Definitions

  • shale is compressed after the migration of oil and becomes Cap rock

Reservoir

in general terms means a pool or an accumulation of petroleum in porous rock formations buried several feet underground or subsurface.

Steps of Reservoir formation

  1. Sedimentation
  2. Turning into hydrocarbons and migration
  3. entrapment

Reservoir types based on rock

Sandstone
  • 60% of reservoirs
  • low storage and production
  • Quartz ()
  • average
  • no fractures
  • water wet
Carbonates
  • 39% of reservoirs
  • high storage and production
  • 60% of oil and 40% of gas in the world
  1. limestone
    • Calcite ()
    • low
    • higher
    • usually oil wet
  2. dolomite
    • dolomite ()
    • average
    • high
    • usually oil wet

Rock

from the standpoint of a reservoir means the natural container that contains or holds the petroleum spread out in tiny pore spaces of the rocks

Fluid

it generally means anything that flows from point A (subsurface location) to B (surface location) under a certain gradient and includes gaseous or liquid hydrocarbons.

The petroleum reservoir rock together with fluids makes up a system, which has a certain areal extent and depth and exists at given pressure and temperature conditions, which is explored and exploited commercially for production of petroleum.

Coring

Coring methods

  1. Rotary method
    • In this method a special kind of hollow bit is used that has a core catcher and a core barrel
    • After drilling the end of the core is caught by the core catcher and using a the core is separated from the formation using tension.
    • To stop the change of saturation because of pressure drop a sponge core barrel is used.
    • This method gives a whole core.
  2. Sidewall coring
    • cheaper compared to rotary method
    • in this method a hollow cylindrical core barrels (bullets) are shot into the formation and it gives core plugs. upsides:
      1. can be used after drilling (the most important upside)
      2. can be used while doing electric logs downsides:
      3. bullets can be lost or malfunction
      4. formation damage
      5. the exact depth of the sample is unknown

Core types

  1. Whole core A whole core sample is basically a complete section of a conventionally drilled core from a given formation. The advantage of whole core analysis is that it measures properties on a larger scale, somewhat closer to that of the reservoir.
  2. Core plug A core plug sample refers to a much smaller portion or subsample of the whole core sample. A core plug sample is obtained by cutting cylindrical plugs of typically 1 or 1.5 in. in diameter and of lengths up to 3 in., from a whole core.

points about whole core and core plug

  • whole core gives a better representation of complex lithology
  • in homogenous rocks it’s better to get a core plug but in heterogeneous rocks like carbonates it’s not.
  • in low porosity formations, the porosity from plug is higher that of the whole core.

Diagrams of core types And the applications of cores

Core analysis

Core analysis is generally categorized into two groups: routine or conventional core analysis or RCAL and special core analysis or SCAL.

  1. RCAL Routine core analysis generally refers to the measurement of porosity, grain density, horizontal permeability (absolute), fluid saturations, and a lithologic description of the core.
  2. SCAL Any laboratory measurements, either on whole cores or core plugs, that are not part of routine core analysis generally fall under the category of SCAL. Probably the most prominent SCAL tests are two-phase or three-phase fluid flow or displacement experiments in the formation rock sample, from which reservoir engineering properties such as relative permeability, wettability, and capillary pressure are determined.

Porosity

porosity is the ratio of the pore volume (or void space) in a reservoir rock to the total volume (bulk volume) and is expressed as a percentage.

Types of porosities

  1. Total or Absolute porosity The total or absolute porosity is the ratio of the total void space in the reservoir rock to the total or bulk volume of the rock:

Therefore, a reservoir rock may have a very high total porosity and no conductivity to fluids residing in the pores due to the lack of interconnectivity. As a result, petroleum reservoir fluids may remain trapped inside the isolated pore spaces and hence immobile or unrecoverable

  1. Effective porosity The effective porosity is defined as ratio of the volume of interconnected pores and the dead end or cul-de-sac pores to the total or bulk volume: From a reservoir engineering standpoint, effective porosity is significant as it is used in all calculations because it represents the pore space that is occupied by mobile recoverable hydrocarbon fluids.

  2. Ineffective porosity Ineffective porosity is defined as the ratio of the volume of isolated or completely disconnected pores to the total or bulk volume:

In summary, generally, for poorly or moderately well-cemented material, the total porosity is approximately equal to the effective porosity; however, for highly cemented material, significant differences between the total and effective porosity can occur, as high degree of cementation may completely isolate or disconnect some pores.

