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RESERVOIR PETROPHYSICS LABORATORY DETERMINATION OF POROSITY

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Porosity: The fraction of the bulk volume of a rock that is porous. POROSITY DEFINITION Porosity is a static property – it can be measured in the absence of flow Determining effective porosity requires fluid flow to determine if pores are interconnected

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ROCK MATRIX AND PORE SPACE matrix pore space

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MEASUREMENT OF POROSITY 1.Core samples (measure two of: V b, V p, or V m ) 2.Openhole wireline logs

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LABORATORY DETERMINATION OF POROSITY Most methods use small samples (core plugs) multiple samples must be analyzed to get statistically representative results sampling technique is important often all samples are taken from “sweet spots” skewing analysis To determine porosity, measure 2 of 3 volumetric parameters: 1.Bulk volume, V b 2.Matrix volume, V m (also called grain volume) 3.Pore volume, V p

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Fraction of volume consisting of pores or voids Fraction of volume consisting of matrix Volume is an extensive property

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MATRIX DENSITIES ( m ) OF TYPICAL PURE COMPONENTS OF RESERVOIR ROCK

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LABORATORY METHODS OF POROSITY DETERMINATION Bulk volume determinations 1. Direct calculation 2. Fluid displacement methods Gravimetric Volumetric – mercury pycnometer ( a precisely calibrated bottle)

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BULK VOLUME BY DIRECT MEASUREMENT Applicable for regularly shaped cores or core plugs Calculate from core dimensions For example; volume of right circular cylinder

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LABORATORY METHODS OF POROSITY DETERMINATION Bulk volume determinations 1. Direct calculation 2. Fluid displacement methods Gravimetric (Archimedes) methods Volumetric – in pycnometer

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ARCHIMEDES METHOD W sat W sub W dry V p = W sat - W dry fluid V m = W dry - W sub fluid = = W sat - W dry W sat - W sub V b = W sat - W sub fluid

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EXAMPLE 1 Bulk Volume Calculated by Displacement A core sample coated with paraffin immersed in a container of liquid displaced 10.9 cm 3 of the liquid. The weight of the dry core sample was 20.0 g, while the weight of the dry sample coated with paraffin was 20.9 g. Assume the density of the solid paraffin is 0.9 g/cm 3. Calculate the bulk volume of the sample.

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Weight of paraffin coating, W paraffin = Weight of dry core sample coated with paraffin - Weight of dry core sample W paraffin = 20.9 g = 20.0 g = 0.9 g Volume of paraffin coating = Weight of paraffin / density of paraffin V paraffin = 0.9 g / 0.9 g/cm 3 = 1.0 cm 3 Bulk volume of core sample = (Bulk volume of core coated with paraffin) – (volume of paraffin) V b =10.9 cm 3 – 1.0 cm 3 = 9.9 cm 3 SOLUTION - Example 1 (V = m/ρ)

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LABORATORY METHODS OF POROSITY DETERMINATION To determine porosity, measure 2 of 3 basic parameters: 1. Bulk volume 2. Matrix volume Assume matrix (grain) density Displacement method Boyles Law Pore volume (Vm) (V b ) (V p )

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LABORATORY METHODS OF POROSITY DETERMINATION Matrix (V m ) 1.Assume rock density based on lithology and measure dry mass Displacement methods volumetric gravimetric (see previous description) Boyle’s Law:

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MATRIX VOLUME FROM MATRIX DENSITY Known or assumed matrix density

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APPLICABILITY AND ACCURACY OF MATRIX MEASUREMENT TECHNIQUES Known or assumed matrix density –Accurate only if matrix density is known and not assumed –Core samples are often mixtures of several components with varying matrix densities, so density must be measured

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LABORATORY METHODS OF POROSITY DETERMINATION To determine porosity, measure 2 of 3 basic parameters: 1. Bulk volume 2. Matrix volume Assumed matrix (grain) density Displacement method Boyles Law 3. Pore volume (Vm) (V b ) (V p )

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MATRIX VOLUME FROM DISPLACEMENT METHOD Reduce sample to particle size Measure matrix volume of particles by –Volumetric method –Archimedes method (gravimetric measurement)

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EXAMPLE 2 SOLUTION Calculating the Matrix Volume and Porosity of a Core Sample Using the Displacement Method

