pickett hingle and others

8/11/2019 Pickett Hingle and Others

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POROSITY RESISTIVITY CROSSPLOT (HINGLE PLOT)The porosity resistivity crossplot is a venerable tool, still used in many areas. In one version,porosity is plotted on a linear scale, and resistivity on a scale such that straight lines on thegraph represent constant water saturation, as determined by the Archie formulae:

1: Sw = (F * RW@FT / RES) ^ (1 / N)2: F = A / (PHIe ^ M)

WHERE:A = tortuosity exponent (fractional)F = formation factor (fractional)M = cementation exponent (fractional)N = saturation exponent (fractional)PHIe = effective porosity (fractional)RESD = deep resistivity (ohm-m)RW@FT = water resistivity (ohm-m)Sw = water saturation (fractional)

This plot is often called the Hingle plot after the man who first publicized the method. Thegraph requires a special grid, since the Y axis is linear in the function RESD ^ (-1 / M) but not

linear in RESD. RESD or COND lines are used to plot and read data points, so these areplotted to fall non-linearly on the graph paper. The log-log Pickett plot described below ismore common today because it is easier to generate with common computer software.

On Hingle plot graph paper the saturation lines fan out from the zero porosity, infiniteresistivity point. The 100% water saturation line can be placed by calculating RESD for anypositive value of porosity from the Archie formula. Similarly other saturation lines can beplaced on the graph. By rearranging the Archie equation we get:

3: RESD = A * RW@FT / (PHIe ^ M) * (Sw ^ N)

WHERE:A = tortuosity exponent (fractional)F = formation factor (fractional)

M = cementation exponent (fractional)N = saturation exponent (fractional)PHIe = effective porosity (fractional)RESD = deep resistivity (ohm-m)RW@FT = water resistivity (ohm-m)Sw = water saturation (fractional)

If we take A = 1.0, M = N = 2.0, PHIe = 0.1 andRW@FT = 0.25, then:Sw = 1.0, RESD = 0.25 / (0.1 ^ 2) / (1 ^ 2) = 25Sw = 0.7, RESD = 0.25 / (0.1 ^ 2) / (0.7 ^ 2) = 50Sw = 0.5, RESD = 0.25 / (0.1 ^ 2) / (0.5 ^ 2) = 100Sw = 0.2, RESD = 0.25 / (0.1 ^ 2) / (0.25 ^ 2) = 625

Therefore, for this example we would draw a linefrom the PHIe = 0, RESD = infinity point to a pointdefined by PHIe = 0.1 and RESD = 25, to obtain the100% water saturation line. The 50% watersaturation line joins the origin with the point PHIe= 0.1 and RESD = 100 and so on, as shown in theillustration at the right.


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If RW@FT is unknown, a line can be drawn slightly above the most northwesterly points onthe graph to intersect at the origin and RW@FT back calculated from any point on the line byusing:

4: RW@FT = RESD * (PHIe ^ M) / A

WHERE:

A = tortuosity exponent (fractional)M = cementation exponent (fractional)PHIe = effective porosity (fractional)RESD = deep resistivity (ohm-m)RW@FT = water resistivity (ohm-m)

If sufficient porosity range exists in the water zone, the northwesterly line can be drawnwithout knowledge of the porosity origin, thus helping to find the matrix point. In the aboveillustration, the data suggests a matrix density of 2.7 gm/cc, so the porosity scale origin isset at this point. If data was in porosity units to begin with, this technique would define thematrix offset to correct the porosity log to the actual matrix rock present.

Any of the three porosity logs, (sonic, density, neutron) or any derived porosity, such as

density neutron crossplot porosity, can be used for the porosity axis. Any deep resistivity orconductivity reading can be used on the Y axis.

If shallow resistivity data are available, the parameter RESS*RW/RMF can be plotted belowthe RESD points. The distance between the RESD and normalized RESS points representsthe moveable hydrocarbon - the larger the better.

The manual construction of this crossplot can be summarized as follows:1. Select proper crossplot paper.2. Scale the X-axis in linear fashion for raw logging parameters (DELT, DENS, PHIN or PHID)

and establish porosity scale. Porosity will be zero at the matrix point and increases to theright.3. Plot resistivity (RESD) vs log data (DELT, DENS, PHIN or PHID). The resistivity scale can

be changed by any order of magnitude to fit the log data. This can be done without changingthe validity of the graph paper grid.4. The straight line drawn through the most north westerly points defines Sw = 1.0.