Classification of porosity

rock porosity can be generally classified by the mode of origin, as either original (primary) or induced (secondary).

  1. Original Original porosity resembles a native porosity, that is, developed in the deposition of the material.
  2. Induced Induced porosity is developed by some geological process following the deposition of the rock.

A common example of induced porosity is the development of fractures or vugs commonly found in limestones (carbonates). sandstones commonly have a primary porosity.

Parameters that influence porosity

Many factors affect the porosity of reservoir rocks including grain size, grain shape, sorting, clay content, compaction, dolomitization, and cementation.

types of sorting

  1. Cubic
  2. Hexagonal
  3. Rhombohedral

Petroleum reservoirs have a range of porosity between 5-30% and most common range is 10-20%

  • 0-5% negligble
  • 5-10% poor
  • 10-15% fair
  • 15-20% good
  • >20% very good

Measurement of porosity

A given reservoir rock sample basically comprises three different volumes: bulk volume (BV), pore volume (PV), and grain volume (GV). These three volumes are related by the following simple relationship:

Therefore, in the laboratory measurement of porosity, it is necessary to determine only two of the three volumes: BV, PV, or GV.

Immersion method (Archimedes method)

Calculating bulk volume using Mercury Pycnometer

We can find the bulk volume using the displaced mercury from the dry sample, we can divide the mass of displaced mercury by it’s density and get the bulk volume.

Helium Porosimeter (Boyle’s method)

The use of helium in the determination of porosity has certain obvious advantages over other gases and liquids: Helium is a clean inert gas and does not cause any unwanted rock–fluid interactions that may affect/change the original porosity; molecules are small that can rapidly penetrate the small pores, and it can be considered an ideal gas (compressibility factor = 1) for pressures and temperatures usually employed in the procedure. All helium porosimeters actually employ the principles of Boyle’s law, that is, PV = constant, where P is the pressure and V the volume, for the determination of porosity of rock samples.

In principle, the apparatus consists of two equal-volume chambers or cells called the reference chamber and the sample chamber. The reference chamber has a volume V1 at initial pressure P1 (usually 100 psig), and the sample chamber has an unknown volume V2 and initial pressure P2 (normally atmospheric). The system is then brought to equilibrium by opening the valve to the sample chamber, allowing the determination of the unknown volume V2 by noting the resultant equilibrium pressure P. The application of Boyle’s law allows the equalization of pressures (for isothermal conditions) before and after the opening of the valve to the sample chamber, as per the following equations:

Vacuum Saturation

The method uses a large enough vacuum flask or a beaker, filled with a degassed liquid, normally water, in which dry rock samples are placed. Subsequently, as soon as the evacuation of the vacuum flask is initiated, air bubbles are seen in the saturating liquid as it replaces air from the pore spaces of the rock samples. The disappearance of the air bubbles gives an indication that the saturation is complete and at this point the evacuation is terminated, and porosity is calculated as follows:

x-ray computerized tomography or x-ray CT scanning

  • the CT scanner for porosity measurement involves imaging the core plug sample when it is clean and dry and then when it is fully saturated with either oil or water.
  • The image of the clean sample is then subtracted from that of the saturated sample to obtain porosity.
  • Scanning process is carried out slice by slice, and porosity is determined for each of the slices.
  • Various images that are obtained by a CT scanner have a characteristic CT number expressed in Hounsfield units
  • This CT number is actually a normalized value of the calculated x-ray absorption coefficient of a pixel Oil-saturated rock

Water-saturated rock

Air-saturated rock

Porosity for each slice

example

Liquid Saturation by Other Methods

The other methods of introduction of a liquid into the pore spaces of a rock sample include forced saturation by either water or synthetic oil. The rock sample is held in a special device called a core holder, and a given liquid is injected through the sample by use of a pump. This method, however, requires advanced apparatus called a core flooding rig or a displacement apparatus.

Grain Volume Measurement

All methods measuring grain volume usually yield total or absolute porosity, simply because the rock samples are normally crushed for grain volume measurements which actually destroy all pores, thus resulting in total porosity as grain volume is subtracted from the bulk volume. Although only the effective pore space has direct application in most reservoir engineering calculations, knowledge of the magnitude and distribution of the isolated pore spaces can reveal other characteristics of reservoir rocks. Grain volume of rock samples is sometimes calculated from dry sample weight and knowledge of average density.