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SOLUTION - Example 2 Calculate the Porosity of a Core Sample Using the Displacement Method and Matrix Volume The core sample from Example 1 was stripped of the paraffin coat, crushed to grain size, and immersed in a container with liquid. The volume of liquid displaced by the grains was 7.7 cm 3. Calculate the matrix volume and the core porosity. Is this effective porosity or total porosity? (It is total porosity) Bulk Volume, V b = 9.9 cm 3 Matrix Volume, V ma = 7.7 cm 3 = 9.9 cm 3 – 7.7 cm cm 3 = 0.22

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LABORATORY METHODS OF POROSITY DETERMINATION To determine porosity, measure 2 of 3 basic parameters: 1. Bulk volume 2. Matrix volume Assumed matrix (grain) density Displacement method Boyles Law (Gas Expansion) 3. Pore volume (Vm) (V b ) (V p )

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MATRIX VOLUME FROM GAS EXPANSION METHOD Involves compression of gas into pores Uses Boyle’s law

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GAS EXPANSION METHOD TO CALCULATE V ma Initial conditions, with volumes of 2 cells known Place core in second cell, evacuate gas (air) from second cell Open valve

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Valve closed Cell 1 Evacuate Cell 2 GAS EXPANSION METHOD TO CALCULATE V ma Initial conditions V1V1 P1 Core

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Valve open Final conditions P2 Core Cell 1 GAS EXPANSION METHOD TO CALCULATE V ma Cell 2 P1

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GAS EXPANSION METHOD TO CALCULATE V ma V f = Volume of Cell 1 + Volume of Cell 2 - Matrix Volume of Core V t =Volume of Cell 1 + Volume of Cell 2 V m = V t - V f

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APPLICABILITY AND ACCURACY OF MATRIX MEASUREMENT TECHNIQUES Displacement method - Very accurate when core sample is crushed without destroying individual matrix grains Gas expansion method - Very accurate, especially for samples with low porosities Neither method requires a prior knowledge of core properties

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LABORATORY METHODS OF POROSITY DETERMINATION To determine porosity, measure 2 of 3 basic parameters: 1. Bulk volume 2. Matrix volume 3. Pore volume (Vm) (V b ) (V p )

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LABORATORY METHODS OF POROSITY DETERMINATION Pore volume determination (Effective) 1. Gravimetric (Archimedes) W sat - W dry fluid 2. Boyle’s Law: (Gas expansion) V p =

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PORE VOLUME FROM SATURATION METHOD Measures the difference between the weight of a core sample saturated with a single fluid and the dry weight of the core Pore volume,

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EXAMPLE 3 Archimedes Method of Calculating Porosity a Core Sample Using the gravimetric method with the following data, calculate the pore and bulk volumes and the porosity. Is this porosity total or effective? Dry weight of sample, W dry = g Weight of sample saturated with water, W sat = g Density of water ( f ) = 1.0 g/cm 3 Weight of saturated sample submerged in water, W sub = g

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EXAMPLE 3 Solution Archimedes Method of Calculating Porosity a Core Sample V p = W sat – W dry = f – g 1.0 g/cm 3 = 21.3 cm 3 V b = W sat – W sub = f – g 1.0 g/cm 3 = cm cm 3 = cm 3 =

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Applicability and Accuracy of Pore Volume Measurement Techniques Saturation (Archimedes) method –Accurate in better quality rocks if effective pore spaces can be completely saturated –In poorer quality rocks, difficult to completely saturate sample –Saturating fluid may react with minerals in the core (e.g., swelling clays)

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LABORATORY METHODS OF POROSITY DETERMINATION Pore volume determination (Effective) 1. Gravimetric (Archimedes) W sat - W dry fluid 2. Boyle’s Law: (Gas expansion) V p =

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Core PORE VOLUME FROM GAS EXPANSION METHOD V1V1 Valve closed Cell 1Cell 2 P1 Initial conditions

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Final conditions Valve open Core PORE VOLUME FROM GAS EXPANSION METHOD Cell 1Cell 2 P1 P2

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Very accurate for both high-quality (high ) and low-quality (low ) core samples Should use low-molecular-weight inert gases (e.g., helium) Measures effective (connected) pore volume PORE VOLUME FROM GAS EXPANSION METHOD

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SUMMARY 1. Bulk volume 2. Matrix volume 3. Pore volume To determine porosity, measure 2 of 3 basic parameters:

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CORES Allow direct measurement of reservoir properties Used to correlate indirect measurements, such as wireline/LWD logs Used to test compatibility of injection fluids Used to predict borehole stability Used to estimate probability of formation failure and sand production

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SOME KEY FORMULAS

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CROSS BEDDING, CARRIZO SANDSTONE

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