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**LABORATORY DETERMINATION OF POROSITY**

RESERVOIR PETROPHYSICS LABORATORY DETERMINATION OF POROSITY

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POROSITY DEFINITION Porosity: The fraction of the bulk volume of a rock that is porous. 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 = Porosity, expressed as fraction Vb = Bulk volume of reservoir rock, ft3 Vm = Matrix volume, ft3 Vp = Pore volume, ft3 Vb = Vm + Vp

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**ROCK MATRIX AND PORE SPACE**

Matrix - non pore space; the grains of sandstone, limestone, dolomite, and/or shale Pore space - filled with fluids: water, oil, and/or gas

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**MEASUREMENT OF POROSITY**

Core samples (measure two of: Vb, Vp, or Vm) Openhole wireline logs Samples of the rock are obtained from drill cuttings or by coring. The drill cuttings are usually tiny and irregularly shaped, which limits our ability to use them. See sketches from previous lecture. Core samples are either obtained using the drilling rig with a special coring bit and barrel (whole core) or using a logging tool (side-wall coring). Whole cores are often 4 to 5 inches in diameter and are usually obtained in 30 or 60-foot segments. They are generally preferred for technical evaluation but they are also more expensive. Side-wall cores can be obtained by making an additional logging run with a special logging device. A geologist usually studies the initial logs and picks intervals where he thinks that he needs a formation sample. Side-wall cores are of less use to the engineer because they are often irregularly shaped and partially damaged (often fractured) from the side-wall coring process. Open-hole porosity measurement logs (density, neutron, and sonic) are routinely used to estimate formation porosity.

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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: Bulk volume, Vb Matrix volume, Vm (also called grain volume) Pore volume, Vp

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**Volume is an extensive property**

Fraction of volume consisting of pores or voids Fraction of volume consisting of matrix

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

These values are important for core and log analysis. Commit them to memory. Unfortunately, few rocks consist of pure components but exist as a mixture of numerous minerals of varying sizes and compositions. Therefore, one can rarely assume the matrix density and get an accurate estimate of matrix volume.

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**LABORATORY METHODS OF POROSITY DETERMINATION**

Bulk volume determinations Direct calculation 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 Vb = Bulk volume d = Diameter L = Length Most core analyses are conducted on core plugs that are cut from the whole core and are right circular cylinders. Special saws are used to cut the core plugs and their faces, so they are ready for special core analyses. Irregularly shaped cores require a different measurement. consistent units, usually cm

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**LABORATORY METHODS OF POROSITY DETERMINATION**

Bulk volume determinations Direct calculation Fluid displacement methods Gravimetric (Archimedes) methods Volumetric – in pycnometer

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**ARCHIMEDES METHOD Wsat - Wdry fluid Vp = Wdry - Wsub Vm = Vb =**

= Wsat - Wsub Vb = Archimedes principle: buoyant force is equal to the weight of the fluid displaced. Self Study: Review difference between mass and weight. Self Study: A boat containing a person and a large rock floats in a swimming pool. The level of the water is marked on the side of the pool. Then, the person throws the rock out of the boat, and it sinks to the bottom of the pool. Does the water level in the pool rise, fall or stay the same?

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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 cm3 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/cm3. Calculate the bulk volume of the sample.

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**SOLUTION - Example 1 Weight of paraffin coating, Wparaffin =**

Weight of dry core sample coated with paraffin - Weight of dry core sample Wparaffin = g = 20.0 g = 0.9 g Volume of paraffin coating = Weight of paraffin / density of paraffin Vparaffin = 0.9 g / 0.9 g/cm3 = 1.0 cm3 Bulk volume of core sample = (Bulk volume of core coated with paraffin) – (volume of paraffin) Vb = 10.9 cm3 – 1.0 cm3 = 9.9 cm3 (V = m/ρ)

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**LABORATORY METHODS OF POROSITY DETERMINATION**

To determine porosity, measure 2 of 3 basic parameters: Bulk volume Matrix volume Assume matrix (grain) density Displacement method Boyles Law Pore volume (Vm) (Vb) (Vp)

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**LABORATORY METHODS OF POROSITY DETERMINATION**

Matrix (Vm) Assume rock density based on lithology and measure dry mass Displacement methods volumetric gravimetric (see previous description) Boyle’s Law: Ideal Gas Law: R = pV/nT; valid at low pressures and high temperatures (e.g. lab conditions). R is the Universal Gas Constant. The value and units of R are determined by specification of the units of p,V, n, and T. For example, R = (psia*ft^3)/(lbmol*deg.R), and R=8.314 (Pa*m^3)/(mol*K) Boyle’s Law simply says pV is constant if nT is constant.

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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: Bulk volume 2. Matrix volume Assumed matrix (grain) density Displacement method Boyles Law 3. Pore volume (Vm) (Vb) (Vp)

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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) Volumetric - submerge particles into a liquid and observe change in liquid volume. Archimedes (gravimetric) - measure change in weight of particles submerged in liquid.

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EXAMPLE 2 SOLUTION Calculating the Matrix Volume and Porosity of a Core Sample Using the Displacement Method Bulk Volume, Vb = 9.9 cm3 Matrix Volume, Vma = 7.7 cm3 Porosity, It is total porosity.

