and -useful petrophysical interpretations that can be linked to gas productivity.

IntroductionThe GFREE gas research team at the University of Calgary has estimated natural-gas endowment in tight gas sands in Canada at 105 Tcf (Aguilera 2010). GFREE stands for an integrated multi-disciplinary team researching geoscience (G); formation evaluation (F); reservoir drilling, completion, and stimulation (R); reservoir engineering (RE); and economics and externalities (EE). The esti-mated endowment corresponds to only 7% of the original gas in place (OGIP) of 1500 Tcf estimated by Masters (1984) and investi-gated in a sensitivity analysis carried out by Contreras and Aguilera (2011). Fig. 1 shows the location of the study area. Fig. 2 shows the stratigraphic column of the study area and corresponding stra-tigraphy from its northwest (Peace and Pine Rivers) and southeast extents (southwestern Alberta and southeastern British Columbia).

The Upper Jurassic to Lower Cretaceous Nikanassin group is generally characterized as “tight gas formations” with low values of permeability (typically a fraction of a millidarcy) and low porosities (usually less than 6%). It is likely that natural micro-fractures and slot pores dominate the productivity of the formation. These secondary pores are stress sensitive. However, in those cases in which fractures and slots are partially mineralized (for example, with partial quartz overgrowths) the secondary minerals might act as natural propping agents that help fractures and slots to remain open. Lack of any secondary minerals might result in partial or total closure, depending on the in-situ stresses. It is also likely that in some cases the values of OGIP might be overestimated because

petrographic studies indicate that the there are rocks in which part of the total porosity is nonconnected (isolated and noneffective).

Triple-Porosity RocksFig. 3 shows an example of a triple-porosity rock in a thin sec-tion of the Cadomin formation in the WCSB. The section clearly shows the presence of intergranular porosity, slot porosity, and micro-fractures cross cutting clasts and sandy matrix*. In this case, it appears that all porosities might be connected. Previous petrophysical studies by Solano (2010) and Solano et al. (2010) indicate that the Nikanassin group is made up of different porosity types that we classify as (1) intergranular, (2) microfractures and/or slots, and (3) isolated (noneffective porosity). Fig. 4 shows image processing of thin-section microphotographs used to analyze the geometry of individual slots within a tight rock in the WCSB. Figs. 4a and 4b correspond to the original image of a thin section under transmitted plane-polarized and cross-polarized light, respectively. Blue staining was used to highlight the porosity of the rock. This sample corresponds to a fine- to medium-grained, well-sorted sublitharenite sandstone that contains between 5 and 25% detrital rock fragments. The abundance of quartz grains and the extensive quartz overgrowth around them are noticeable. There are also vis-ible isolated partially altered chert and shale fragments, authigenic kaolinite (probably former feldspar fragments), and detrital mica fragments forming secondary-microporosity spots. Porosity and maximum permeability from routine core analysis of an adjacent sample were reported as 5.1% and 0.18 md, respectively. The image in Fig. 4c represents results of several filters applied to the original image to highlight the porosity of the sample. The image in Fig. 4d is a simplified representation of the pore geometry observed in the previous images. Vertical and horizontal axes are in micrometers, and the vertical axis coincides with the stratigraphic up/down orientation of the sample. These data have been used for simulations at the pore-scale level (Rahmanian et al. 2010).

Several characteristics of the sandstones cause the effective-porosity values to be lower than the total porosity including pyrobitumen in pores; compaction and squeezing of shale clasts into pore spaces; compaction of quartz and other grains into pore spaces; common microporosity in chert grains; and shale clasts, degraded volcanic rock fragments, and quartz overgrowths. The percentage of micropores vs. mesopores and macropores is com-monly greater than 50%, often up to 100%. Although micropo-rosity is generally noneffective porosity, in the case of the rocks considered in this study, microporosity can be effective if present in cherts, particularly when examined at the scale of drill cuttings. At the scale of core plugs it can be partially disconnected. At the scale of the reservoir it can be either partially disconnected or completely disconnected. As a result, from the point of view of the petrophysical triple-porosity model, part of the microporosity can be effective and part ineffective. The same reasoning applies to the case of dissolution porosity in which portions of this porosity can be completely isolated and portions can be communicated through slots and microfractures.

