1. composed of natural Mineral and Fluid molecules. Second and higher order physical variability also depend the earths primary constituents. The easiest way to integrate physically meaningful data is to follow the natural hierarchal order. The natural hierarchal order for subsurface data integration by Phil Holbrook Ph.D. The Earth is principally

2. The natural hierarchal order for subsurface data integration by Phil Holbrook Ph.D. Natural Mineral and Fluid molecules are the earths fundamental physical constituents. A minimum petrophysical logging suite will almost always contain a measure of scalar Rt. The Effective Stress Theorem relates scalar [stress/strain] and fluid pressure to average mineralogy and porosity during natural geologic loading. The Minimalist Earth Mechanical Theory balances scalar stresses, strains and fluid pressures in [closed mathematical forms]. The scalar mineralogic mixing laws are smooth and continuous. copyright Force-Balanced Petrophysics 2007, all rights reserved

3. R t The central role of R t in Earth Mechanics calculated from Log Data. by Phil Holbrook Ph.D. The mass inertia relationship is discontinuous for low mass particles. Down hole sensors are designed to either induce and/or sense energy in the near borehole environment. Natural and induced -rays are short wavelength electromagnetic energy. Free electrons and ions are larger particles that are excited by medium wavelength electromagnetic energy. Acoustic body waves involve physical charge inertia interactions between natural molecules. copyright Force-Balanced Petrophysics 2007, all rights reserved

4. Mineralogy and porosity affect all sensors. All unit transformations used are dimensionally correct and physically balanced.. copyright Force-Balanced Petrophysics 2007, all rights reserved

5. The natural hierarchal order for subsurface data integration by Phil Holbrook Ph.D. The data are from regional porosity permeability studies. Scalar Permeability is a second and third order continuous function of average non-clay mineralogy and fractional shale volume. copyright Force-Balanced Petrophysics 2007, all rights reserved

6. The natural hierarchal order for subsurface data integration by Phil Holbrook Ph.D. Permeability is actually a mixed second and third order vector not an isotropic scalar. Measurement errors in cements contribute significantly to the scatter of data. High clay volume often dominates local fluid flow. copyright Force-Balanced Petrophysics 2007, all rights reserved

7. The natural hierarchal order for subsurface data integration by Phil Holbrook Ph.D. The inherent accuracy of the first order variables is about three (3) significant figures. –Porosity ranges from about 2 to 85 PU when mineral grains are in proximity. –Bulk densities range from 1.55 to 3.00 g/cc –Conductivity ranges from 5 to 2000 mhos – t p ranges from 22 to 500 microseconds/foot for natural mineral and fluid mixtures. Out of range data are replaced with null codes so that sensor errors do not propagate. The inherent accuracy of second and third order variability is about two (2) significant figures. copyright Force-Balanced Petrophysics 2007, all rights reserved

