Subject:
QUICK LOOK ANALYSIS
Introduction Overlays Crossplots Histograms Algorithms
Introduction Quick-look log analysis refers to a number of techniques for plotting log data in a reasonably effortless and simple way that reveals either the formation content or the formation lithology. These methods are widely used by log analysts for wellsite evaluations. Their great appeal lies in their simplicity and subtlety. Most quick-look methods can be applied without any special equipment and produce quite acceptable results. Broadly speaking, there are three branches to quick-look analysis:
• compatible overlays of curves • crossplots of selected curve readings • simple algorithms for calculators In general, compatible overlays manage to eliminate some unknown quantity by taking a ratio, while revealing another quantity that is of interest; for example, water saturation.
Crossplots are indispensable for computer-generated analysis, but also offer a quick and convenient means of determining endpoints such as Rw. Algorithms offer a quick and simple means of calculating items of interest, such as porosity and water saturation. They are widely incorporated into log analysis routines on both programmable calculators and computers.
Compatibly scaled overlays entail comparison of two or more log curves. In practice, one curve is overlaid on the other and a tracing made (either by hand or via a computer graphics display) so that the end result is a composite with two curves. The relative deflection between the two curves usually indicates a formation property of interest. The basis for all overlays is that the curves being compared be compatibly scaled, i.e., both must be in the same system of units. Apples must be compared with apples and not oranges. Many of the quick-look overlays in use today are quite subtle in that they eliminate some quantity that is either unknown or of no interest. The most commonly used are:
· for hydrocarbon detection: SP with Rxo/Rt Ro with Rt dielectric logderived porosity with porosity · for lithology, porosity, and hydrocarbon typing: neutron porosity with density porosity density porosity with sonic porosity SP with Rxo/Rt This overlay is by no means universally applicable, since it requires conditions that result in healthy SP developments. However, where those conditions are met (i.e., in wells drilled with fresh mud having salty connate water) it is an elegant way to detect hydrocarbons without the need to know porosity. A natural candidate for wells where only an induction-SP log is available, it is usually produced at the time the log is run and requires some manipulation of the raw data in the logging service company’s surface equipment. Inputs required are an SP, a deep resistivity measurement (usually a deep induction), and a shallow resistivity measurement (usually a shallow-focused electric log). The theory behind the method depends only on Archie’s equation and the SP relationship, which we may write as:
SP = -K log (Rmf/Rw)
Note that for the purposes of this overlay Rmf and Rw are used rather than their "equivalent" values Rmfe and Rwe. Archie’s equation, if written for both the invaded and undisturbed zones, allows a ratio to be taken which eliminates F, the porosity-dependent formation factor: Swn = F Rw/Rt Sxon = F Rmf/Rxo
If an assumption is made that Sxo is related to Sw--, for example, that
Sxo = (Sw) 1/5
--then the quantity (Sw/Sxo)n can be replaced by (Sw)8/5 if "n" is assumed equal to 2. Thus, the term Rmf/Rw can be replaced by (Rxo/Rt) (Sw) 8/5 and the SP equation rewritten as:
-SP = K log [(Rxo/Rt) (Sw) 5/8]
-SP = K (log (Rxo/Rt)) + K log (Sw 5/8)
or:
In a water-bearing zone with Sw=1, the term K log (Sw) 5/8 is equal to 0, and thus the term K log (Rxo/Rt) is numerically equal to -SP. However, in an oil-bearing zone with Sw less than 1, the term K log ((Sw) 5/8) will be less than 1, and hence the term K log (Rxo/Rt) will be numerically less than -SP. Provided that no substantial SP reduction is due to the presence of hydrocarbons (usually the case in all but very shallowly invaded formations), a comparison of the actual SP with the quantity K log (Rxo/Rt) will have the following characteristics: • •
In wet zones, the two curves will "track." In hydrocarbon-bearing zones, the K log (Rxo/Rt) curve will separate from the SP curve ( Figure 1 ).
Figure 1
•
•
(Note that in the lower sand, which is wet, the SP and the massaged Rxo/Rt ratio closely coincide, and in the upper sand which is hydrocarbon bearing, the two curves se parate.) In shales, since the Rxo/Rt ratio is close to 1, the massaged Rxo/Rt is effectively zero.
In practice some experimentation is usually required in order to obtain a valid overlay with the two traces overlaying in both shales and wet zones. This requires using the correct K value for the formation temperature in question and correct offsetting of either the SP baseline or the massaged Rxo/Rt curve.