The relationship between total porosity from core/log calibra-tion and effective porosity is nonlinear and is controlled by several independent variables, as well as the relation between total porosity and permeability. Therefore, correction of the log interpretation with a triple-porosity model becomes critical.

Copyright © 2011 Society of Petroleum Engineers

This paper (SPE 144590) was accepted for presentation at the SPE Western North American Regional Meeting, Anchorage, 7–11 May 2011, and revised for publication. Manuscript received for review 9 April 2011. Paper peer approved 13 July 2011. *Personal communication with T. Moslow, 2011, Calgary.

October 2011 SPE Reservoir Evaluation & Engineering 567

Solano (2010) has used ternary diagrams to illustrate the various types of porosity present in the Monteith formation of the Nikanassin group. An example is presented in Fig. 5 with corners represented by dissolution (DISS) + microporosity (MP) pores, microfractures (MFr) + slot-like pores (SP), and intergranular porosity (INTERG). Fig. 5a shows a ternary diagram with poros-ity values estimated from thin sections prepared from drill-cut-ting samples (PHI_TS). Fig. 5b shows porosity from laboratory measurements on drill cuttings (PHI_DCs). In this example, the dissolution and microporosity pores are dominant.

Petrophysical Triple-Porosity ModelThe recognition from petrographic studies of three main porous media discussed earlier for tight gas formations has led to the

introduction of a triple-porosity model for evaluation of these types of reservoirs. The model is represented by the equation (Al-Ghamdi et al. 2010; Deng 2010; Leguizamon and Aguilera 2011)

mnc

nc

nc bmb

=− + −

+ − −⎡

⎣⎢

⎤

⎦⎥−log

( )( ) /

��

� � � �

11

2

2 2

llog�, . . . . . . . . . . . . (1)

where � is total porosity, fraction; �b is matrix block porosity scaled relative to the bulk volume of the matrix system, fraction; �nc is nonconnected porosity (PHInc) scaled relative to the bulk volume of the composite system, fraction; and �2 is porosity of natural fractures (PHI2) scaled relative to the bulk volume of the composite system, fraction. The development of Eq. 1 has been presented by Al-Ghamdi et al. (2010) where it was used for evalu-ation of fractured and vuggy carbonates in the Middle East. The use of the equation was extended to evaluation of tight gas forma-tions by Deng (2010) and Leguizamon and Aguilera (2011). The porosities in Eq. 1 can be integrated as follows:

v vncnc

m nc

b m nc

= = = − −

= − −

�

�

�

��

� � � �

22

21

; ; ;

/ ( ), . . . . . . . . . . . . . . . . . (2)

where v is partitioning coefficient, fraction; vnc is nonconnected porosity ratio (it could be nontouching vugs, moldic, and/or fenestral porosity), fraction; and �m is matrix block porosity scaled relative to the bulk volume of the composite system, fraction.

The porosity exponent mb of only the intergranular (or matrix) porosity is determined preferentially in the laboratory from unfrac-tured plugs. The total porosity of the composite system in Eqs. 1 and 2 is calculated from well logs and is represented by �. The vug porosity ratio (vnc), a concept introduced by Lucia (1983), was used initially for evaluation of carbonate reservoirs (Al-Ghamdi et al. 2010, 2011) and has been extended successfully by Deng (2010) and Leguizamon and Aguilera (2011) for the case of isolated dissolution porosity and other types of nonconnected porosities present in tight gas sands. In this case, vnc is equal to the isolated nonconnected porosity (�nc) divided by total porosity (�). The partitioning coefficient (v) is equal to fracture porosity (�2) divided by total porosity (�).