8. These four sensor specific data types are sensitive to mineralogy and porosity. Each sensor has an allowable range for clay bearing sedimentary rocks. A null code is inserted for data that is either out of range or the sensor is missing. The criteria for each sensor are different. The raw Gamma Ray sensor is sensitive to Potassium, Radium and Thorium. The deep sensing (isotropic Rt) Resistivity sensor The Density (grams/cc) The Sonic interval transit time P wave (isotropic or minimum) TVD raw -Ray Resistivity Density Sonic ttp (feet) (AAPI) (ohm-meters) (g/cc) (msec/ft) 7645.00 64.72.700 -99.250 318.5 7646.00 58.27.620 -99.250 318.3 7647.00 56.18.780 -99.250 -99.3 7648.00 57.21.790 -99.250 477.7 7649.00 49.66.790 -99.250 347.3 7650.00 55.94 -99.250 -99.250 347.3 7651.00 51.59 -99.250 -99.250 341.0 7652.00 48.87 -99.250 -99.250 414.0 7653.00 51.48.700 -99.250 545.9 7654.00 59.57.680 -99.250 318.3 7655.00 50.52.680 -99.250 305.2 7656.00 47.93.570 -99.250 318.3 7657.00 62.80.720 -99.250 51.0 continuous log with a probable unconformity 7658.00 53.13.790 -99.250 58.3 7659.00 56.58.560 -99.250 79.9 7660.00 56.98 1.320 -99.250 91.8 7661.00 62.69.810 -99.250 37.5 7662.00 57.13.580 -99.250 -99.3 7663.00 49.60 -99.25 -99.250 -99.3 7664.00 48.82.640 -99.250 57.4 7665.00 45.36.630 -99.250 44.8 7666.00 48.11.610 -99.250 -99.3 7667.00 45.58.640 -99.250 -99.3 7668.00 56.57.610 -99.250 229.6 long data gap 14401.00 76.80.410 -99.250 35.0 14402.00 78.11.410 -99.250 -99.3 14403.00 77.42.430 -99.250 -99.3 14404.00 77.15.460 -99.250 37.2 14405.00 78.38.480 -99.250 36.1 14406.00 75.42.470 -99.250 -99.3 14407.00 72.07.420 -99.250 -99.3 14408.00 83.48.420 -99.250 35.7 14409.00 79.53.400 -99.250 35.4 The Force Balanced GRPD program filters null data before processing. Short gaps are subsequently replaced with interpolated data. The sensor output data fields are a most compact ASCII file format having four significant figures. The Density sensor was missing from this dataset causing no serious problems! copyright Force-Balanced Petrophysics 2007, all rights reserved