To sum up, use this method, by all means, if you have sand-shale sequences, good SP development (high Rmf/Rw ratio), and you do not envisage recording a porosity log. This method cannot be used with oil-base mud. An unusual variation of this method uses the SP to generate a pseudo Rxo/Rt ratio, which may then be compared with the actual Rxo/Rt ratio. A refinement of the method allows a more accurate computation of the real Rxo/ Rt ratio by taking into account invasion effects. In deeply invaded formations, for example, the ratio of RSFL to RILd is not as large as the real Rxo/Rt ratio. This refinement requires a solution to the "tornado" chart to be carried in the surface equipment software package. Ro versus Rt -- The F Overlay Another popular and extremely effective overlay is the F overlay, which effectively compares Ro with Rt. In clean formations of known lithology this is a simple matter for the logging service company’s surface equipment. It merely requires values of ρ ma, ρ f , a, and m to be dialed in, and F appears as an output. In practice, this F curve is recorded on a logarithmic scale as a separate log. The analyst then uses the logarithmic F curve in conjunction with a logarithmic Rt curve (a deep induction or deep laterolog) in the manner of a slide rule to normalize the two curves so that they overlay each other in clean wet zones. By so doing, the log (F) curve has in fact been shifted by an amount equal to log (Rw) . Since the product of F and Rw is Ro, the net effect is an overlay that compares Ro to Rt. Wherever the two curves separate, with Rt greater than Ro, the implication is that Sw is less than 1 a nd therefore hydrocarbons are expected. Figure 2 shows an F overlay.
Figure 2
Note that in the water-bearing section the normalized F curve (i.e., R o) coincides with the Rt curve and that in the hydrocarbon-bearing section the Rt curve separates from the Ro curve. This separation can be quantified in Sw units by using an appropriate logarithmic scaler such as that illustrated (not to scale) in Figure 3 .
Figure 3
The scaler is placed across the overlay so that its long axis parallels the depth lines on the log. The Sw - 100 mark is placed on the normalized F curve, and the Sw value is read at the Rt curve. Another useful feature of this overlay is that Rw need not be known. The act of normalizing the F curve to the deep resistivity trace in a wet zone effectively computes Rw for you. If the F curve is on top of the resistivity log when the normalization is made, locate the 100 line on the F scale at the top of the F log and read the resistivity value on the resistivity scale that lies immediately beneath it. This is numerically equal to 100 times Rw. For example, after normalizing in a wet zone, F = 100 lies over the Rt scale line corresponding to 20 Ohm-m. This means that Rw is 0.2 Ohm-m.
The Logarithmic Movable Oil Plot An extension of the F overlay is the logarithmic movable oil plot, which requires that two overlays be made, one to indicate Sw and a second to indicate Sxo. In practice, both are made on a single log and the result is a movable oil plot (MOP) on a logarithmic scale. The production of a MOP proceeds in two stages. First, the F curve is normalized to Rt in a wet zone and the resulting Ro curve traced onto the resistivity log (or, if preferred, the Rt curve may be traced onto the normalized F log). Second, the F curve is normalized to an Rxo trace (such as a focused, or microelectric log) in a wet zone, and the resulting Rxoo curve (Rxoo = Rxo in a rock 100% saturated with a fluid of resistivity Rmf) is traced onto the resistivity log (or, as noted, the Rxo curve may be traced onto the normalized F log) . The result of such tracings will be as shown in Figure 4 .
Figure 4
Note that the area between the Ro and Rt curves is representative of the hydrocarbon-filled pore space. The MOP adds a further dimension by subdividing that space into two parts, one containing residual oil and the other movable oil. This presentation can help assess the most productive intervals (i.e., those with high movable oil). Consider the bulk volume model shown in Figure 5 .
