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WELCOME TO CRAIN'S PETROPHYSICAL HANDBOOK Please be fair to the author. Pay your Shareware Fee HERE and receive a copy of CPH by download. WATER SATURATION CROSSPLOTS Hingle Plots Pickett Plots Buckle's Plots Combined Pickett + Buckle's Examples 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 the graph 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. The graph 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 are plotted to fall non-linearly on the graph paper. The log-log Pickett plot described below is more 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, infinite resistivity point. The 100% water saturation line can be placed by calculating RESD for any positive value of porosity from the Archie formula. Similarly other saturation lines can be placed 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 and RW@FT = 0.25, then: Sw = 1.0, RESD = 0.25 / (0.1 ^ 2) / (1 ^ 2) = 25 Sw = 0.7, RESD = 0.25 / (0.1 ^ 2) / (0.7 ^ 2) = 50 Sw = 0.5, RESD = 0.25 / (0.1 ^ 2) / (0.5 ^ 2) = 100 Sw = 0.2, RESD = 0.25 / (0.1 ^ 2) / (0.25 ^ 2) = 625 Therefore, for this example we would draw a line from the PHIe = 0, RESD = infinity point to a point defined by PHIe = 0.1 and RESD = 25, to obtain the 100% water saturation line. The 50% water saturation line Crain's Petrophysical Handbook - WATER SATURATION CROSSPLOTS https://www.spec2000.net/14-swxplot.htm 1 of 12 12/08/2015 12:02

Water Saturation Crossplots

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WELCOME TOCRAIN'S PETROPHYSICAL HANDBOOKPlease be fair to the author. Pay your Shareware Fee HERE and receive a copy of CPH by download.WATER SATURATION CROSSPLOTSHingle Plots Pickett Plots Buckles Plots Combined Pickett + Buckles ExamplesPOROSITY 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 scalesuch that straight lines on the graph represent constant water saturation, asdetermined 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. The graph requires a specialgrid, since the Y axis is linear in the function RESD ^ (-1 / M) but not linear in RESD. RESD or COND lines are used toplot and read data points, so these are plotted to fall non-linearly on the graph paper. The log-log Pickett plotdescribed below is more common today because it is easier to generate with common computer software.On Hingle plot graph paperthe saturation lines fan out from the zero porosity, infinite resistivity point. The 100%water saturation line can be placed by calculating RESD for any positive value of porosity from the Archie formula.Similarly other saturation lines can be placed 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 and RW@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) = 625Therefore, for this example we would draw a line from the PHIe = 0,RESD = infinity point to a point defined by PHIe = 0.1 and RESD = 25, toobtain the 100% water saturation line. The 50% water saturation lineCrain's Petrophysical Handbook - WATER SATURATION CROSSPLOTS https://www.spec2000.net/14-swxplot.htm1 of 12 12/08/2015 12:02joins the origin with the point PHIe = 0.1 and RESD = 100 and so on, asshown in the illustration at the right.If RW@FT is unknown, a line can be drawn slightly above the mostnorthwesterly points on the graph to intersect at the origin and RW@FTback calculated from any point on the line by using:4: RW@FT = RESD * (PHIe ^ M) / AWHERE: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 drawn without knowledge of theporosity origin, thus helping to find the matrix point. In the above illustration, the data suggests a matrix density of2.7 gm/cc, so the porosity scale origin is set at this point. If data was in porosity units to begin with, this techniquewould define the matrix 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 crossplotporosity, can be used for the porosity axis. Any deep resistivity or conductivity reading can be used on the Y axis.If shallow resistivity data are available, the parameter RESS*RW/RMF can be plotted below the RESD points. Thedistance between the RESD and normalized RESS points represents the moveable hydrocarbon - the larger thebetter.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 porosityscale. Porosity will be zero at the matrix point and increases to the right.3. Plot resistivity (RESD) vs log data (DELT, DENS, PHIN or PHID). The resistivity scale can be changed by any orderof magnitude to fit the log data. This can be done without changing the validity of the graph paper grid.4. The straight line drawn through the most north westerly points defines Sw = 1.0. Extrapolate this to theintersection 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. Iflogs are in porosity units, this line will determine the matrix offset.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 thatall 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 avoidconfusion, particularly if very long sections are analyzed.9. As an extension of this method, in case RESS data are also available, the moveable hydrocarbon can bedetermined 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 inmost service company chart books, as well as here:Hingle plot M = 2.00 Full SizeHingle plot M = 2.15 Full SizeRESISTIVITY POROSITY CROSSPLOT (PICKETT PLOT)Since the non-linear graph paper of the Hingle plot is difficult to construct, another style of porosity resistivity plot ispopular. It is called a Pickett plot, and both resistivity and porosity are plotted on logarithmic scales.Again, by rearranging the Archie equation we get:5: log RESD = -M * log PHIe + log (A * RW@FT) - N * log SwWhen Sw = 1.0, then:6: log RESD = -M * log PHIe + log (A * RW@FT)7: M = (log(A*RW@FT) - log(RESD)) / log(PHIe)Crain's Petrophysical Handbook - WATER SATURATION CROSSPLOTS https://www.spec2000.net/14-swxplot.htm2 of 12 12/08/2015 12:02This is the equation of a straight line on log - log paper. The line has a slope of (-M) and the intercept when PHIe = 1 isthe value of A * [email protected] resistivity increases upward and porosity increases to the right, a line drawn slightly below the south westerly datapoints should represent