Fig. 1—Location of the “Deep Basin” in the WCSB. Source: Masters (1984).

SERIES STAGEPeaceand Pine Rivers,

Northeastern BritishBritish ColumbiaColumbia

Central Alberta Foothills

Southwestern Alberta and Southeastern

LOW

ERCR

ETAC

EOUS

Albian

Bullh

eadG

p.

Lusc

arG

roup Gladstone

Blai

mor

eGp. Gladstone

Barremian

Hauterivian

Valanginian

Min

nesG

roup

Koo

tena

y Gro

up

Mist Mountain

Berriasian Monteith

Morrisey

UPPE

R JU

RASS

IC

Tithonian / Volgian

Kimmeridgian

Oxfordian

???

???

??

?

? ?

Fig. 2—Stratigraphic column of the study area and corresponding stratigraphy from its northwest (Peace and Pine Rivers) and southeast extents (southwestern Alberta and southeastern British Columbia). Adapted from Stott (1998).


Application of Triple-Porosity Model to Petrographic DataThe strength of the petrophysical triple-porosity model is demon-strated with the use of data from four different tight gas formations in the WCSB.

Fig. 6 shows a crossplot of total porosity vs. effective porosity, the latter represented by the summation of intergranular or matrix porosity (PHIm = �m) and fracture + slot porosity (PHI2 = �2). The data, represented by the red triangles, were obtained from a petrographic study. At first glance, it appears that there is not a good correlation. Originally, the data were interpreted by gener-ating a best-fit regression through all the data points. However, following development of the triple-porosity model, the data were reinterpreted, resulting in the realization that there were three different formations (A, B, and C) with different characteristics and different production potential. Formation A has the best contribu-tion of effective porosity, and in reality it has proved to be the most prolific formation. By contrast, Formation C has the worst effective porosity, and in fact it is the worst producer.

Fig. 7 is the same type of crossplot for Formation D, using data from a petrographic study. The data are represented by blue squares. A regression, provided by the dashed line, was used before develop-ment of the triple-porosity model. Results from the model are shown by the continuous red line. Upper and lower bounds of the data are given by the dotted lines. The comparison with the regression line is excellent, and actually, the triple-porosity model provides a better fit to the last two data points from the petrographic work.

For example, in the case in which the total porosity is 7% and vnc is 0.6, the nonconnected isolated porosity is 4.2%. If for the same case the partitioning coefficient (v) is 0.05, then the frac-ture- and slot-porosity (�2) is 0.35%. This leaves an intergranular (matrix) porosity attached to the bulk volume of the composite system (�m) equal to 2.45%. The intergranular porosity attached to only the bulk volume of the matrix block (�b) is equal to 0.0245/(1−0.042−0.0035) = 2.57%. The results in this example indicate that only 40% of the total porosity is effective porosity.

Note that there is a significant difference between Figs. 6 and 7. In Fig. 6, the calculated lines go through the origin. On the

other hand, the calculated line in Fig. 7 shows an effective porosity equal to zero at a total porosity of approximately 2.1%. The triple-porosity model is robust enough to handle these different cases and those situations in which some intervals might contain only matrix porosity; or only matrix porosity along with fractures + slots; or the matrix porosity, fractures + slots, and nonconnected porosity.

An important advantage of the model over the regression best fit is that it allows estimating reservoir properties and calculating vari-able values of the cementation exponent with depth and porosity.

Fig. 8 shows a crossplot of the cementation exponent (m) for the A, B, C, and D formations calculated with the triple-porosity model. Unfortunately, at this time there are no electrical measure-ments on cores for the formations considered in this study. How-ever, the graph includes values of m from the tight Mesaverde gas formation in the USA determined from core samples. There are some similarities, and, in general, the values of m decrease with smaller porosities, which is a comparison in the proper direction. Also, the same types of porosities just discussed for the Nikanassin group—including slots, microfractures, and dissolution pores—have been observed in tight gas sands in the USA. However, the Mesaverde data are included only for illustration purposes.