Figure 5
Note that in the undisturbed zone the saturating fluids are connate water and oil and that the water saturation is Sw. In the invaded zone, however, the saturating fluids are mud filtrate and residual oil and the water saturation is Sxo. If Sxo is high (i.e., residual oil saturation, ROS, is low) then a large fraction of the oil in place has been moved by the mini-waterflood effected by the drilling process. If, however, Sxo is close to Sw, then very little of the oil in place has been moved, and in such cases a formation may be less productive. Thus, on the MOP, the area between the Ro curve and the Rxoo curve is a measure of the residual oil saturation and the area between the Rxoo curve and the Rt curve is a measure of the movable oil saturation . In practice, once a tracing of this sort has been prepared, it is common to color in the appropriate areas by use of high-lighters of different colors, e.g., red for residual oil, orange for movable oil, and blue for water. Note that zero porosity point never appears on such a logarithmic plot, since F or Rt corresponding to zero porosity is infinity. Thus some arbitrary line is chosen as the right-hand limit for the purpose of coloring in water with a blue highlighter. The Neutron-Density Overlay The neutron-density overlay is probably the most commonly used presentation. Its popularity stems from (a) the fact that the two logs are nearly always run together and (b) the enormous wealth of information that can be gathered from such a presentation, even with a cursory inspection. Two distinct types of overlay are considered here: the compatible sandstone-scaled overlay and the compatible limestone-scaled overlay. In sand-shale sequences the former is needed and in carbonate-evaporite sequences the latter. The compatibly scaled sandstone presentation requires that the neutron log (and here the dual-spacing thermal neutron log is the norm) be recorded on a sandstone matrix setting and displayed on a 0 to 60% scale. Likewise the bulk density
recording, ρ b should be converted to an apparent sandstone porosity curve by choice of an appropriate value for ρ ma (2.65 or 2.68 gm/cc, for example) and displayed on the same scale as the neutron log. The choice of a scale, be it 0 to 60% or 0 to 50%, is immaterial provided both curves are on the same scale and the shale readings do not exceed the high end of the scale (i.e., a presentation on a 0 to 30% scale is inappropriate if φ N in the shales is 45% and thus off-scale) . Figure 6 shows such an overlay.
Figure 6
Note that in shales, φ N is much larger than φ D (dotted curve to the left of the solid curve) . Note that in water-bearing intervals, φ N equals φ D where the formation is clean. Note that in gas-bearing zones, .N reads a lower apparent porosity than does φ D and that the traces. tend to be mirror images of each other. Even in oil-bearing sections it is common to note φ N reading slightly less than φ D. Thus, on one plot it is possible to quickly distinguish porous and permeable sections from shales and, within the potential reservoir rocks so defined, to distinguish gas, oil, and water.
Since the purpose is slightly different in carbonate reservoirs, a slightly different presentation is used. Here the norm is not sandstone or shale but limestone and possibly evaporites. Porosities in general are lower than in sandstone reservoirs and dolomite may be present as well. The compatible limestone presentation, therefore, calls for the neutron log on a limestone matrix setting, with the density log on an apparent limestone porosity basis as well. Since dolomite and anhydrite may compute apparent porosities less than zero on a limestone basis (remember ρ ma for dolomite is higher than ρ ma for limestone), an appropriate scale for this type of overlay is 45% to -15% (left to right). In some locations 30% to -10% is favored. However, the 45% to -15% scale has an added advantage. If the bulk density curve has not been converted to an apparent porosity curve then all Is not lost. By appropriate shifting, the neutron porosity and bulk density curves may be overlain so that on the neutron log 2.95 gm/cc coincides with -15% and 1.95 gm/cc coincides with 45%. The reader may satisfy himself that 1.95 gm/cc translates to approximately 45% porosity on a limestone scale, and 2.95 gm/cc to -15%. Figure 7 illustrates a neutron density compatible limestone overlay.
Figure 7
It is constructed for a formation porosity of 15%. Note that in limestone the two traces coincide. In dolomite the apparent neutron porosity is higher than the
apparent density porosity and in sandstone the reverse is true. This sandstone "crossover" is due entirely to the matrix effects on the two porosity devices and is the result of the limestone porosity scaling used. It should not be confused with crossover produced by gas. Note that in sandstone intervals, both curves have a similar character although separated from one another. The gas effect "mirror imaging" is not evident. If gas were present it would manifest itself by an additional separation, with neutron even lower than density. The evaporites salt and anhydrite are also shown along with shale. Such a presentation is extremely valuable for a quick-look guide to the rock types in the column drilled and is a very good starting point for other more detailed analysis. Density-Sonic Overlay Although not as widely used as a neutron-density overlay, the density-sonic overlay is particularly useful for detection of secondary porosity, i.e., vugs and fractures. Figure 8 shows a formation with both matrix (intergranular) porosity and fracture porosity.