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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 cm3. Calculate the matrix volume and the core porosity. Is this effective porosity or total porosity? (It is total porosity) Bulk Volume, Vb = 9.9 cm3 Matrix Volume, Vma = 7.7 cm3 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 cm3. Calculate the matrix volume and the core porosity. Is this effective porosity or total porosity? = 9.9 cm3 – 7.7 cm3 9.9 cm3 = 0.22

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**LABORATORY METHODS OF POROSITY DETERMINATION**

To determine porosity, measure 2 of 3 basic parameters: Bulk volume 2. Matrix volume Assumed matrix (grain) density Displacement method Boyles Law (Gas Expansion) 3. Pore volume (Vm) (Vb) (Vp)

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**MATRIX VOLUME FROM GAS EXPANSION METHOD**

Involves compression of gas into pores Uses Boyle’s law p1 = Pressure at initial conditions, psia p2 = Pressure at final conditions, psia V1 = Initial volume V2 = Final volume Consistent units

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**GAS EXPANSION METHOD TO CALCULATE Vma**

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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**GAS EXPANSION METHOD TO CALCULATE Vma**

Initial conditions P1 Core V1 With V1 known, record p1 p1 = pressure at initial conditions V1 = Volume of cell 1 Place cleaned, dried core sample in cell 2 Evacuate cell 2 Open valve Valve closed Evacuate Cell 2 Cell 1

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**GAS EXPANSION METHOD TO CALCULATE Vma**

Final conditions P1 P2 Core With V1 known, record p1 p1 = pressure at initial conditions V1 = Volume of cell 1 Place cleaned, dried core sample in cell 2 Evacuate cell 2 Open valve Valve open Cell 1 Cell 2

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**GAS EXPANSION METHOD TO CALCULATE Vma**

Vf = Volume of Cell 1 + Volume of Cell 2 - Matrix Volume of Core Vt = Volume of Cell 1 + Volume of Cell 2 Vm = Vt - Vf This method assumes that the core becomes saturated with the gas. Incomplete saturation would lead to an overestimate of the matrix volume.

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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: Bulk volume Matrix volume Pore volume (Vb) (Vm) (Vp)

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**LABORATORY METHODS OF POROSITY DETERMINATION**

Pore volume determination (Effective) Gravimetric (Archimedes) Wsat - Wdry fluid 2. Boyle’s Law: (Gas expansion) Vp =

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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, Vp = Pore volume, cm3 Wsa = Weight of core saturated with fluid, g wdry = Weight of dry core, g f = Density of saturated fluid, gm/cm Method follows Archimedes Principle: A body wholly or partly immersed in a fluid is buoyed up with a force equal to the weight of the fluid displaced by the body.

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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, Wdry = g Weight of sample saturated with water, Wsat = g Density of water (f ) = 1.0 g/cm3 Weight of saturated sample submerged in water, Wsub = g 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, Wdry = g Weight of sample saturated with water, Wsat = g Density of water, f = 1.0 g/cm3 Weight of saturated sample immersed in water, Wsat,I = g

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**EXAMPLE 3 Solution Archimedes Method of Calculating Porosity a Core Sample**

Vp = Wsat – Wdry = f 448.6 – g 1.0 g/cm3 = 21.3 cm3 Vb = Wsat – Wsub = 448.6 – g = cm3 It is effective porosity. 0.12 21.3 cm3 = 179.0 cm3

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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) This method is more difficult to apply to core samples that require a jacket or rubber sleeve such as an unconsolidated sandstone. The jacket creates experimental problems, reducing its accuracy. This method cannot be used for determining porosity under confining stress, whereas the gas expansion (Boyle’s law) method can be conducted at multiple values of confining stress.

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**LABORATORY METHODS OF POROSITY DETERMINATION**

Pore volume determination (Effective) Gravimetric (Archimedes) Wsat - Wdry fluid 2. Boyle’s Law: (Gas expansion) Vp =

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**PORE VOLUME FROM GAS EXPANSION METHOD**

Initial conditions P1 V1 Core The core plug is placed in a Hassler sleeve, making the volume of Cell 2 equal to the bulk volume. This method is a continuation of the measurement of the matrix volume and uses Boyle’s law. The experiment is set up differently to measure pore volume. Boyle’s law: Initial cell conditions: measure V1 in Cell 1 Put core in Hassler sleeve, evacuate Valve closed Cell 1 Cell 2

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**PORE VOLUME FROM GAS EXPANSION METHOD**

Final conditions P1 P2 Core Valve open Cell 1 Cell 2

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**PORE VOLUME FROM GAS EXPANSION METHOD**

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 The gas expansion method (Boyle’s law method) is probably the preferred method for measurement of core porosity, except for samples that are not perfect right cylinders or ones with large surface vugs or chips. The method is preferable for poorly consolidated samples that require a rubber sleeve or jacket. One advantage of the method is that it is accurate and reasonably fast. Another important feature is that the measurement can be made at confining pressures approximating reservoir stress conditions.

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**SUMMARY To determine porosity, measure 2 of 3 basic parameters:**

Bulk volume Matrix volume Pore volume

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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 Cores from the reservoir allow direct measurements of important reservoir properties. It is important to gather cores from a representative part of the reservoir, as reservoir properties vary horizontally and vertically. If a reservoir is known to be highly heterogeneous, many core samples will be required to describe the reservoir accurately.

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SOME KEY FORMULAS

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**CROSS BEDDING, CARRIZO SANDSTONE**

Tabular crossbedding in Carrizo Sandstone. Note diagenetic effects near boundaries of co-sets and along some laminae. Where should porosity be measured?

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