LAMINATED RESERVOIR basicS
A core photo, roughly full size, of a short interval of the Second White Specks, a laminated sand tight gas or tight oil play in Alberta. Some sand lenses are as thin as a pencil line.
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 socalled "low resistivity pay zones". These are usually laminated shaly sands but can also be sandstones or carbonates with thinly bedded variations in porosity. In resistivity log analysis, anisotropy is present when the bedding is thinner than the tool resolution and is sometimes described as a "thinbed" problem.
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 at the same time. The newest induction logs measure horizontal and vertical resistivity (directions relative to tool axis). Azimuthal laterologs read in eight directions (perpendicular to the tool axis) and could be used to look for horizontal anisotropy in semivertical wells. A modern thin bed log, called the TBRt by Baker Hughes 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 shallow, the resistivity approaches a deep resistivity measurement. This is very useful in laminated shaly sands where the laminae are relatively thick. Thin bed Rt log used to shape final log analysis Other 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. 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 resistivity microscanner can see beds as thin 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.
None of the tools listed above provide a useful deep resistivity value when laminations are thinner than the tool resolution, so unconventional log analysis models are needed. While laminated shaly sands are best known, laminated porosity is also a problem for log analysts. The Bakken and Montney reservoirs in Canada are good examples. The illustrations below give a clear example of how porosity logs and analysis results smooth out the porosity variations, which in turn smooth out the saturation and permeability answers. The latter is especially critical, since productivity estimates for laminated reservoirs can be seriously underestimated because the high permeability streaks tend to be ignored.
A similar problem exists in laminated porosity. The low porosity laminations have higher water saturation than oil or gas bearing higher porosity laminations. The measured resistivity of the laminated hydrocarbon bearing reservoir is often close to the truth, but the calculated water saturation of water zones may be misleading. To illustrate the simplest case, assume a laminated shaly sand 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 at the right.
The average total porosity in this example is 0.20; the average effective porosity is only 0.10 – that’s what the density neutron logs see. The actual porosity in the sand fraction is 0.20 but conventional log analysis cannot tell us that.
The
effect of laminations on resistivity is even more serious because
the logs really measure conductivity, not resistivity. Again
assuming a 50:50 mix of sand and shale laminations, the average
conductivity in the illustration at the left is 127 mS, which
translates to 7.9 ohmm.
To get a good answer for water saturation using an Archie type method, you need to use the 200 ohmm of the sand fraction (not the measured value of 7.9) with the sand fraction porosity of 0.20 (not the measured value of 0.10).
The lower part of the previous illustration shows the calculation for a laminated water sand. The error in measured resistivity is small, but the resistivity contrast between a water zone and a hydrocarbon zone is small – less than 2:1. The rule of thumb for detecting hydrocarbons is usually 3:1 or more.
The case of laminated porosity is slightly different. The resistivity contrasts are smaller than the laminated shaly sand case. The resistivity of the higher porosity streaks with low water saturation may be close to that of the low porosity streak with higher water saturation. But water zones may look pretty resistive, again giving misleading water saturation.
In this example, the measured resistivity for a 50:50 mix of 4 and 8% porosity laminations in a clean sand is 210 ohmm, very close to the average of the resistivity values assumed for the two rock types. However, we need to use the 250 ohmm resistivity of the good quality sand for the saturation calculation, along with the 0.12 porosity to understand the quality of the reservoir. Using the average resistivige and porosity seen by logs will be very misleading.
Modeling laminated shaly sands or laminated porosity with a spreadsheet is the only way to understand the resistivity response and resulting water saturation – usually counterintuitive, always surprising. A spreadsheet for these models is available as a free download on my website at www.spec2000.net .
