CHAPTER SEVENTEEN: LOG ANALYSIS IN LAMINATED SHALY SANDS

Table of Contents
17.00 Introduction to This Chapter
17.01 Resistivity in Anisotropic Reservoirs
17.02 Resistivity in Dipping Beds
17.03 Conventional Shaly Sand Model A
17.04 Laminated Sand Model B - Pessimistic
17.05 Laminated Sand Model C - Realistic
17.06 Laminated Sand Model D- Response Equation
17.07 Laminated Sand Model E - Vertical Resistivity
17.08 Reservoir Quality - Net Reservoir
17.09 Reservoir Quality - Shale Indicators
17.10 Reservoir Quality - Hester's Number
17.11 Reservoir Quality - Productivity Index
17.12 Case History - Milk River, Alberta
17.13 In Conclusion
17.14 Exercises for Chapter Seventeen
17.15 Bibliography for Chapter Seventeen

Continue to Chapter Eighteen.

Publication History: Section 17.02 to 17.12 were originally part of a research project undertaken for Rakhit Petroleum Consultants Ltd and was submitted for publication as "Productivity Estimation in the Milk River Laminated Shaly Sand, Southeast Alberta and Southwest Saskatchewan" by E. R. (Ross) Crain, P.Eng. and D. W. (Dave) Hume, P.Geol. in CWLS Journal, 2004. This electronic version created Nov 2003.

CHAPTER SEVENTEEN: LOG ANALYSIS IN LAMINATED SHALY SANDS

17.00 Introduction to this Chapter
Porosity and water saturation in laminated shaly sands, and in other cases of anisotropic reservoirs, is a special case, not amenable to solutions given previously in Chapters Seven and Eight. Isotropic reservoirs are those in which the physical properties are the same regardless of the direction of measurement. Anisotropic reservoirs have one or more properties that vary with direction.
The best known anisotropic property is resistivity, which can vary by a factor of 100 or more, depending on whether the measurement is made parallel to the bedding or perpendicular to it. This is the situation that exists in most so-called "low resistivity pay zones". These are usually laminated shaly sands but can also be sandstones or carbonates with thinly bedded variations in porosity.

Rocks of this type are called transverse isotropic; there is little horizontal anisotropy, so resistivity differs between only two axes - vertical and horizontal. Channel sands with significant cross bedding and other linear depositional features could be anisotropic on all three axes. There are no logs that measure resistivity in 3 orthogonal axes. The newest logs measure horizontal and vertical resistivity (directions relative to tool axis) and all conventional resistivity logs measure horizontal only (relative to tool axis).

In resistivity log analysis, anisotropy is present when the bedding is thinner than the tool resolution and is sometimes described as a "thin-bed" problem. This Chapter will describe various models that have been used to solve this environment.

The next best known anisotropic property is acoustic travel time, which can vary by several percent from the maximum. This is caused by tectonic stress and is discussed in Chapters Nineteen and Twenty. Stress induced acoustic travel time anisotropy is in the horizontal plane but can also be found in all three axes.

The laminated case is illustrated in Figure 17.00.

Figure 17.00: Laminated sand model compared to conventional shaly sands

The top left element of Figure 17.00 illustrates the clean sandstone model used by all log analysts. The illustration immediately to the right of the clean sandstone case represents the model for laminated shaly sands and other anisotropic layered reservoirs. Contrast this image with the dispersed and structural shale cases shown at the top right. The laminations can vary in thickness from 1 millimeter to several centimeters.

Conventional porosity logging tools measure the average rock properties over 0.5 to 1.0 meters, much thicker than the centimeter sized laminations. Resistivity logs measure 2 or more meters of rock, although newer ones can be processed to represent 0.3, 0.6, or 1.2 meters (1, 2, or 4 feet). As a result, the rock properties of the good quality sand laminations are averaged with the low quality shaly laminations, making the laminated shaly sand look unattractive on standard log analysis.