9. standard Force Balanced ASCII file program output format Short data gaps are interpolated so that when parameters are calculated from multiple sensors, the output is continuous. Depth Pore P Frac P Ovrbdn EffStv Ov-PP Vshl Poros Perm tt p rhob HC ql (feet) (ppg) (ppg) (ppg) (ppg) (ppg) (frac) (frac) (frac) (log 10 ) (ms/ft) (g/cc) (1-Sw) 7645.0 10.835 13.815 12.200 14.864 4.030.862.260 -3.987 131.2 2.285.000 7646.0 10.834 13.803 12.200 14.865 4.031.754.263 -2.878 125.1 2.273.000 7647.0 10.833 13.931 12.200 14.865 4.033.715.232 -2.971 115.2 2.322.000 7648.0 10.831 13.929 12.200 14.866 4.035.735.232 -3.136 116.3 2.322.000 7649.0 10.831 13.986 12.200 14.867 4.036.568.218 -2.077 105.8 2.336.000 7653.0 10.831 13.918 12.200 14.869 4.038.614.235 -2.139 111.4 2.310.000 7654.0 10.828 13.842 12.200 14.869 4.041.778.254 -3.223 124.2 2.289.000 7655.0 10.828 13.912 12.200 14.870 4.042.590.237 -1.954 110.8 2.307.000 7656.0 10.829 13.842 12.200 14.871 4.042.524.254 -1.286 111.9 2.276.000 7657.0 10.815 13.845 12.200 14.871 4.056.832.253 -3.772 127.3 2.295.000 7658.0 10.814 13.961 12.200 14.872 4.057.654.225 -2.559 110.5 2.330.000 7659.0 10.816 13.762 12.200 14.872 4.056.722.274 -2.457 125.7 2.255.000 7660.0 10.800 14.140 12.200 14.873 4.073.730.180 -3.815 103.4 2.407.000 7661.0 10.778 13.894 12.200 14.873 4.095.831.239 -3.946 123.6 2.317.000 7662.0 10.780 13.768 12.200 14.874 4.094.733.270 -2.596 125.5 2.261.000 7664.0 10.780 13.887 12.200 14.875 4.095.547.241 -1.614 110.1 2.298.000 7665.0 10.780 13.907 12.200 14.876 4.095.459.237 -1.106 105.5 2.301.000 7666.0 10.780 13.869 12.200 14.876 4.096.529.246 -1.431 110.3 2.289.000 7667.0 10.781 13.914 12.200 14.877 4.096.465.235 -1.162 105.4 2.304.000 7668.0 10.781 13.802 12.200 14.877 4.096.722.262 -2.610 123.0 2.273.000 7669.0 10.781 13.900 12.200 14.878 4.097.486.239 -1.255 107.0 2.300.000 Depth Pore P Frac P Ovrbdn EffStv Ov-PP Vshl Poros Perm tt p rhob HC ql (feet) (ppg) (ppg) (ppg) (ppg) (ppg) (frac) (frac) (frac) (log 10 ) (ms/ft) (g/cc) (1-Sw) 9017.0 9.966 14.447 13.000 15.560 5.593.918.199 -5.495 118.4 2.419.000 9018.0 9.947 14.483 13.000 15.560 5.613.877.192 -5.096 113.9 2.425.000 9019.0 9.933 14.532 13.000 15.561 5.627.777.183 -4.195 106.2 2.428.000 9020.0 9.916 14.575 13.000 15.561 5.645.925.175 -5.917 119.6 2.460.710 9021.0 9.891 14.593 13.000 15.562 5.670.898.171 -5.633 118.4 2.463.734 9022.0 9.865 14.601 13.000 15.562 5.698.831.169 -4.919 117.8 2.457.744 9023.0 9.834 14.560 13.000 15.563 5.729.869.175 -5.235 119.7 2.452.699 9024.0 9.818 14.481 13.000 15.563 5.745.924.188 -5.721 115.9 2.438.000 9025.0 9.801 14.478 13.000 15.564 5.763.916.188 -5.610 115.3 2.436.000 Depth Pore P Frac P Ovrbdn EffStv Ov-PP Vshl Poros Perm tt p rhob HC ql (feet) (ppg) (ppg) (ppg) (ppg) (ppg) (frac) (frac) (frac) (log 10 ) (ms/ft) (g/cc) (1-Sw) (10258.0 11.722 15.293 13.200 16.084 4.362.916.181 -5.710 113.4 2.475.000 10259.0 11.805 15.259 13.200 16.084 4.279.955.193 -6.098 119.5 2.463.000 10260.0 11.638 15.327 13.200 16.085 4.447.856.170 -5.152 118.2 2.482.751 10261.0 11.586 15.301 13.200 16.085 4.499.959.174 -6.423 119.5 2.496.737 10262.0 11.601 15.294 13.200 16.086 4.485.994.177 -7.104 120.1 2.504.730 10263.0 11.496 15.353 13.200 16.086 4.590.948.160 -6.452 115.0 2.519.819 10264.0 11.443 15.351 13.200 16.087 4.643.937.159 -6.303 114.6 2.518.822 10265.0 11.719 15.092 13.200 16.087 4.368.953.228 -5.588 129.3 2.403.000 10266.0 11.645 15.106 13.200 16.087 4.442.932.221 -5.379 125.6 2.411.000 copyright Force-Balanced Petrophysics 2007, all rights reserved