Application of Triple-Porosity Model to Well-Log InterpretationFig. 9 shows results of log interpretation in a tight gas well of the WCSB where the triple-porosity model is used for calculat-ing effective porosity and pore-throat apertures (rp35). Tracks 1 and 2 containing depth and name of the formation have been deleted from Fig. 9 for reasons of confidentiality. Track 3 is the gamma ray (GR). Track 4 shows porosity logs including neutron (NPHIC), bulk density (RHOL), and ITT2 logs. Track 5 presents deep (ILD) and shallow (LLSC) resistivity laterologs. Track 6 shows apparent water resistivity (RwApp) and apparent mud filtrate (RmfApp) resistivity logs. Track 7 includes matrix density (RHOMA), compressive sonic (DTMA) and hydrocar-bon density (RHOHY) logs. The black bars in Track 8 (Logi) show the perforated intervals. Track 9 shows water (SWTU and SW) and flushed (SXOTU) saturations. Track 10 presents the values of the cementation exponent (m) calculated with the pet-rophysical triple-porosity model. Track 11 shows pore-throat radii

2

3 slot

1

Intg. φ

φ

Fig. 3—Thin section showing intergranular porosity, slot porosity, and microfractures cross cutting clasts and sandy matrix, Cadomin formation—Elmworth, Deep Basin*.

*Personal communication with T. Moslow, 2011, Calgary.


(Rp35 = rp35) calculated at 35% cumulative pore volume. Track 12 shows core (KCOR) and calculated permeabilities. Track 13 presents core (PCOR) and effective (PHIEFF) porosities. Column 14 displays total (PHIT) and effective (PHIE) porosities, flushed saturation bulk volume (BVWSXO), water bulk volume (BVW), and core porosity (PCOR). The last column shows lithologies including dispersed (Vdis), laminar (Vlam), and structural (Vstruc) shales; effective porosity (PHIE), and silt volume (VSILT).

Water saturation in Fig. 9 was calculated with the use of Simandoux’s equation and presented in Schlumberger’s Interac-tive Petrophysics manual (2009). Permeability was calculated with Morris-Briggs equation (Morris and Briggs 1967). Winland’s pore-throat aperture (Rp35) was calculated using Aguilera’s correlation (Aguilera 2010).

Application of Triple-Porosity Model to Hydraulic FracturingThe petrophysical interpretation proved valuable for helping to secure reliable input data into a commercial 3D hydraulic simula-tor. For example, the porosity used in the simulation is effective and eliminates the nonconnected porosity. The petrophysical model also helped in the determination of advanced reservoir parameters (Green et al. 2007a, 2007b) such as pressure-dependent modulus stiffness factor, pressure-dependent leakoff (PDL) coefficient and transverse-storage coefficient (TSC) as explained by Leguizamon (2011). There are preliminary indications that larger fracture porosities from the triple-porosity model correspond to larger PDL coefficients and TSCs. However, a definitive correlation is not available yet. An example comparing an actual fracturing job vs. the proposed optimized fracturing is presented in Figs. 10 and 11.

Fig. 10 shows proppant-concentration (kg/m2) evolution of the actual job in a well drilled in a tight gas formation in the WCSB. The graphs show fracture growth after 25, 35, 50, and 68.5 minutes. At the end of the job, the fracture has not been contained vertically and the maximum propped-fracture length is approximately 50 m. Fig. 11 shows proppant-concentration evolu-

tion of a simulated optimized job, which pumps in advance 1 t of 100-mesh sand, for the same well 25, 35, 55, and 68.5 minutes after initiating the job. Note that in this optimized job, the fracture is contained vertically, something that did not happen in the actual job. The fracture length with a reasonable proppant concentration at the end of the job is approximately 80 m. The total length with smaller amounts of proppant going to the bottom of the fracture reaches more than 160 m. The increase in the simulated fracturing job vs. the actual job is significant. The same holds true for the effective fracture lengths.