Thin bed logging tools are the microlog, microlaterolog, proximity log, and micro spherically focused log. These tools measure 3 to 12 centimeters of rock but have a depth of investigation of similar dimensions. In some laminated sands, these tools can be used to determine net to gross sand ratio, but they will not give an accurate porosity or deep resistivity in the sand layers.

The electromagnetic propagation log measures in the order of 6 cm but it is a porosity and shale indicator tool, not a deep resistivity tool. Some sonic logs can be run with a 15 cm (6 inch) bed resolution.

The formation microscanner can see beds as then as 0.5 cm and fractures as thin as 1 micron. The acoustic televiewer can resolve beds to 1 or 2 cm. Accurate net to gross ratios can be determined, but again the resistivity of the sand fraction beyond the invaded zone cannot be determined from these tools.

FIGURE 17.01: Thin bed Rt log used to shape final log analysis

The newest thin bed tool is described as a thin bed Rt tool. It is a microlaterolog type of device with a bed resolution of 5 cm and a depth of investigation between 30 and 50 cm (12 to 20 inches) - about 2 to 3 times deeper than earlier microlaterologs. If invasion is reasonably shallow, the resistivity approaches a deep resistivity measurement. This is very useful in laminated shaly sands where the laminae are relatively thick.

All these tools are described briefly in Chapter Three. This Chapter assumes that net to gross sand fraction can be obtained from an appropriate thin bed log. Or if no such log is available, net to gross ratio is defined as (1 - VSHgross), where VSHgross is the average shale volume over the gross interval, as determined by one of the usual shale volume methods (Chapter Six).

17.01 Resistivity in Anisotropic Reservoirs
The analysis models for laminated shaly sands are quite varied and none are perfect solutions. The problem lies in how logs average laminations that are thinner than the tool resolution. Most logs average the data in a linear, thickness weighted fashion, but resistivity must be averaged as conductivity and then converted back to resistivity. Since the conductivity of the shale laminations is usually much higher than the gas or oil sand laminations, the resulting conductivity is high (resistivity is low). This makes the zone look like a poor quality reservoir, maybe so poor that it will not be tested, thus bypassing considerable oil or gas.

Conventional induction logs and laterologs measure conductivity in a plane perpendicular to the borehole axis. When the beds are parallel to that plane, we get a measurement that is the average conductivity of the rock layers within the vertical resolution of the logging tool (neglecting shoulder bed effects for the moment).

To illustrate the simplest case, assume a laminated sequence with shale laminations equal in thickness to the sand laminations. This gives a shale volume (Vsh) averaged over the interval of 50%. Assume the porosity and resistivity values are as shown below:

In the early days of log analysis, this phenomenon was attributed to many different, almost mystical, reasons because the parallel nature of the conductive paths was not understood by many analysts. Note, too, that the resistivity contrast between a water zone and a gas zone is small, so it may not be possible to recognize gas when it is present, especially if water resistivity varies between one hydrodynamic regime and another.

Some newer induction logging tools provide a vertical conductivity measurement as well as the usual horizontal measurement. If the beds are still parallel to the normal induction log signal, the vertical induction signal will give an average of the resistivity of the beds instead of averaging the conductivity. This is because the normal induction averages the beds in a parallel electrical circuit and the vertical induction sees a series circuit.

The situation gets more complicated when the tool and the beds are not at right angles to each other. The math to solve the dipping bed environment is explained later in this Section.

Assume a laminated shaly sand with horizontal bedding, a vertical borehole, and a logging tool that can measure both vertical and horizontal conductivity:
1. CONDhorz = Vsh * CONDshl + (1 - Vsh) * CONDsand
2. RESvert = Vsh * RESshl + (1 - Vsh) * RESsand
3. REShorz = 1000 / CONDhorz
4. CONDvert = 1000 / RESvert
5. AnisRatio = RESvert / REShorz
OR 6. AnisRatio = CONDhorz / CONDvert
7. AnisCoef = AnisRatio ^ 0.5

Equations 5 and 6 are as defined by Schlumberger in 1934. Some authors, including Hogiwara at Shell, invert the equations so the coefficient is less than or equal to 1.0.