Figure 8
Provided the matrix is known, the density porosity will be equal to the total porosity:
•
=
=
matrix +
secondary
The sonic tool, however, responding as it does to the first compressional wave arrival, will only respond to the matrix porosity. Compressional waves traveling through a vertical, fluid-filled fracture, for example, will travel more slowly than those traveling through the matrix system. Since the sonic tool triggers on the first (faster traveling) arrival, the later arrivals passing through the fracture system will be ignored. Thus: •
S=
matrix
An overlay of φ S and φ D, has the interesting property that in fractured or vuggy intervals the two curves separate. Figure 9 illustrates such an overlay.
Figure 9
A number of scaling options are available. Compatible limestone scaling on a 45% to -15% scale (left to right) is adequate for most applications. If bulk density and A are to be overlaid, then compatible scaling is 1.95 to 2.95 gm/cc (left to right) for ρ b and 108 to 28 µsec/ft (left to right) for D, equivalent to 40 µsec/ft per track. In
metric units a scaling of 350 to 90 µsec/meter is adequate (equivalent to 65 µsec/meter per track) . Dielectric Porosity Overlay The compatible porosity overlay ( Figure 10 ) of a dielectric log-derived porosity with another porosity curve is useful for quick-look hydrocarbon detection.
Figure 10
The theory behind the overlay is simple. A dielectric log-derived "porosity" is effectively the water-filled pore space, whereas a density porosity, for example, is effectively the total porosity. If the formation is wet, traces will overlay. In hydrocarbon-bearing zones separation may be expected. The usual cautions are appropriate: clean formations and the correct choice of matrix parameters are required when computing the two porosities.
Theory Crossplots of log data are indispensable tools for the analyst. A crossplot is a twodimensional representation of the variation of data with respect to two or more
properties. Although widely used in conjunction with computer processing of log data, crossplots may, of course, be prepared by hand using only limited amounts of data that have been screened by the analyst. The end result of using a crossplot is finding a parameter needed for quantitative log analysis, for example, Sw and Rw. Figure 1 , a graphical representation of the Archie equation, shows a crossplot of porosity versus resistivity.
Figure 1
Within a given formation, an Ro line is determined that is representative of 100% water saturation. Then, an arbitrary Ro line can be determined to examine points that have water saturations less than a given value. Points below this line could be subjected to further analysis. Crossplots come in many other forms; here follows an overall view of crossplotting techniques . Trend Analysis and Groupings In logging terms, crossplots can be used to discern trends or groups. Suppose a well is extensively cored and core analyses are made to find porosity and permeability throughout the section. A plot of permeability against porosity might look like the plot shown in Figure 2 .
Figure 2
Note that three distinct rock types are revealed by the crossplot. Rock type A is of low porosity and permeability (perhaps a carbonate), rock type B is of moderate porosity and high permeability (perhaps a sandstone), and rock type C is of high porosity and moderate permeability. Thus, crossplots visually show us trends and groupings of data points that, in turn, help us understand the nature of the population being plotted. Extrapolations Another useful feature of the crossplot is in making extrapolations. The extrapolation of patterns and trends on crossplots is an extremely valuable tool for predicting such key analysis parameters as porosity. In the example shown in Figure 3 , φ D-ls = 15 and φ N-ls = 21.
Figure 3
This defines point P, lying between the limestone and dolomite curves and falling near a line connecting the 18% porosity graduations on the two curves. Assuming a matrix of limestone and dolomite and proportioning the distance between the two curves, the point corresponds to a volumetric proportion of a bout 40% dolomite and 60% limestone; porosity is 18%. Frequency Plots Computers are particularly adept at manipulating log data to produce frequency plots. These are crossplots on which the number of occurrences of a particular pair of data points is printed at a particular map location. Figure 4 shows a neutron-density frequency crossplot for data from a section logged through a sand-shale sequence.
Figure 4
For the purpose of the plot, each axis is divided into one-porosity-unit cells. There are thus 2500 (50 x 50) cells on the plot. Each data point on the log is inspected and its φ N and φ D coordinates used to place a point on the plot. Where many points fall in the same cell their total number is accumulated, and this number (or frequency) is the item printed on the final plot at that particular cell address. Where no data are found the plot remains blank. Where the majority of the points lie gives a good visual image of the distribution of the formation properties in the logged section. Such plots are used extensively for log data normalization (i.e., recalibration shifts), shale picks, etc. Z Plots The Z plot is a companion plot to the conventional frequency crossplot (or X-Y plot) described above. The purpose of the Z plot is to map the distribution of three variables instead of two. Given the limitations of a two-dimensional sheet of paper, this task is accomplished by printing the scaled average of the third variable (Z) at any given X-Y cell address.