The finding is important because the 3D hydraulic-fracturing simulation for all cases evaluated within the study area demon-strated that longer fractures in tight gas reservoirs result in higher recoveries over long periods of time. This agrees with detailed analytical developments and numerical simulation of horizontal wells that suggest that fracture half-length appears to have the highest effect on cumulative-production volumes. This is under-stood as larger fracture half-lengths increasing the area of drain-age in these types of reservoirs (Brohi 2011; Brohi et al. 2011).This in turn leads to higher economic returns (Leguizamon and Aguilera 2011).

A Link to Gas ProductivityThe petrophysical triple-porosity model has also been used to obtain information that has been entered into a commercial res-ervoir simulator (Deng 2010). The same type of data shown in Fig. 9 was generated for 35 wells in the study area, providing a wealth of information on tight gas formations of the WCSB. As an example, some of the data that proved valuable include the effec-tive porosity [matrix (�m) plus microfractures and slots (�2)]. This led to smaller but more-realistic volume of OGIP by eliminating the noneffective porosity (�nc).

Pore-throat aperture (rp35) has been shown to be valuable for determining flow units in conventional reservoirs for several decades. H.D. Winland of Amoco (Kolodzie 1980) introduced the concept of pore-throat apertures at 35% cumulative pore volume (with 35% mercury injection during a capillary pressure test). In

Fig. 4—Image processing of thin-section microphotographs used to analyze the geometry of individual slots within a tight rock [source: Rahmanian et al. (2010)].


Deng’s simulation (Deng et al. 2011), we use a modification pro-posed by Aguilera (2010):

r kp35

0 452 665 100= [ ]. / ( )

.� , . . . . . . . . . . . . . . . . . . . . . . . . . . (3)

where k is permeability, md; and � is porosity, fraction.The porosity used in Eq. 3 for the tight gas sandstone in the

study area was an effective porosity from the triple-porosity model that corresponds to the sum of matrix (�m) plus microfractures and slots (�2). This effective porosity from well-log interpretation was calibrated with results of the petrographic work shown on Figs. 6 and 7. Also, a good correlation between rp35 values and lithofacies has been obtained (Deng 2010). Therefore, the simulation 3D

geomodel was populated with rp35 values as a replacement for the lithofacies to define the fluid units with good results (Deng et al. 2011). These results and several empirical observations in different types of natural-gas reservoirs (conventional and unconventional) lead to proposing a range of preliminary possible rates that can be obtained on the basis of knowledge of rp35, as shown on Fig. 12. Pore-size classes are grouped on the basis of pore-throat (port) apertures as megaports (r35 >10 μm), macroports (2.5–10 μm), mesoports (0.5 to 2.5 μm), microports (0.1 to 0.5 μm), and nano-ports (0.01 to 0.1 μm).

For convenience, the Winland format of the graph shown in Fig. 12 has always been presented using unstressed porosities and permeabilities to make it as universal as possible while determining

PHI_TS (%):

≤ 3

(a)

(b)

3–6

6–9

> 9

PHI_DCs (%):

≤ 3

3–6

6–9

> 9

Fig. 5—Ternary-plot diagrams representing percentages of the principal pore geometries observed on thin sections prepared from drill-cutting samples. Ranges of porosity values estimated from thin sections and from measurements on drill cutting samples are used as additional constraint in Figs. 5a and 5b, respectively. Fig. 5a shows a ternary diagram with porosity values estimated from thin sections (PHI_TS). Fig. 5b shows porosity from laboratory measurements on drill cuttings (PHI_DCs). In this example, the dissolution and microporosity pores are dominant. Source: Solano (2010).