Equations 1 and 2 can be solved simultaneously for any two unknowns if the other parameters are known or computable. For example, we can solve for RESsand and RFSshl if RESvert and REShorz are measured log values and Vsh is computed from (say) the gamma ray log over an interval. Alternatively, we can solve for RESsand and Vsh if we assume RESshl = RSH from a nearby shale:
8. CONDsand = CONDvert * (CONDshl - CONDhorz) / (CONDshl - CONDvert)
9. Vsh = (CONDhorz - CONDsand) / (CONDshl - CONDsand)

If you prefer to think in Resistivity terms:
10. RESsand = REShorz * (RESvert - RESshl) / (REShorz - RESshl)
11. Vsh = (RESsand - RESvert) / (RESsand - RESshl)

RESsand is then used in Archie's water saturation equation, along with porosity from core or from a laminated sand porosity method described in Section 17.02.

Vertical resistivity logs are still very rare, but are the tool of choice for laminated shaly sands. An example is shown in Figure 17.02. Notice the large difference between Rv and Rh on the raw log and the difference in Sw on the computed log.

Figure 17.02: Example of vertical and horizontal resistivity in laminated shaly sand

17.02 Resistivity in Dipping Beds
The example given in the Introduction involved a laminated shaly sand with bedding perpendicular to the borehole axis (horizontal bedding, vertical borehole). When beds dip relative to the borehole, the situation becomes more complicated.

The relative dip is the important factor and takes a bit of thought when the borehole is not vertical. The following table may assist:

Dipmeter results are presented as true dip angle and direction relative to a horizontal plane and true north. To obtain dip and direction of beds relative to a logging tool in a deviated borehole, you need the borehole deviation and direction from a deviation survey. This is often obtained at the same time as the dipmeter, but may come from some other deviation survey, either continuous or station by station. You need to rotate the true dips into the plane perpendicular to the borehole to get the final relative dip. The math for this is in Chapter Twenty-Seven, Section 27.07.

For a conventional induction log, the apparent conductivity is:
1. CONDlog = ((CONDhorz * cos(RelDip))^2 + CONDvert * CONDhorz * (sin(RelDip))^2)^0.5

When relative dip is 0 degrees, the conventional log reads CONDhorz, as we know it should. However, if relative dip is 90 degrees, as in a horizontal hole in horizontal laminated sands, the log reading is (CONDhorz*CONDvert)^0.5. This is a surprise, as we might have expected the tool to measure CONDvert.

If two deviated wells are logged through the same formation (at considerably different deviation angles), two equations of the form of equation 12 can be formulated and solved for CONDhorz and CONDvert. RESsand and Vsh can then be calculated as in equations 7 through 11.

XXXXX Equations for adjusting directly measured REShorz and RESvert in dipping beds will be added here as soon as I find them.

17.03 MODEL A: Conventional Dispersed Shaly Sand Model
In the next five Sections, we contrast five different models, two of which are known in advance to be inappropriate or pessimistic in laminated shaly sands. They are presented in order to emphasize the modeling problem and illustrate the quantitative differences in the methods. Although these are called laminated shaly sand models, they can be adapted to any laminated situation where the logging tool resolution is greater than the laminae thickness.
This model is the one we run in most shaly sands, but it is not appropriate for laminated shaly sands:
1. Vsh = Minimum from GR, Neutron-density crossplot, resistivity methods
2. PHIe = (PHID * PHINSH - PHIN * PHIDSH) / (PHINSH - PHIDSH)
3. Sw = Dual Water, Simandoux, or Buckles model if gas; Sw = 1.0 if not gas
4. Perm = porosity vs permeability transform from core data
5. Payflag = (Vsh < VSHMAX) * (PHIe > PHIMIN) * (Sw < SWMAX) * (Perm > PERMIN)
6. Hnet = SUM (INCR * PAYFLAG)
7. PV = SUM (PHIe * INCR * PAYFLAG)
8. HPV = SUM (PHIe * (1 - Sw) * INCR * PAYFLAG)
9. KH = SUM (Perm * INCR * PAYFLAG)
10. PHIavg = PV / Hnet
11. SWavg = 1 - (HPV / PV)
12. PERMavg = KH / Hnet

Sums and averages for reservoir properties are determined in the usual way. The conventional model may fail to find any net reservoir unless cutoffs, especially shale cutoffs, are very liberal. Even if net reservoir is found, it will be smaller than the true net reservoir and rock properties are likely to be pessimistic. The model requires a full log suite.