the 100% water saturation line (as long as a water zone exists in the interval). If A * RW@FTis known, the line should pass through this point 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 Mis seldom less than 1.7 or more than 2.8 in non-fractured reservoirs.The slope is determined manually by measuring a distance on the RESD axis (in cm. or inches) and dividing it by thecorresponding distance on the porosity axis, or by using equation 7. The result will always be negative.To construct the other water saturation lines, first draw a line upwardfrom the point where the 100% water saturation line meets the lineRESD = 1.0. Then mark points on the vertical line at RESD values of 2.0,4.0 and 25.0. Draw a line through each of these marks parallel to the100% water saturation line. These lines are 70%, 50% and 20% watersaturation lines respectively.An example is shown at right, using the same data as in the Hingle plotshown earlier. Because A and M and the matrix values for rocks areseldom the world wide averages commonly assumed, the porosityresistivity crossplot is often used to find reasonable values prior to orin lieu of special core studies.If RW@FT varies, this may be noticed by parallel groupings of databelonging to several distinct water zones. The sequence should bezoned to create a separate plot for each different water resistivity value.Comparisons of these plots between wells are often useful. A shift ofdata in the porosity direction may indicate a mis-calibrated porositylog.A shift in the resistivity direction may indicate a mis-calibratedresistivity log, differences in invasion, a change in pore geometry, or achange in A * RW@FT. In the example above, the W axis (colour) iscoded 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 through the red data is differentthan that through the blue data. This demonstrates that the pore geometry for the dolomite interval is different thanthat for the limestone. The M value for the dolomite is less than 2.0 for the dolomite and considerably higher than 2.0for 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 varies primarily with grain size andsorting. This is a function of position in the basin and distance from source rock.Again, as for the Hingle plot, values of RESS * RW / RMF can be plotted to estimate moveable hydrocarbon. If nowater zone exists in the interval, plotting RESS vs PHIe may find the slope M, since RESS sees mostly a water filledzone.Crain's Petrophysical Handbook - WATER SATURATION CROSSPLOTS https://www.spec2000.net/14-swxplot.htm3 of 12 12/08/2015 12:02Example of Computer-drawn Pickett PlotThe Pickett plot above shows that cementation exponent (M) varies with lithology. The slope of the line through thedolomite data (red) is less than that through the limestone (blue). For a good estimate of water saturation in bothzones, the appropriate value of M must be used in each zone. An average line through this data set will make the highporosity dolomite look too 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 a constant, and the product iscalled Buckles Number, after the man who first described this factor:8: KBUCKL = PHIe * SWirKBUCKL is found in a clean hydrocarbon bearing zone with a known RW and is used to calculate SWir in depletedreservoirs or in water zones, or in zones of similar rock type with an unknown RW.It can also be found by plotting core porosity vs minimum wettingphase saturation at an arbitrary capillary pressure from special coreanalysis data. A graph of this relationship is shown at right. LowerBuckles Numbers indicate larger average grain size, lower surfacearea, and lower irreducible water saturation. Water saturation versus porosity-saturation product (Buckles Method)Buckles equation is used to estimate water saturation byrearranging the terms:9 : SWb = KBUCKL / PHIe / (1 - Vsh)If regression is used to determine SW from PHIe, the relationship isusually hyperbolic (KBUCKL = constant) or a skewed hyperbola(KBUCKL varies with porosity).The shale term has been added by the author to raise KBUCKL andSwb automatically for the finer grained nature of shaly sands.Crain's Petrophysical Handbook - WATER SATURATION CROSSPLOTS https://www.spec2000.net/14-swxplot.htm4 of 12 12/08/2015 12:02TYPICAL VALUESSandstonesCarbonatesKBUCKL Very fine grainChalky0.120 Fine grain Cryptocrystalline0.060 Medium grain Intercrystalline 0.040 Coarse grain Sucrosic 0.020 Conglomerate Fine vuggy 0.010 Unconsolidated Coarse vuggy 0.005 FracturedFractured 0.001 COMBINING POROSITY - WATER SATURATION CROSSPLOTCombining a Pickett Plot and a Buckles Plot on the same graph gives some interesting results. The following is fromDr. Gene Ballays "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 ofconstant 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 orwater saturation may bealong the vertical axis, with the other being along the horizontal. In the LogLog 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 Buckle's Plot of PHI * SW (left) and log-log plot of same(right). Hyperbolic PHI * SW lines becomestraight lines in the log-log domain.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 theintercept of the 100% SW line with the 100% porosity lines. The same technique can be applied to the flushed zones, using flushedzone measurements.Crain's Petrophysical Handbook - WATER SATURATION CROSSPLOTS https://www.spec2000.net/14-swxplot.htm5 of 12 12/08/2015 12:02Picket Plot on log-log grid for M =N =2.00.The full Archie equation:log Rt = -M * log PHI + log (A * RW@FT) - N * log SWcan be rearranged when M = N to give:log Rt = log Rw - N * log (PHI * SW) = ConstantThus vertical lines on a Pickett Plot represent constant PHI * SW (Buckles Numbers) when M = N.Pickett Plot with constant PHI * SW lines (vertical lines when M =N)Crain's Petrophysical Handbook - WATER SATURATION CROSSPLOTS https://www.spec2000.net/14-swxplot.htm6 of 12 12/08/2015 12:02Pickett Plot with constant PHI * SW lines when M >NCrain's Petrophysical Handbook - WATER SATURATION CROSSPLOTS https://www.spec2000.net/14-swxplot.htm7 of 12 12/08/2015 12:02Pickett Plot with constant PHI * SW lines when M