flow units. These graphs use, for example, helium porosities and air permeabilities. These unstressed properties have been compared empirically with actual oil- and gas-production rates to generate a wide range of anticipated production outcomes. For example, for the case of oil wells, Martin et al. (1997) indicate that compara-tively megaports can reach medium-gravity-oil production rates of tens of thousands of barrels per day if “zonal thickness and other factors are constant;” and without mechanical constraints, macroports can reach thousands of barrels per day, and mesoports hundreds of barrels per day. Microports can produce several tens of barrels per day on pump. However, Martin et al. (1997) state that “microport flow units are decidedly nonreservoir in this com-parative completion of moderate thickness and medium gravity oil

Fig. 6—Petrographic data are represented by red triangles. The triple-porosity model permitted separating the data and quantify-ing porosities and m for three different formations (Petrography courtesy of ConocoPhillips).

Fig. 7—Petrographic data of Formation D are represented by blue squares. A regression is provided by the dashed line. Results from the triple-porosity model are shown by the continuous red line. Upper and lower bounds of the data are given by the dot-ted lines (Petrography courtesy of ConocoPhillips).

without mechanical constraints. These flow units are of far more interest as potential seals for higher quality reservoir downdip.”

In the case of gas wells, we have observed production-rate potentials of more than a 100 MMscf/D for macro- and megaports, more than 10 MMscf/D for mesoports, more than 1 MMscf/D for microports, and more than 0.1 MMscf/D for nanoports (shale gas and coalbed methane are not included in this preliminary estimate). The rates are for vertical wells. This might prove valu-able, particularly in those cases with a limited number of wells and information, and in exploration areas in which a “feeling” for values of porosity and permeability is available. In general, the same restrictions mentioned before for oil, plus the big restriction of backpressures, apply to the gas rates shown in Fig. 12. Also, in


the case of low-permeability formations, the assumption is made that all wells will be hydraulically fractured. For the case of low-permeability formations in horizontal wells, we use the assumption that each fracturing stage is approximately equivalent, regarding production rates, to a vertical well.

Stress-Dependent RocksAll rocks are stress dependent to a major or minor degree. For situations or conditions where there is a need for showing stress-dependent porosities, permeabilities, and pore-throat aperture, laboratory work is the optimum way for evaluating this depen-dency. Under favorable circumstances, the in-situ permeability can be estimated from coupled geomechanical reservoir simula-tion including numerical modeling of flow and buildup tests of individual wells. The optimum way of accomplishing this task is by cutting slices of the fully characterized heterogeneous 3D simulation model and matching the flow and buildup pressures. This can lead to a significant reduction of permeability in tight-gas formations with a negligible amount of secondary mineralization. However, in those cases where there is partial secondary min-eralization (for example, partial quartz overgrowths inside slot porosity), the reduction in the value of in-situ permeability might be very small (Deng 2010).

The rp35 graph can also be developed for different net-stress conditions, ideally with the support of core data. The reduction in porosity and permeability can be calculated with sophisticated models or with simplified but solid equations. One example is

1.00

1.20

1.40

1.60

1.80

2.00

2.20

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

m

Total Porosity

Form. AForm. BForm. CForm. DCore Mesaverde

Fig. 8—Values of the cementation exponent m for Formations A, B, C, and D calculated using the petrophysical triple-porosity model. Core data from the Mesaverde formation in the USA are taken from Byrnes et al. (2008a, 2008b).