17.04 MODEL B: Laminated Shaly Sand - Pessimistic Version
Most laminated shaly sand models use the shale volume from a conventional analysis averaged over the gross interval (VSHgross). Net to gross ratio is (1 - VSHgross) and net reservoir thickness (NetRes) is then found by multiplying (1 - VSHgross) times the gross thickness. The model then derives everything else from empirical rules. One such set of rules is to use the rock properties (porosity, saturation, permeability) from the conventional analysis.
1. VSHgross = SUM (Vsh * INCR) / Gross
2. Net2Gross = (1 - VSHgross) or from core, televiewer, or microscanner
3. NetRes = Gross * net2Gross
4. PHIavg, SWavg, PERMavg = Values from Conventional Analysis Model A

Cumulative reservoir properties are found in an unconventional way:
5. PV = PHIavg * NetRes
6. HPV = PHIavg * (1 - SWavg) * NetRes
7. KH = PERMavg * NetRes

This model will usually find more net reservoir than the conventional shaly sand model, but rock properties and hence reserves are still pessimistic because they come from the conventional analysis. Some authors have used the density log porosity instead of the shaly sand crossplot porosity. Neither approach is recommended as they give pessimistic porosity values in laminated sands.

17.05 MODEL C: Laminated Shaly Sand - Realistic Version
A more realistic model uses different rules for finding the rock properties, usually based on shale volume rules or constants based on core analysis. These empirical rules can be calibrated to core and then used where there is no core data. The PHIMAX porosity equation and Buckles water saturation equation given below are widely used in normal shaly sands where the log suite is at a minimum:
1. VSHgross = SUM (Vsh * INCR) / Gross
2. Net2Gross = (1 - VSHgross) or from core, televiewer, or microscanner
3. NetRes = Gross * Net2Gross
4. PHIavg = PHIMAX * (1 - VSHgross ^ KVSH)
5. SWavg = KBUCKL / PHIavg / (1 - VSHgross)
6. PERMavg = MIN (2000, 10^(CPERM * PHIavg + DPERM))
7. PV = PHIavg * NetRes
8. HPV = PHIavg * (1 - SWavg) * NetRes
9. KH = PERMavg * NetRes

The PHIMAX value is the critical factor. If a moderate amount of core data is available for the sand fraction of the laminated sand, this data can be mapped and used in a batch processing environment. The exponent KVSH in equation 3 also needs tuning and can range from 1.0 to 3.0.

A very minimum log suite can be used, since the only curve required is a gamma ray shale indicator, but only if there are no radioactive elements other than clay. This is not the case in the Milk River, so a minimum log suite will not work here. We have used the minimum suite successfully in laminated shaly sands in Lake Maracaibo.

17.06 MODEL D: Laminated Shaly Sand - Response Equation Version
Another model uses the linear log response equation to back-out the clean sand fraction rock properties from the actual log readings and the shale properties. The response equations are used on the average of the log curves over the gross sand interval. We still assume:
1. VSHgross = SUM (Vsh * INCR) / Gross.
2. Net2Gross = (1 - VSHgross) or from core, televiewer, or microscanner
3. NetRes = Gross * Net2Gross
4. PHINsand = (PHINavg – VSHgross * PHINSH) / (1 - VSHgross)
5. PHIDsand = (PHIDavg – VSHgross * PHIDSH) / (1 - VSHgross)
6. CONDsand = (CONDavg – VSHgross * 1000 / RSH) / (1 - VSHgross)
7. PHIavg = (PHINsand + PHIDsand) / 2
8. RESDsand = 1000 / CONDsand
9. SWavg = KBUCKL / PHIavg
OR SWavg = (A * RW@FT / ((PHIavg^M) * RESDavg))^(1/N)
10. PERMavg = MIN (2000, 10^(CPERM * PHIavg + DPERM))
11. PV = PHIavg * NetRes
12. HPV = PHIavg * (1 - SWavg) * NetRes
13. KH = PERMavg * NetRes

Summations are calculated as in Model C. Note that the (1 - Vsh) term is not included in the Buckles water saturation equation since the method has generated clean sand porosity. For the same reason, the Archie water saturation equation can be used instead of a more complicated shale corrected saturation model.