Steven’s method (gas expansion method)

if we read air volume in multiple steps

Averaging of porosity

  • properties that are measured as part of the routine core analysis must be averaged and scaled up from the core scale to the reservoir scale
Types of averaging
  1. Arithmetic average

  1. Thickness-weighted average

  1. Areal-weighted average

  1. Volumetric-weighted average,

where

  • is the total number of core samples
  • is the thickness of core sample i or reservoir area i
  • is the porosity of core sample i or reservoir area i
  • is the reservoir area i

Fluid Saturation

  • fluid saturation or pore space saturation actually quantifies how much of core available capacity actually does contain various fluid phases
  • initial fluid saturations defined as fractions of the pore space occupied by gas, oil, and water

Saturation of gas

Saturation of oil

Saturation of water

Special Types of Fluid Saturations

  1. Critical gas saturation
  2. Residual oil saturation
  3. Irreducible water saturation
Critical gas saturation
  • Due to this high pressure, hydrocarbon gas is normally dissolved in the liquid phase.
  • Because production from a petroleum reservoir is initiated, the reservoir pressure begins to decrease, while the reservoir temperature generally remains constant.
  • The steadily declining reservoir pressure results in the evolution of a gas phase (gas saturation increases from 0) when pressure falls below a certain solubility limit, known as bubble point pressure.
  • Subsequently, the saturation of the gas phase increases as the depletion of reservoir pressure continues.
  • This gas phase, however, remains immobile or is trapped until its saturation exceeds a certain saturation value, called critical gas saturation and denoted by
  • The gas phase then begins to move above this critical gas saturation. The entire process is attributed to the physical process of the gas phase becoming continuous through the system in order to flow.
Residual oil saturation
  • Residual oil saturation generally is denoted by , and is basically the oil that remains in the pore space after a certain displacement process.

Irreducible water saturation
  • The terms irreducible water saturation, connate water saturation, and critical water saturation, generally denoted by (or ), are extensively used interchangeably to define the water saturation at which the water phase remains immobile.
  • To understand the concept of irreducible water saturation, first consider an idealized petroleum reservoir showing gas, oil, and water distribution, as shown in this figure
  • The fluids in most petroleum reservoirs, shown in the figure, have reached a state of equilibrium and have become somewhat separated as per their densities, that is, gas on top followed by the oil phase, and underlain by water.
  • It is believed that in most hydrocarbon-bearing formations, the rock was fully saturated with water prior to the invasion and trapping of hydrocarbons.
  • However, due to the competition between capillary and gravity forces, during this migration process, complete gravity segregation between the fluid phases never takes place and the connate water is distributed throughout the gas and oil zones, as shown in the figure.
  • The water in these zones is reduced to some irreducible minimum that is nothing but the irreducible water saturation, .
  • A range of 20%–40% in irreducible water saturation in petroleum reservoirs is rather common; however, values ranging from as low as 5% to those as high as 60% (depending on the capillary properties of rocks) have also been reported for some North Sea chalk reservoirs.

Saturation Averaging

where is gas, oil, or water refers to the subscript for any individual measurement represents the depth interval to which and apply

Absolute Permeability

  • the petroleum reservoir fluids contained in the pore spaces of reservoir rock have to flow so that they can be produced or brought to the surface from the reservoir. This particular property of a reservoir rock, denoted by , is called permeability.
  • Unlike porosity, which is a static property of the porous medium, permeability is basically a flow property (dynamic) and therefore can be characterized only by conducting flow experiments in a reservoir rock.

Absolute permeability

or, simply, permeability of the porous medium, that is, when a reservoir rock is 100% saturated with a given fluid.

absolute permeability is a property of the rock alone and not the fluid that flows through it, provided no chemical reaction or undesired interaction takes place between the rock and the flowing fluid.