Fig. 9—Log interpretation of well in tight gas formation of the WCSB showing effective porosity (intergranular plus microfractures and slots) and variable values of m calculated from the petrophysical triple-porosity model.


shown in Fig. 13, for the case in which the rp35 curve is equal to 0.2 μm at room conditions. For this example, changes of porosity and permeability are calculated from (Jones 1975; Walsh 1981)

�

�1 1

1 3

1

=⎛⎝⎜

⎞⎠⎟

= −−

k

k

p p

p pk h

k h

/log log

log log. . . . . . . . . . . . . . . . . . . . . . . (4)

Jones’ equation is based on empirical observations stemming from rock experiments in the laboratory. The Walsh equation is based on

theoretical developments. Both lead to Eq. 4, making it very valu-able from theoretical and practical points of view. This equation takes into account the presence of natural fractures. We use it on tight gas formations because of the presence of microfractures and slot porosity. The net stress on the rocks is represented by pk. The pressure at which a fracture would heal is ph. Subscript 1 is used to represent the initial net-stress condition. However, any other equation can be used to estimate the reductions on these proper-ties as a function of net stress. Results are shown in Fig. 13 with curves developed at room conditions and net stresses equal to 500

kg/m2

kg/m2kg/m2

kg/m2

Fig. 10—Proppant-concentration (kg/m2) evolution of the actual job in example well showing fracture growth after 25, 35, 50, and 68.5 minutes. Maximum fracture length at the end of the job is approximately 50 m. There is no vertical containment between the fracture intervals.


and 5,000 psi. Note from Eq. 4 and Fig. 14 that the reductions in permeabilities are larger than the reductions in porosity. The reductions in pore-throat apertures (rp35) are shown in the right-hand side of Fig. 13.

Conclusions1. A petrophysical triple-porosity model has been shown to be a useful

tool for characterization of tight gas formations in the WCSB. 2. The model distinguishes between effective and noneffective

porosity. The effective porosity is the summation of intergranular

porosity plus microfractures and slot porosities. The noneffec-tive porosity is nonconnected porosity.

3. The model provides useful information for 3D simulation of hydraulic-fracturing jobs in tight gas formations. This in turn permits optimizing hydraulic-fracturing jobs.

4. A preliminar empirical link has been established between rp35 and oil and gas rates.

5. Porosities, permeabilities, and pore-throat apertures calculated at room conditions can be adjusted to reflect the effects of net stress in Winland-type crossplots, as needed.

kg/m

2

kg/m

2kg

/m2

kg/m

2

Fig. 11—Proppant-concentration evolution of simulated optimized job in the same well as in Fig. 10, pumping initially 1 t of 100-mesh sand. Results are shown at 25, 35, 55, and 68.5 minutes. The fracture length with good proppant concentration at the end of the job is approximately 80 m. The total length with smaller amounts of proppant going to the bottom of the fracture reaches more than 160 m. Note that in this optimized job the fracture is contained vertically.


Nomenclature k = permeability, md k1 = initial permeability, md m = porosity exponent (cementation factor) of triple-porosity

reservoir mb = porosity exponent (cementation factor) of only the ma-

trix block ph = apparent healing pressure, psi (kPa) pk = net stress, psi (kPa) pk1 = initial net stress, psi (kPa) rp35 = pore-throat apertures at 35% cumulative pore volume (35%

mercury saturation during a capillary pressure test) v = partitioning coeffi cient, fraction

vnc = nonconnected-porosity ratio, fraction Vdis = dispersed shale volume Vlam = laminar shale volume Vstruc = structural shale volume VSLT = silt volume � = total porosity, fraction �1 = initial porosity, fraction �2 = porosity of natural fractures (PHI2) scaled relative to

the bulk volume of the composite system, fraction �b = matrix block porosity scaled relative to the bulk volume

of the matrix system, fraction

0.001

0.01

0.1

0 5 10 15 20 25 30

POROSITY (%)

Source: GFREE Research Team, U of Calgary, 2011

CHART FOR ESTIMATING PORE THROAT APERTURE (Extension to Stress-Dependent Properties)

rp35 microns

0.141

0.098

0.2Net Stress, psi

Room

500

5000

Fig. 13—Effect of net stress at room conditions and at 500 and 5,000 psi on porosity, permeability, and rp35.