This model has the advantage of using fewer arbitrary rules and more log data. The critical values are PHINSH and PHIDSH, which are picked by observation of the log above the zone. It can still be calibrated to core by adjusting these two parameters.

The layer average PHIDsand and PHINsand can be compared to see if they are close to each other. They could cross over if gas effect is strong enough. Our results showed a 0.02 porosity unit variation on the best behaved wells, indicating that the inversion of the response equations is working well. However, on some intervals in some wells, the results are not nearly so good. In some cases, nonsensical negative answers are obtained, and in others the porosity results are unrealistically high.

This model is very noisy and ill-behaved except in rare circumstances, so it is not recommended. It may have application in the analysis of shorter discrete zones in individual log analyses but it is not appropriate for batch processing. CONDsand is quite sensitive to RSH and impossible negative answers can result if RSH is too low. In the Case History shown later, we found that the RSH needed to obtain rational results was twice the value of RSH in the overlying shale. If one wished to do so, RSH could be optimized in a few iterations by giving some reasonable constraints on CONDsand.

The equations become unstable at very high values of VSHgross, so there should be a VSH limit above which the calculation will be bypassed. It might be better to use the Buckles approach to avoid this problem, but the chance of distinguishing gas from water zones will be lost.

It is important to eliminate pure shale beds from the gross interval of the laminated shaly sand by careful zonation; including them will distort the final reservoir volume. This is true for all three laminated sand models.

17.07 MODEL E: Vertical and Horizontal Resistivity Model
Where a modern 3-D induction log is available, the sand resistivity can be developed more directly:
1. RESsand = REShorz * (RESvert - RSH) / (REShorz - RSH)
2. Vsh = (RESsand - RESvert) / (RESsand - RSH)
3. PHINsand = (PHIN - Vsh * PHINSH) / (1 - Vsh)
4. PHIDsand = (PHID - Vsh * PHIDSH) / (1 - Vsh)
5. PHIe = (PHINsand + PHIDsand) / 2
6. Sw = KBUCKL / PHIe
OR Sw = (A * RW@FT / ((PHIe^M) * RESsand))^(1/N)
7. Perm = MIN (2000, 10^(CPERM * PHIe + DPERM))
8. VSHgross = SUM (Vsh * INCR) / Gross
9. Net2Gross = (1 - VSHgross) or from core, televiewer, or microscanner
10. NetRes = Gross * Net2Gross
11. Payflag = (Vsh < VSHMAX) * (PHIe > PHIMIN) * (Sw < SWMAX) * (Perm > PERMIN)
12. PV = SUM (PHIe * INCR * PAYFLAG) * Net2Gross
13. HPV = SUM (PHIe * (1 - Sw) * INCR * PAYFLAG) * Net2Gross
14. KH = SUM (Perm * INCR * PAYFLAG) * Net2Gross
15. PHIavg = PV / NetRes
16. SWavg = 1 - (HPV / PV)
17. PERMavg = KH / NetRes

I have no experience with this method so I cannot attest to its efficacy. An advantage of the method is that it gives continuous results instead of zone by zone sums and averages. This may be misleading on depth plots unless some special annotation or coding is displayed.