Absolute permeability has been variously defined as follows:

  • The measure of specific flow capacity of a rock
  • The measure of the capacity of the porous medium to transmit fluids
  • The measure of the fluid conductivity of a particular porous medium
  • The ability to flow or transmit fluids through a rock that is fully saturated with a single-phase fluid
  • The measure of the reciprocal of the resistance the porous medium offers to fluid flow
  • The proportionality constant between the fluid flow rate and the applied pressure gradient

Darcy’s law

where: volumetric flow rate permeability viscosity the cross-sectional area pressure length

under the following assumptions:

  • The core plug is 100% saturated with the flowing fluid
  • The flowing fluid is incompressible
  • The flow is horizontal, steady state, and under the laminar regime.
  • The flow of fluid through the porous medium takes place under viscous regime (i.e., the rate of flow is sufficiently low so that it is directly proportional to the pressure differential or the hydraulic gradient).
  • The flowing fluid does not react with the porous medium (i.e., no fluid–rock interactions) because it may alter the characteristics of the porous medium, thereby changing its permeability as flow continues. we can rearrange by integrating and get the following equation:

this equation is commonly known as Darcy’s law and is extensively used in petroleum engineering calculations for determining the absolute permeability of a reservoir rock. this equation represents a combination of the following:

  • The property of the porous medium or the reservoir rock is represented by , the absolute permeability.
  • The property of the fluid is represented by , its viscosity.
  • The geometry of the porous medium is represented by and , or as a combined effect by the ratio of .
  • The fluid flow characteristics are represented by , , and . This shows that that the absolute Permeability is entirely a property of a porous medium and is independent of the properties of the flowing fluid.

Flow Velocity

Free flow

Flow under head

Vertical flow upward with head

Darcy’s law in field units

where

  • = volumetric flow rate,
  • = absolute permeability of the rock, millidarcy ()
  • = cross-sectional area in the flow direction,
  • = inlet pressure,
  • = outlet pressure,
  • = fluid viscosity,
  • = length of rock,
Darcy’s law for inclined flow

Darcy’s law for radial flow

where:

  • is the pressure at drainage radius,
  • is the flowing pressure,
  • is the drainage radius,
  • is the well-bore radius,

Dimensional analysis of Darcy’s law

Averaging or permeabilities

Parallel flow

or by cross section

Series flow

or

Permeability of fractures

in porous space: in field units:

Permeability of channels

in porous space: in field units:

Types of permeability

  1. Absolute permeability
    • when
    • a function of rock properties
    • calculated through Darcy’s law
  2. Effective permeability
    • when two or more phases
    • a function of: 1. Saturation 2. rock properties 3. fluid properties
  3. Relative permeability

Measurement of absolute permeability using gases

in most cases for measuring permeability instead of liquids, dry gasses (Air, Nitrogen, Helium) are used. Because gases are more accessible and fill through all pores and don’t change the properties of the rock. A low flow rate is used to have a laminar flow, because the Darcy’s equation doesn’t work for high flow rates. On the other side, because of the compressibility of gasses, the volumetric flow rate changes with pressure. Therefore, in Darcy equation, we should use a flow in average pressure to reduce the effect of compressibility.

Using Boyle’s law: and are the inlet and outlet flow rates.

The Darcy equation can be expressed in terms of the average gas flow rate to account for gas expansion in the sample: the flow rate is normally measured at the outlet of the core plug, . or

Klinkenberg’s effect

Another artifact associated with the use of gases for absolute permeability measurement is the higher permeability value obtained in comparison to the liquid flow for the core sample. Klinkenberg first reported this particular artifact when he discovered that there were variations in the absolute permeability as determined using gases as the flowing fluid from those obtained when using nonreactive liquids.

  • Klinkenberg’s observations showed increasing permeability as a function of increasing reciprocal mean pressure when hydrogen, nitrogen, and carbon dioxide were used.
  • It was due to a phenomena called gas slippage that occurs when the diameter of the capillary openings approaches the mean free path of the gas.
  • The gas slippage phenomenon is sometimes also called the Klinkenberg effect.
  • The Klinkenberg effect is a function of the gas with which permeability of a core sample is determined because the mean free path of the gas is a function of its molecular size and kinetic energy. A straight line is obtained for all gases when gas permeabilities are plotted as a function of reciprocal mean pressures.
  • Lower molecular weight, higher slope and higher slippage effect.
  • The straight lines for all gases, when extrapolated to an infinite mean pressure or zero reciprocal mean pressure, that is, , intersect the permeability axis at a common point. This common point is designated as a Klinkenberg-corrected or equivalent liquid permeability because gases tend to behave like liquids at such high pressures. where: is the measured gas permeability is the equivalent liquid permeability or the Klinkenberg-corrected liquid permeability. is the slope of the straight-line fit mean pressure

Since the slippage effect causes the gas to flow faster:

Factors affecting absolute permeability

  1. Rock related factors
    • structure
    • grain size
    • shape
    • clay cementing
  2. Artificial factors The type of fluid medium (i.e., gas/brine/water) used for permeability measurement as well as the physical and chemical characteristics of these fluids are also major factors that affect the absolute permeability.
  3. Thermodynamic factors The thermodynamic factors affecting absolute permeability basically consist of temperature effects.
  4. Mechanical factors The mechanical factors are related to the effect of mechanical stresses or confining pressures on absolute permeability and also fall under the category of laboratory artifacts.