Fig. 14—Reductions in porosity, permeability, and pore-throat apertures (rp35) as a function of net stress.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1,000 2,000 3,000 4,000 5,000

Perc

ent D

ecre

ase

Net Stress, psi

rp35 reduction

Permeability reduction

Porosity reduction

Thousand BO

PD

MM

scf/D

10’s

1’s

0.1’s

0.01’s

100’s

10’s

1’s

0.1’s

PE

RM

EA

BIL

ITY

(m

d)

rp35

Fig. 12—Flow units as a function of pore-throat apertures (rp35); porosities and permeabilities and possible ranges of oil- (thousands of BOPD), and gas-flow rates (millions of scf/D) for different pore-throat apertures.


�m = matrix block porosity scaled relative to the bulk volume of the composite system, fraction

�nc = nonconnected porosity (PHInc) scaled relative to the bulk volume of the composite system, fraction

AcknowledgmentsParts of this work were funded by the Natural Sciences and Engi-neering Research Council of Canada (NSERC agreement 347825-06), ConocoPhillips (agreement 4204638), Alberta Innovates Energy and Environment Solutions (AERI agreement 1711), and the Schul-ich School of Engineering at the University of Calgary. The 3D hydraulic fracturing simulation was performed using GOHFER, contributed to the GFREE research program by R.D. Barree of B&A and Core Lab. The commercial-based well testing and rate-transient analyses were performed using software provided by Fekete associ-ates. The well-log interpretation using the petrophysical triple-poros-ity model was carried out using Interactive Petrophysics provided by Schlumberger. Their contributions are gratefully acknowledged.

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Hui Deng is currently a PhD degree candidate in the chemical and petroleum engineering department at the University of Calgary. Previously, he worked for PetroChina for 10 years. Deng’s PhD research is focused on coupled geomechanical modeling for underground coal gasification (UCG) and carbon capture and storage (CCS). He holds a BSc degree in petroleum geology from Northwest University and an MSc degree in petroleum engi-neering from the University of Calgary, where he concentrated on reservoir simulation of tight gas reservoirs as part of the GFREE team in the Schulich School of Engineering. Javier Leguizamon is a stimulations engineer in the production enhancement team of Halliburton Canada. He also has more than 5 years experience in production optimization of conventional reservoirs, working for Ecopetrol in Colombia as a production engineer. Leguizamon holds a MS degree in chemical and petroleum engineering from the University of Calgary. His research work as part of the GFREE research team in the Schulich School of Engineering focused on modeling and optimization of hydraulic fracturingtreatments in tight gas formations. Leguizamon also holds a


BS degree in petroleum engineering from the Universidad de America at Bogota, Colombia. Roberto Aguilera is professor and ConocoPhillips-NSERC-AERI Chair in the Schulich School of Engineering, chemical and petroleum engineering depart-ment at the University of Calgary, Canada; guest professor of the China University of Petroleum (Eastern China), a principal of Servipetrol, and a director of Junex in Quebec. He heads the GFREE tight gas research program at the University of Calgary. Aguilera is a petroleum engineering graduate from the Universidad de America at Bogota, Colombia and holds MEng and PhD degrees in petroleum engineering from the Colorado

School of Mines. He was an AAPG instructor on the subject of naturally fractured reservoirs from 1984 through 1996. Aguilera is a Distinguished Author of the SPE J. of Canadian Petroleum Technology (1993 and 1999), a recipient of the Outstanding Service award (1994) and the Distinguished Service Medal (2006) from the Petroleum Society of CIM, an SPE Distinguished Lecturer on the subject of naturally fractured reservoirs for the 2000–2001 Season, the 2011 SPE Canada Regional Distinguished Achievement Award recipient for Petroleum Engineering Faculty, and past Executive Editor of the SPE J. of Canadian Petroleum Technology.

p. spe-144590-pa-p petrophysics of triple-porosity tight gas reservoirs with a link to gas...

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