17.08 Reservoir Quality from Net Reservoir Data
There are a number of ways to assess reservoir quality. In laminated sands, one approach is to correlate first three months or first year production with net reservoir properties from the laminated models described above. We chose to use the first 8760 hours of production (365 days at 24 hours each) divided by 4 (3 months of continuous production) as our “actual” production figure. This normalizes the effects of testing and remedial activities that might interrupt normal production.
The normalized initial production was correlated with net reservoir thickness, pore volume (PV), hydrocarbon pore volume (HPV), and flow capacity (KH) from the laminated Model C. Correlation coefficients (R-squared) are 0.852, 0.876, 0.903, and 0.906 respectively. The correlation is made using data calculated over the total perforated interval. The other three analysis models did not give useful correlations nor did model C when only a single shale indicator was used. Results of the correlations are shown in Figure 17.07A and 17.07B.

Average shale volume was correlated with actual production but the correlation coefficient was only 0.296, although the trend of the data is quite clear.

17.09 Reservoir Quality from an Enhanced Shale Indicator
Another approach is to calculate a quality curve:
1. Qual2 = RSH * GR / RESD

This amplifies the shale indicator in cleaner zones and is scaled the same as the GR curve. A net reservoir cutoff of Qual2 <= 50 on this curve was a rough indicator of first three months production, but the correlation coefficient was as poor as for average shale volume. QUAL2 does make a useful curve on a depth plot as it shows the best places to perforate when density and neutron data are missing.

17.10 Reservoir Quality from Hester’s Number
Another quality indicator was proposed by Hester (1999). It related neutron-density porosity separation and gamma ray response to production, based on the graph in Figure 17.03.

This graph is converted to a numerical quality indicator (Qual1) in a complex series of equations that represents predicted flow rate.

The equations, as displayed in the Lotus 1-2-3 spreatsheet are as follows:

1: ND_DN = 100 * (PHIN - PHID)

2: E = @IF(ND_DN>(0.425*GR)-14,0,@IF(ND_DN>(0.425*GR)-17,4,

@IF(ND_DN>(0.425*GR)-20,5,@IF(ND_DN>(0.425*GR)-23,6,
@IF(ND_DN>(0.425*GR)-26,7,@IF(ND_DN>(0.425*GR)-29,8,
@IF(ND_DN>(0.425*GR)-32,9,@IF(ND-DN>(0.425*GR)-35,10,11))))))))

3: F = @IF(ND_DN>(0.425*GR)-35,0,@IF(ND_DN>(0.425*GR)-38,11,12))

4: G = @IF(ND_DN>(0.425*GR)-14,0,@IF(ND_DN>29,0,

@IF(ND_DN>26,1,@IF(ND_DN>23,2,@IF(ND_DN>20,3,
@IF(ND_DN>17,4,@IF(ND_DN>14,5,0)))))))

5: H = @IF(ND_DN>14,0,@IF(ND_DN>11,6,@IF(ND_DN>8,7,@IF(ND_DN>5,8,
@IF(ND_DN>2,9,@IF(ND_DN>-1,10,@IF(ND_DN>-4,11,12)))))))

6: I = @IF(E=0,F,E)

7: J = @IF(G=0,H,G)

8: QUAL1 = @IF(GR<80,I,J)

Where:
ND_DN = neytron minus density porosity difference in sandstone units (percent)
PHID = density porosity sandstone units (fractional)
PHIN = neutron porosity sandstone units (fractional)
GR = gamma ray (API units)
QUAL1 = Hrster Quality Number (unitless)
E, F, G, H, I, J = intermediate terms

Note that these nested IF statements are slightly different than those originally published by Hester. The changes correct for typographical errors in the original paper.

Figure 17.03: Hester’s reservoir quality indicator (QUAL1)

There is a flaw in Hester’s paper that can be cured. He does not account for zone thickness or attempt to find a net reservoir number. He uses only the average quality number over the zone, which presupposes that all perforated intervals are equal in thickness. To overcome this, we can use a quality cutoff and obtain a thickness weighted quality and correlate this to actual production.

A Hester quality of 4.0 or higher reflects reservoir rock that is worth perforating, and gives similar net reservoir thickness as the previous indicators. Graphs showing the correlation of actual production to net reservoir with QUAL1 >=5 and >=4 are shown in Figure 17.07B. The regression coefficients are 0.856 and 0.837 respectively. Although this looks pretty good, the low rate data is clustered very badly and other indicators work better in low rate wells.