Extrapolate this to the intersection with X-axis (PHIe = 0, RESD = infinity).5. At the intersection, determine the matrix value (DELTMA or DENSMA) for a proper

porosity scaling of the X-axis. If logs are in porosity units, this line will determine the matrixoffset.6. Calculate RW@FT from any corresponding pair of PHIe and RESD data along the water

line.7. Determine lines of constant Sw values based on the Archie equation (for any given PHIe

value). Keep in mind that all these lines must converge at the matrix point.8. Read and evaluate Sw values for all points plotted on the crossplot. Make sure points are

numbered to avoid confusion, particularly if very long sections are analyzed.

9. As an extension of this method, in case RESS data are also available, the moveablehydrocarbon can be determined by plotting RESD * RW / RMF below each RESD point.

The grid for a Hingle plot is difficult to draw by hand as the resistivity axis is non-linear.Blank forms are available in most service company chart books, as well as here:

Hingle plot M = 2.00Full SizeHingle plot M = 2.15Full Size
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RESISTIVITY POROSITY CROSSPLOT (PICKETT PLOT)Since the non-linear graph paper of the Hingle plot is difficult to construct, another style ofporosity resistivity plot is popular. It is called a Pickett plot, and both resistivity and porosityare plotted on logarithmic scales.

Again, by rearranging the Archie equation we get:5: log RESD = -M * log PHIe + log (A * RW@FT) - N * log Sw

When Sw = 1.0, then:6: log RESD = -M * log PHIe + log (A * RW@FT)7: M = (log(A*RW@FT) - log(RESD)) / log(PHIe)

This is the equation of a straight line on log - log paper. The line has a slope of (-M) and theintercept when PHIe = 1 is the value of A * RW@FT.

If resistivity increases upward and porosity increases to the right, a line drawn slightly belowthe south westerly data points should represent the 100% water saturation line (as long as a

water zone exists in the interval). If A * RW@FT is known, the line should pass through thispoint at PHIe = 1.0.

If the cementation exponent M is known, the line can be drawn with this slope to find A *RW@FT. Remember that M is seldom less than 1.7 or more than 2.8 in non-fracturedreservoirs.

The slope is determined manually by measuring a distance on the RESD axis (in cm. orinches) and dividing it by the corresponding distance on the porosity axis, or by usingequation 7. The result will always be negative.

To construct the other water saturation lines, firstdraw a line upward from the point where the

100% water saturation line meets the line RESD =1.0. Then mark points on the vertical line at RESDvalues of 2.0, 4.0 and 25.0. Draw a line througheach of these marks parallel to the 100% watersaturation line. These lines are 70%, 50% and20% water saturation lines respectively.

An example is shown at right, using the samedata as in the Hingle plot shown earlier. BecauseA and M and the matrix values for rocks areseldom the world wide averages commonlyassumed, the porosity resistivity crossplot isoften used to find reasonable values prior to or in

lieu of special core studies.

If RW@FT varies, this may be noticed by parallelgroupings of data belonging to several distinctwater zones. The sequence should be zoned tocreate a separate plot for each different waterresistivity value. Comparisons of these plotsbetween wells are often useful. A shift of data inthe porosity direction may indicate a mis-calibrated porosity log.
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A shift in the resistivity direction may indicate a mis-calibrated resistivity log, differences ininvasion, a change in pore geometry, or a change in A * RW@FT. In the example above, theW axis (colour) is coded red for PE near 3.0 and blue for PE near 5.0, thus segregatingdolomite from limestone. Note that the porosity distribution and the slope of the line throughthe red data is different than that through the blue data. This demonstrates that the poregeometry for the dolomite interval is different than that for the limestone. The M value for thedolomite is less than 2.0 for the dolomite and considerably higher than 2.0 for this limestone.(RESD is on the X axis in this plot).

If RW@FT is known from water samples, it may help define the value for A, which variesprimarily with grain size and sorting. This is a function of position in the basin and distancefrom source rock.

Again, as for the Hingle plot, values of RESS * RW / RMF can be plotted to estimatemoveable hydrocarbon. If no water zone exists in the interval, plotting RESS vs PHIe mayfind the slope M, since RESS sees mostly a water filled zone.

Example of Com puter-drawn Pickett Plot

The Pickett plot above shows that cementation exponent (M) varies with lithology. The slopeof the line through the dolomite data (red) is less than that through the limestone (blue). Fora good estimate of water saturation in both zones, the appropriate value of M must be used

in each zone. An average line through this data set will make the high porosity dolomite looktoo wet. The low porosity limestone would appear not wet enough.

POROSITY - WATER SATURATION CROSSPLOT (BUCKLES PLOT)The product of porosity and minimum water saturation, PHI * SWir, in many rocks is aconstant, and the product is called Buckles Number, after the man who first described this


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factor:8: KBUCKL = PHIe * SWir

KBUCKL is found in a clean hydrocarbon bearing zone with a known RW and is used tocalculate SWir in depleted reservoirs or in water zones, or in zones of similar rock type withan unknown RW.