3D
Induction logs Assume a
laminated shaly sand with horizontal bedding, a vertical borehole,
and a logging tool that can measure both vertical and horizontal
conductivity: Where: Equations 5 and 6 are as defined by Schlumberger in 1934. Some authors 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 RESshale if RESvert and REShorz are measured
log values and VSHavg is computed from (say) the gamma ray log over
an interval. Alternatively, we can solve for RESsand and VSHavg if
we assume RESshale = RSH from a nearby thick shale: If you
prefer to think in Resistivity terms: RESsand
is then used in Archie's water saturation equation, along with
porosity from core or from a laminated sand porosity method, for
example: Where:
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. For a
conventional induction log, the apparent conductivity is: When relative dip is 0 degrees (horizontal bed, vertical wellbore), 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 18 can be formulated and solved for CONDhorz and CONDvert. RESsand and VSHavg can then be calculated as in equations 10 and 11.
MODEL 1: An obvious solution is to use the math for the vertical resistivity model (equations 10 through 17 given earlier) with assumed values of RESsand (based on a model of a clean sand) and Vsh (based on the GR log). The results would give an indication of the reservoir quality of the individual layer analyzed. Permeability, pore volume (PV), hydrocarbon pore volume (HPV), and flow capacity (KH) are calculated from the above results, just as for conventional sands, bearing in mind that the results apply only to the NetSand portion of the gross interval. No depth plot would be available as the results apply to the whole layer.
MODEL
2: Another model uses rules for
finding the rock properties based on shale volume, along with
constants derived from 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, and are equally useful in the laminated case:
This model presupposes that the laminated sand is hydrocarbon bearing. Again, permeability, pore volume (PV), hydrocarbon pore volume (HPV), and flow capacity (KH) are calculated from the above results, just as for conventional sands, bearing in mind that the results apply only to the NetSand portion of the gross interval. 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 to control PHIMAX spatially. RESsand can be assumed from a nearby clean hydrocarbon bearing sand or by inverting the Archie equation with reasonable values of PHIMAX, RW@FT, and SW. KBUCKL is usually in the range 0.035 to 0.060, varying inversely with grain size of the clean sand fraction. 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.
MODEL
3: This model uses the linear log
response equation to backout the clean sand fraction 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: This model has the advantage of using fewer arbitrary rules and more log data, including resistivity log data. The critical values are RESshale, PHINSH, and PHIDSH, which are picked by observation of the log above the zone. It can still be calibrated to core by adjusting these parameters. If the Archie water saturation equation is used, it might distinguish hydrocarbon from water. The Buckle’s saturation presupposes hydrocarbons are present. The layer average PHIDsand and PHINsand can be compared to each other to see if they are similar values – they should be if the parameters are reasonably correct. 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 was working well. However, on some intervals in some wells, the results were not nearly so good.
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). Correlation coefficients (Rsquared) are 0.852, 0.876, 0.903, and 0.906 respectively. The correlation is made using data calculated over the total perforated interval. 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. Correlation of actual production versus the various reservoir properties are shown below.
Productivity estimate based on Model 3 results and a log analysis
version of the productivity equation can be used as well. The
equation is: Where:
Where: This amplifies the shale indicator in cleaner zones (higher net sand) and is scaled the same as the GR curve. A net reservoir cutoff of QualGR <= 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. The QualFR cutoff varies from place to place and can be as high as 100 or more. QUALGR does make a useful curve on a depth plot as it shows the best places to perforate when density and neutron data are missing.
This graph is converted to a numerical quality indicator (Qual1) in a complex series of equations that represents predicted flow rate. An Excel and Lotus 123 spreadsheet for solving this graph is available free on my website at www.spec2000.net . The equations, as displayed in the Lotus 123 spreadsheet are as follows: 1: ND_DN
= 100 * (PHIN  PHID) Where: 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. Hester’s
paper only looked at the average quality of a laminated reservoir
and did not consider the thickness of a particular quality level. To
overcome this, we can use a quality cutoff and obtain a thickness
weighted quality and correlate this to actual production, similar to
a net pay flag using porosity and saturation cutoffs: Where: 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 below. 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. Some of these wells were not perforated optimally and the Qual1 pay flag is helpful for workover planning.
"META/LAM"
SPREADSHEET  LAMINATED SHALY SAND MODELS


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