The Hester quality number QUAL1 is the only quality indicator that shows where to perforate. The other indicators described here give a reasonable estimate of reservoir performance, but do not give any indication of how to economically complete the well. A typical perforation table, generated from QUAL1 >] 4, is shown in Figure 17.05.

17.11 Reservoir Quality from Productivity Estimates
A productivity estimate based on a log analysis version of the productivity equation has been included on each summary table, as illustrated in Figure 17.05. The equation used was:
1. ProdEst = 6.1*10E-6 * KH * ((PF - PS)^2) / (TF + 273) * FR * 90

The leading constant takes into account borehole radius, drainage radius, viscosity, and units conversions. KH is flow capacity in md-meters. (PF - PS) is the difference between formation pressure and surface pressure in KPa. A constant value of 1300 KPa was assumed for this study. Clearly, more detailed data could be used if time permits. TF was chosen constant at 20 degrees Celcius.

FR is a hydraulic fracture multiplier, chosen as 2.0 for this study, based on the 9 wells used to calibrate to 3-month initial production data. The constant 90 converts e3m3/day into an estimated 3-month production for comparison to actual. The 3 month numbers were chosen instead of daily rate as they have more “heft” and can be equated to income more readily.

The correlation graph is in the top left of Figure 17.07A. Note that the equation used is a constant scaling of KH, so the correlation coefficient is the same as the KH graph at 0.906.

17.12 Case History - Milk River, Alberta
The sample depth plot in Figure 17.04 shows typical results of the prototype analysis. The majority of the results are from the conventional analysis Model A, including the PayFlag. Some of the input curves are shown in Tracks 1 and 2. Hester’s quality factor (QUAL1) and the GR/RESD quality factor (QUAL2) are shown in Track 4. This is a gas producing well with an excellent set of perforations, shown on the right-hand edge of Track 2.

The conventional analysis, plotted in Track 5, gives a clear picture of why the conventional approach is so discouraging. Unfortunately, the laminated models do not create output curves that are consistent with a depth plot, so it is impossible to make pretty pictures of the results except in map form.

In the current Milk River study, this model appears to be the most effective in predicting reasonable reservoir properties. PHIMAX was set at 0.20, based on core data, and KBUCKL was set at 0.040, based on experience. CPERM and DPERM were chosen as 18.3 and -3.00 respectively from the core data crossplot shown earlier.

A sample Net Reservoir summary from the prototype program is shown in Figure 17.05. The changes in Net Reservoir and average rock properties between the models illustrate the need to find an appropriate model for laminated reservoirs. This work has been calibrated to core and production data, but the results shown here are still tentative. Each well can be tuned to match ground truth more closely.

A total of 10 reservoir quality indicators for each of 3 reservoir layers, plus the cored interval and the perforated interval are given for each of 4 different analysis models. The best model for predicting productivity is Model C, using the minimum of 3 shale indicators. The density neutron porosity separation indicator is essential to the success of Model C.

The best productivity indicator is the flow capacity (KH) or its equivalent productivity estimate in e3m3 for 90 days (1st 3 months production estimate). Five other indicators have strong correlationns with productivity (Net Reservoir, PV, HPV, Hester’s QUAL1 >=5, and QUAL1 >=4). Hester’s number does not have much resolution at low flow rates, but clearly separates poor from good wells.

An important use of the summary tables is to determine whether a well is under-achieving due to limited perforation interval or a poor frac job. A comparison of the total KH for the Milk River compared to the KH for the perforated interval will point out any problem wells. Even if KH is badly mis-calibrated, the comparison is useful. Over-achievers may be producing commingled, intentionally or otherwise, from deeper horizons or may point to log data or analytical difficulties.

Figure 17.04: Depth plot showing Hester quality factor in Track 4 (shaded black)

Figure 17.05: Sample Net Reservoir calculations for four shaly sand models.

The models can be used to generate a perforation list from Hester’s quality number or from VSHminimum. A portion of such a list is shown in Figure 17.06. An acceptance/rejection filter on the list will shorten it considerably. This will eliminate intervals that are too thin to bother with and group intervals that are close enough to be considered as single intervals.