10. standard Force Balanced ASCII file program output format Depth Pore P Frac P Ovrbdn EffStv Ov-PP Vshl Poros Perm tt p rhob HC ql (feet) (ppg) (ppg) (ppg) (ppg) (ppg) (frac) (frac) (frac) (log 10 ) (ms/ft) (g/cc) (1-Sw) (10567.0 11.573 15.419 13.200 16.206 4.634.885.170 -5.491 108.5 2.494.000 10568.0 11.517 15.396 13.200 16.207 4.690.937.173 -6.111 112.5 2.500.000 10569.0 11.511 15.399 13.200 16.207 4.696.984.172 -6.920 118.8 2.515.647 10570.0 11.400 15.406 13.200 16.208 4.808.943.167 -6.275 117.1 2.512.685 10571.0 11.354 15.424 13.200 16.208 4.854.921.161 -6.051 115.5 2.516.724 10572.0 11.759 15.122 13.200 16.208 4.449 1.000.244 -6.471 140.8 2.399.000 Depth Pore P Frac P Ovrbdn EffStv Ov-PP Vshl Poros Perm tt p rhob HC ql (feet) (ppg) (ppg) (ppg) (ppg) (ppg) (frac) (frac) (frac) (log 10 ) (ms/ft) (g/cc) (1-Sw) 12278.0 13.231 16.011 14.200 16.759 3.527.986.212 -6.423 128.2 2.489.000 12279.0 13.156 16.041 14.200 16.759 3.603.979.199 -6.437 123.6 2.508.000 12280.0 13.076 16.075 14.200 16.759 3.683.985.186 -6.760 123.0 2.535.556 12281.0 13.100 16.071 14.200 16.760 3.660 1.000.188 -7.232 123.7 2.542.543 12282.0 13.117 16.049 14.200 16.760 3.643 1.000.195 -7.136 125.8 2.529.000 12283.0 13.001 16.065 14.200 16.760 3.759.972.185 -6.500 122.7 2.531.557 12284.0 13.023 16.060 14.200 16.761 3.737.998.187 -7.111 123.5 2.540.546 12285.0 13.007 16.049 14.200 16.761 3.755.992.190 -6.893 124.2 2.532.511 12286.0 12.877 16.058 14.200 16.762 3.884.943.181 -6.088 121.5 2.527.590 12287.0 12.942 16.040 14.200 16.762 3.820.986.189 -6.743 121.5 2.530.000 12288.0 12.877 16.036 14.200 16.762 3.886.966.187 -6.360 118.7 2.524.000 Depth Pore P Frac P Ovrbdn EffStv Ov-PP Vshl Poros Perm tt p rhob HC ql (feet) (ppg) (ppg) (ppg) (ppg) (ppg) (frac) (frac) (frac) (log 10 ) (ms/ft) (g/cc) (1-Sw) 12812.0 13.953 16.235 14.400 16.900 2.946.966.226 -5.844 130.0 2.469.000 12813.0 13.764 16.313 14.400 16.900 3.136.972.187 -6.470 119.3 2.540.000 12814.0 13.481 16.357 14.400 16.901 3.420.926.159 -6.142 114.8 2.572.765 12815.0 13.373 16.409 14.400 16.901 3.528.963.140 -6.955 108.8 2.620.879 12816.0 13.316 16.447 14.400 16.901 3.586.924.127 -6.559 104.8 2.628.917 12817.0 13.465 16.295 14.400 16.902 3.436.946.176 -6.195 114.1 2.547.000 12818.0 13.266 16.315 14.400 16.902 3.636.916.161 -5.985 115.5 2.564.739 12819.0 13.228 16.303 14.400 16.902 3.674.931.163 -6.153 116.0 2.566.735 12820.0 13.066 16.359 14.400 16.903 3.836.898.142 -6.022 109.4 2.593.855 12821.0 13.031 16.233 14.400 16.903 3.872.821.173 -4.754 105.8 2.518.000 12822.0 12.881 16.315 14.400 16.903 4.022.802.146 -4.934 110.8 2.560.825 12823.0 12.892 16.018 14.400 16.904 4.011.714.221 -3.109 133.7 2.281.925 12824.0 12.904 16.021 14.400 16.904 4.000.715.221 -3.125 133.7 2.281.896 12825.0 12.897 16.145 14.400 16.904 4.008.837.190 -4.694 111.0 2.494.000 12826.0 12.706 16.395 14.400 16.904 4.198.752.121 -4.820 103.2 2.592.921 Depth Pore P Frac P Ovrbdn EffStv Ov-PP Vshl Poros Perm tt p rhob HC ql (feet) (ppg) (ppg) (ppg) (ppg) (ppg) (frac) (frac) (frac) (log 10 ) (ms/ft) (g/cc) (1-Sw) 13114.0 13.278 16.475 14.800 16.976 3.698.935.136 -6.587 101.8 2.623.000 13115.0 13.359 16.386 14.800 16.977 3.618.940.163 -6.282 109.9 2.575.000 13116.0 13.184 16.588 14.800 16.977 3.793.944.103 -7.166 97.5 2.685.935 13117.0 13.119 16.561 14.800 16.978 3.859.939.108 -7.016 99.1 2.673.917 13118.0 13.048 16.513 14.800 16.978 3.930.956.118 -7.144 102.3 2.662.876 13119.0 12.972 16.435 14.800 16.978 4.007.935.136 -6.590 101.8 2.623.000 The HC ql cutoff is very accurate at defining producible Hydrocarbon feet. Hydrocarbon interference with calculated porosity from resistivity had negligible effect even though the Density sensor was missing! Copyright Force Balanced Petrophyics(2007) all rights reserved