Mechanical and Electrical Properties of Reservoir Rocks

Mechanical properties

The determination of mechanical properties of reservoir rocks falls under a specialized area called rock mechanics, which includes the study of strength properties of rocks.

Stress (تنش)

Stress, , refers to the force applied to a rock that tends to change its dimensions. The external force applied to a rock is normally referred to as load.

  • Reservoir rock stresses are usually in the range of megapascals. The three basic recognized stress conditions are:
  1. Tensile
  2. Compressive
  3. Shear The ability of a rock material to react to compressive stress or pressure is called rock compressibility.

Strain (کرنش)

Strain, commonly denoted by ɛ, is the relative change in shape or size of a rock due to externally applied forces (i.e., stress). In other words, strain is a measure of the deformation of a material when a load is applied. For example, consider a core plug of original length that has been subjected to tensional stress. After applying the stress, if the original length is increased to , then the axial strain is defined as

Stress-strain relationship

In most materials, for a certain time, increase in stress results in an increase in strain, and subsequently if the stress is removed, the strain goes back to zero. In other words, if the stress is withdrawn, the material returns to its original shape and size. This is called elastic deformation or elastic strain. . However, if the stress continues to increase, it reaches the yield point, defined as a change from elastic limit to plastic deformation, which is permanent and non-recoverable.

Rock mechanics parameters

The following rock mechanics parameters are generally used to characterize the mechanical properties of reservoir rocks.

Poisson’s Ratio

If a cylindrical rock sample is subjected to stress parallel to its long axis, its length will increase and diameter will decrease, whereas under compression perpendicular to the axis, the length will decrease and the diameter will increase. These changes in the length (longitudinal) and diameter (latitudinal), respectively, are used to define an elastic constant, mathematically expressed in the form of a dimensionless ratio, known as Poisson’s ratio, denoted by:

Young’s Modulus

Young’s modulus, denoted by , is defined as the ratio of longitudinal stress, which is force () per unit area () of cross-section, to longitudinal strain and is mathematically expressed by the following equation:

Modulus of Rigidity

Modulus of rigidity or shear modulus, denoted by , is an important elastic constant simply expressed as the ratio of shear stress to shear strain:

Bulk Modulus

The bulk modulus, denoted by , represents the change in volume corresponding to the change in hydrostatic pressure and is mathematically expressed as: The ratio of and is basically nothing but the matrix compressibility, ; therefore,

Reservoir rock compressibility

As fluids are depleted from reservoir rocks, a change in the internal stress in the formation takes place that causes the rocks to be subjected to an increased and variable overburden load. This change in the overburden load results in the compaction of the rock structure due to an increased effective stress. This compaction results in changes in the grain, pore, and bulk volume of the rock. Out of these three volume changes, of principal interest to the reservoir engineer is pore compressibility.

Three kinds of compressibilities must be distinguished in reservoir rocks, which are:

  1. Rock matrix compressibility Rock matrix (grains) compressibility is the fractional change in the volume of the solid rock material with a unit change in pressure and is mathematically expressed as:
  2. Rock bulk compressibility Rock bulk compressibility is the fractional change in volume of the bulk of the rock with a unit change in pressure and is mathematically expressed as:
  3. pore compressibility Pore compressibility is the fractional change in the pore volume of the rock with a unit change in pressure and is mathematically expressed as or Since the rock and bulk compressibilities are considered small in comparison with the pore compressibility, the formation compressibility is the term commonly used to describe the total compressibility of the formation and is equated to : based on the previous equations and the relationship between bulk and pore volume (): The total reservoir compressibility, denoted by , is extensively used in reservoir engineering calculations and reservoir simulations defined by the following expression:

Electrical properties

All reservoir rocks are comprised of solid grains and void spaces that are occupied by the fluids of interest in petroleum reservoirs (i.e., hydrocarbon gas and oil and water). The solids that make up the reservoir rocks, except certain clay minerals, are nonconductors. Similarly, the two hydrocarbon phases, gas and oil, are also nonconductors. However, water is a conductor when it contains dissolved salts such as , , and normally found in formation reservoir water. Electrical current is conducted in water by movement of ions and can therefore be termed electrolytic conduction.