Figure 17.06: Portion of unfiltered perforation list generated by the prototype program

Plots of first 3-month production versus various reservoir quality parameters are given in the graphs in Figures 17.07A and 17.07B for the 17 wells with production data and a full log suite. All graphs show a reasonable trend. Correlation coefficients were given earlier in this report.

The numerical data for these graphs is shown in Figure 17.08. These tables and the graphs in Figure 17.07 summarize the 17 wells with full log suites and reasonable initial production numbers. Results are based on the laminated shaly sand Model C using the minimum of three shale volume indicators, namely gamma ray, resistivity, and density-neutron separation. Results from the other three numerical models described earlier have not been summarized because the models are either inappropriate, pessimistic, or too erratic in their predictions.

Figure 17.07A: Comparison of Actual 3-month initial production with reservoir quality indicators

Figure 17.07B: Comparison of Actual 3-month initial production with reservoir quality indicators

Because a full log suite was available in the 9 wells used for calibration, we have obtained the most likely shale volume (Vsh) result. The 8 wells held in reserve to test the model also showed very good agreement with initial production. One well that calculated an IP higher than actual can be brought into line with a small tune-up of the shale density parameter.

Figure 17.08A: Numerical data for initial production comparison

Figure 17.08B: Stratigraphic data for initial production comparison

17.13 In Conclusion
The Laminated Sand Model C works very well with a full log suite, possibly because the gas effect on the density and neutron log curves enhances their ability to detect sands. It did not have any significant predictive capability with a minimum log suite in the Milk River Case History, However in a study undertaken in Lake Maracaibo with a minimum log suite, the technique worked well. It is likely to be successful where net to gross sand can be calibrated to televiewer, formation microscanner, or core data.
Hester’s quality number (QUAL1) is computable when a full log suite is present. It is a good visual indicator of reservoir quality on a depth plot. If we move to poorer log suites, Vsh from density neutron crossplot will not be available, nor will Hester’s quality number. This degrades results dramatically. Using the models with a minimum log suite is not recommended.

The most rigorous model, theoretically, is the Response Equation Model D. It requires a full suite of open hole logs but results were quite erratic. The Conventional Shaly Sand Model A and the Laminated Model B should be avoided as the assumptions behind the models are inappropriate for this environment. Model E, which uses 3-D induction data to overcome some of the problems with Model D, has not been tested and the effects of deviated hole geometry is not known.

The log analysis results in the Milk River laminated sands from Model C should be considered as reasonable approximations for reservoir quality assessments and resource estimates. Considerably more detailed analysis may be required to refine the evaluation for individual wells after high-grade sweet spots are located.

17.14 Exercises for Chapter Seventeen
Calculate the average resistivity and porosity for the laminated shaly sand described in the following table: (10 marks)

2. Describe the differences between the five laminated shaly sand models. (50 marks)

3. Describe the differences between the reservoir quality models that might be used for laminated shaly sands. (40 marks)

17.15 Bibliography for Chapter Seventeen
Hester, T. C., 1999, An algorithm for Estimating Gas Production Potential Using Digital Well Log Data, Cretaceous of North Montana, USGS Open File Report 01-12

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ABOUT THE AUTHOR

E. R. (Ross) Crain, P.Eng. is a Consulting Petrophysicist and a Professional Engineer with over 35 years of experience in reservoir description, petrophysical analysis, and management. He has been a specialist in the integration of well log analysis and petrophysics with geophysical, geological, engineering, and simulation phases of oil and gas exploration and exploitation, with widespread Canadian and Overseas experience.

His textbook, "Crain's Petrophysical Handbook on CD-ROM" is widely used as a reference to practical log analysis. Mr. Crain is an Honourary Member and Past President of the Canadian Well Logging Society (CWLS), a Member of Society of Petrophysicists and Well Log Analysts (SPWLA), and a Registered Professional Engineer with Alberta Professional Engineers, Geologists and Geophysicists (APEGGA)