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

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

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

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

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

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

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

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) continuous log with a probable unconformity long data gap 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

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) 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) 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) ( copyright Force-Balanced Petrophysics 2007, all rights reserved

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) ( 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) 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) 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) 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

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

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

. 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.

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.

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

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

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.

Real- time Unloading- limb pore pressure log example

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.

. 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.

. 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.

Deterministic Earth Mechanical Science builds upon Minimalist Earth Mechanical Theory.