11. The natural hierarchal order for subsurface data integration by Phil Holbrook Ph.D. All eleven (11) standard output fields are calculated from the first order plastic mechanical system. Fluid hydrocarbon effects on the resistivity (R t ) sensor have little effect on calculated porosity, bulk density, or overburden. A water saturation cutoff of 15% seems to be very accurate at defining probable producible hydrocarbon intervals. Continuous traces of all natural variables are calculated; The accuracy of the second and higher order function can be improved by using additional sensor input data. A physically representative reservoir or basin model can be constructed from these eleven standard parameters. First order –Pore fluid pressure, Bulk Density, –Overburden, Fracture propagation pressure, –fractional shale volume, fractional porosity. Second and higher order –water permeability, liquid hydrocarbon feet, –P wave transit time. copyright Force-Balanced Petrophysics 2007, all rights reserved

12. Each Tectonic Regime has a two dimensional Plane of Symmetry that includes the vectors Gravity, minimum, and Maximum horizontal stress. The three positive integer stress multipliers are symmetrical about the positive scalar mean of two ! copyright Force-Balanced Petrophysics 2007, all rights reserved

13. . Gravity (S vertical ) is a principal stress and first order variable in the earths sedimentary crust! The vectorial stresses around a borehole are a second and third order function of the far field stresses. At minimum energy the far field vector and scalar forces in the earth can be summarized on two dimensional planes! The natural hierarchal order for subsurface data integration by Phil Holbrook Ph.D.

14. The [Stress/Strain] limits of natural mineral mixtures. copyright Force-Balanced Petrophysics 2007, all rights reserved These limits explain the [Stress/Strain] hysteresis involved in the calibration of non- elastic unloading. This causes reservoir compaction to lag and limits fluid expansion pore pressure regimes.

15. The Elastic Wave Field depends on Rock, Mineral and Fluid cross-field terms. The Vp 2 and Vs 2 axes are related to mineral and fluid coefficients that are shown on this two dimensional plane. The elastic mechanical systems relationships shown are continuous from 0% to 100% porosity. A symmetrical fluid - mineral lever rule governs two phase mixing. copyright Force-Balanced Petrophysics 2001, all rights reserved

16. This synthesis of Physical Laws has the fewest possible coefficients. They are mineral and fluid physical properties. copyright Force-Balanced Petrophysics 2002, all rights reserved

18. Western Australia well planning log showing loading and un-loading limb pore pressure regimes with respect to the fluid expansion caprocks peak loading limb point.

19. Real- time Unloading- limb pore pressure log example

21. Two books and the website Force-Balanced.net explain Deterministic Earth Mechanical Science. These books can be ordered from the author, the SPE online store, Amazon, or other book distributors.

22. . The natural hierarchal order for subsurface data integration by Phil Holbrook Ph.D. Diverse data types are most easily integrated by following natures hierarchal order. The earth is almost entirely composed of natural mineral and fluid molecules. Secondary i.e. textural variability is superimposed on nine (9) interdependent primaries. Permeability, water saturation, and interval transit time are the most important secondary parameters. One can reliably build upon the Balanced Forces in the Earth.

23. . The universe may be (n) dimensional. At minimum energy, the forces in the three (3) dimensional earth can be quantified on symmetrical two dimensional planes without loss of mechanical information! The natural hierarchal order for subsurface data integration by Phil Holbrook Ph.D.

24. Deterministic Earth Mechanical Science builds upon Minimalist Earth Mechanical Theory.