For example, in Figure 4 there were 8 occurrences of the condition φ N (PHIN-the X axis) = 26% and φ D (PHID-the Y axis) = 12%. The same cell on the Z plot of Figure 5 shows a scaled average of a third parameter, the gamma ray.
Figure 5
At the chosen address the scaled average of the 8 values of gamma ray occurring at φ N = 26% and φ D = 12% is seen to be 8. On this particular plot the scaling of the Z axis was accomplished by applying the formula
and z-min and z-max were chosen so that the least radioactive levels "scored" 0 and the most radioactive levels 10. Note that two-digit numbers (10 or more) are represented by symbols such as "*."
Reviewing the Z plot of Figure 5 , it is evident that the shaliest points lie to the southeastern corner of the plot (high z values of 8, 9, and *), and the least radioactive points lie to the northwestern part of the plot (low z values of 1, 2, and 3). Z plots are useful for data analysis where three variables are of interest.
Histograms Histograms of raw log data and computed results of log analysis also provide useful tools for the analyst. Figure 1 illustrates a histogram.
Figure 1
The Y axis of such a plot is either scaled in actual number of occurrences or in percent of the total number of data points analyzed. The X axis is scaled over the useful range of the data analyzed. Among the better known uses for histograms are picking minima and maxima, re-scaling logs, and checking the validity of computed results.
Illustrations of particularly useful histograms will be given in the appropriate modules of this logging series when discussing particular aspects of log analysis.
Quick-Look Algorithms With the advent of the hand-held calculator, especially the programmable type, log analysts have tended to condense their wisdom into algebraic manipulations to ease their daily toil. Today much of what used to be done by reference to charts is done via pocket computer. This has advantages and disadvantages. On the plus side, obviously more data points can be analyzed in a shorter time and with greater precision. On the minus side, however, the analyst no longer has the latitude to shift points on a chart to get an immediate feel for the sensitivity of a computed answer to a change in the raw data values used. Algorithms for solving many of the common manipulations that log analysts use will be given in the appropriate modules as the particular analysis method is discussed. A word of caution is in order. Although the calculator/ computer is a useful device for the crunching of numbers and relieves the analyst of that chore, it also places a greater burden on the analyst, that of ensuring (a) that the model fits the circumstances and (b) that legitimate data is submitted to be processed. A more precise answer should not be confused with a more accurate one.
Figure 1
Inspect the logs of Figure 1 and estimate the depth difference between core depths and log depths.
Figure 1
The log curves of Figure 1 have been depth-correlated by sliding one over the other until the major correlatable peaks match each other. The core log shows the depths as being 8 ft greater than the wireline logs. The solution is 8 ft.
(a) If ρ f = 1.0 gm/cc and ρ b = 2.54 gm/cc and φ N (Lime) = 18%, find the corresponding crossplot porosity, φ X using Figure 1 .
Figure 1
(b) Convert ρ b to φ following formula: f D= ρ
ma
− ρ
b/ ρ
ma
D (Lime) and compute the quick-look value of φ
− ρ
X using the
f
(a) Plot 2.54 on the ordinate versus 18 on the abscissa, and find a point corresponding to a line between 14 on limestone and 14 on dolomite.
The solution is φ X = 0.14, or 14%. (b) To convert from ρ b to φ ρ
B = ρ ma (1 - φ
D use the following equation:
D) + ρ f φ
D
The quick formula is the average of the two readings:
The solution is 14%.
Figure 1
If ∆ t = 79µ-sec/ft and φ N (Lime) = 18%, use Figure 1 to compute a crossplot porosity. Enter Figure 1 and crossplot the values. The resulting point falls between lines drawn between the sandstone and the limestone lines at 20 and 21 porosity units (%).
The solution is φ
X = 0.206, or 20.6%.
Use Figure 1 to determine ρ The ratio φ N/ φ
D
hy
when φ
N
= 12.5%, φ
D = 33%, and Sxo = 55%.
is 0.125/0.33 = 0.38.
Enter Figure 1 and plot Sxo = 55% versus the above-computed ratio of 0.38 to find ρ hy = 0.2 gm/cc.
Figure 1
The solution is ρ
hy
= 0.2 gm/cc.