It can also be found by plotting core porosityvs minimum wetting phase saturation at anarbitrary capillary pressure from special coreanalysis data. A graph of this relationship isshown at right. Lower Buckle's Numbersindicate larger average grain size, lowersurface area, and lower irreducible watersaturation.

Water saturation versus porosity-saturationproduct (Buckles Method)

Buckle's equation is used to estimate watersaturation by rearranging the terms:

9 : SWb = KBUCKL / PHIe / (1 - Vsh)

If regression is used to determine SW fromPHIe, the relationship is usually hyperbolic(KBUCKL = constant) or a skewed hyperbola(KBUCKL varies with porosity).

The shale term has been added by the author to raise KBUCKL and Swb automatically forthe finer grained nature of shaly sands.

TYPICAL VALUES

Sandstones Carbonates KBUCKL

Very fine grain Chalky 0.120

Fine grain Cryptocrystalline 0.060Medium grain Intercrystalline 0.040Coarse grain Sucrosic 0.020Conglomerate Fine vuggy 0.010Unconsolidated Coarse vuggy 0.005Fractured Fractured 0.001

COMBINING POROSITY - WATER SATURATION CROSSPLOTCombining a Pickett Plot and a Buckle's Plot on the same graph gives some interestingresults. The following is from Dr. Gene Ballay's "Double Duty" newsletter article(www.geoneurale.com).

Reservoir performance can often be evaluated in terms of the Bulk Volume Water BVW = PHI * SW.

Contour lines of constant bulk volume water may be used as cutoff boundaries. Permeability estimates

may also be possible in favorable situations. The graphic consists of Water

Saturation versus Porosity. Depending upon local conventions, either attribute (porosity or

water saturation may be along the vertical axis, with the other being along the horizontal. In the Log-
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Log world (such as used in a Pickett Plot), these BVW trends are straight lines, as illustrated on the

Buckle's Plots shown below.

Linear axis Buc kle's Plot of PHI * SW (left) and log-log p lot of s ame (right). Hyperbol ic PHI *

SW l ines become stra ight l ines in the log- log dom ain.

On a Pickett Plot, points of constant water saturation will plot on a straight line with slope related to

cementation exponent M. Saturation exponent N determines the separation of the Sw = constant grids,

as shown below. A*Rw@FT can be deduced from the intercept of the 100% SW line with the 100%

porosity lines. The same technique can be applied to the flushed zones, using flushed

zone measurements.

Picket Plot on log-log g rid fo r M = N = 2.00.


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The full Archie equation:log Rt = -M * log PHI + log (A * RW@FT) - N * log SW

can be rearranged when M = N to give:log Rt = log Rw - N * log (PHI * SW) = Constant

Thus vertical lines on a Pickett Plot represent constant PHI * SW (Buckle's Numbers) when M= N.

Pickett Plot with cons tant PHI * SW lines (vert ical l ines when M = N)


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Pickett Plot with con stant PHI * SW lines when M > N


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Pickett Plot with con stant PHI * SW lines when M < N

EXAMPLESThese examples of linear axis porosity versus water saturation plots show three differentsituations in three different wells. First is a well with no water zone and irreducible water thatvaries along a single hyperbolic trend (constant PHI * SW). The second illustrates a pay zoneat constant PHI * SW underlain by a water zone in which PHI * SW varies with porosity. Thethird example illustrates the need to see the production history and perforated interval data.The well shows increasing SW with depth, as well as increasing PHI * SW with depth. But thewell is perforated over the entire interval and produces very little water, so these changesare related to pore geometry, and not a transition zone between water and oil.


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Example of a 4-dimensio nal Buck le's Plot. X-axis = Sw, Y-axis = PHIe, Z-axis (numb ers) =

Vsh, W-axis (colour) = frequency o f occu rrence. Hyperbo l ic l ines are constant B uckle's

Num bers lines (PHIe*Sw = 0.02, 0.04, 0.06, 0.08, 0.10, 0.12). Numb ers alo ng b ott om and r igh t

edge are histograms o f frequency of occurrence. Al l data points fo l low near the KBUCKL =

0.025 l ine and no data points fal l to the right sid e, so th is interval wi l l produ ce no water upon

in i t ial produ ct ion.


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Ano ther example in w hich m ost d ata fal ls along th e KBUCKL = 0.02 to 0.04 l ines. These

point s wi l l prod uce no w ater. Data point s at the far right are from th e water zone and w il l

prod uce w ater. X, Y, Z, and W axes are as above.

Porosi ty vs w ater saturat ion plot in a reservo i r wi th vary ing po re geometry. Most of these


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data

point s prod uce clean oi l with no w ater, except the X's on the far right, past Sw = 90%.

pickett hingle and others

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