Fundamental concepts and the Archie equation

The resistivity of a given material can be defined by the following simple generalized equation: where is the resistivity expressed in is the resistance in is the cross-sectional area in is the length in

Formation factor

The most fundamental concept considering electrical properties of rocks is the formation factor , defined by Archie as where: is the resistivity (opposite of conductivity) of the rock when saturated with brine, expressed in is the resistivity (opposite of conductivity) of the saturating brine in

Tortuosity

A relationship among formation factor, porosity, and tortuosity can be developed on the basis of simple pore (capillary) models:

Generalized Humble formula

A different form of tortuosity equation is generally suggested to describe the relationship between the formation factor and porosity, known as the generalized Humble formula by introducing the cementation factor m where:

Resistivity index

In a pore space containing hydrocarbons (gas or oil), both of which are nonconductors of electricity, with a certain amount of water, resistivity is a function of water or brine saturation . For the given porosity, at partial brine saturations, the resistivity of a rock is higher than when the same rock is 100% saturated with brine. Archie determined experimentally that the resistivity factor of a formation partially saturated with brine can be expressed as: where: is the resistivity of the same rock when fully saturated with brine expressed in is the resistivity of the rock when partially saturated with brine in is the saturation exponent

The resistivity of the rock partially saturated with brine, , is also referred to as true resistivity of formation containing hydrocarbons and formation water. combining the previous equations gives a generalized relationship for water saturation: The ratio is commonly referred to as the resistivity index, . The resistivity index is equal to 1 for a fully brine-saturated rock, whereas when the rock is partially saturated with brine or hydrocarbons present. the previous equation can also be expressed in terms of the resistivity index:

Fluid Saturation

While porosity represents the maximum capacity of a reservoir rock to store fluids, fluid saturation or pore space saturation actually quantifies how much of this available capacity actually does contain various fluid phases; in other words, how is that storage capacity, pore volume, or pore space distributed or partitioned among the three typical reservoir fluid phases: gas, oil, and water (usually referred to as brine or formation water). Therefore, initial fluid saturations defined as fractions of the pore space occupied by gas, oil, and water are key factors in the determination of initial hydrocarbons in place.

Definition and mathematical expressions for fluid saturation

Generally, fluid saturation is defined as the ratio of the volume of a fluid phase in a given reservoir rock sample to the pore volume of the sample. In other words, fluid saturation is defined as that fraction or percent of the pore volume occupied by a particular fluid phase (gas, oil, or water) expressed by a generalized mathematical expression:

Laboratory measurement of fluid saturation

Fluid saturation in reservoir rocks can be determined by essentially two different approaches: direct and indirect. The direct approach involves using preserved core plug samples, The indirect method is further divided into two categories: use of some other measurement on core plug capillary pressures based on which the fluid saturations are determined and use based on traditional well-logging techniques. All the methods for measurement of original reservoir rock saturation are based on the principle of leaching that abasically refers to the process of removal of liquids from a solid. Based on the principle of leaching, two methods are devised for the determination of fluid saturation. The first method involves using heat to extract the fluids present in the pore spaces of the rock and is termed retort distillation. The second method involves using both heat and an organic solvent to extract the pore fluids and is called Dean-Stark extraction*.

Retort Distillation

The retort distillation method is a technique used to measure the fluid saturations in a core sample. Here’s how it works:

  1. Sample Preparation: The core sample is crushed and weighed before being placed in the retort.

  2. Heating: The sample is then heated, either in stages or directly to 650°C (1200°F). This process causes the fluids in the sample to vaporize.

  3. Collection: The vaporized fluids are collected, condensed, and separated. This is done by heating the sample and measuring the volumes of water and oil driven off.

  4. Measurement: The volumes of water and oil are measured directly, but corrections are needed to account for alterations in the oil. The volume of gas also is needed for accurate results. This is measured on a separate, adjacent sample by injecting mercury under pressure and measuring the volume absorbed.

  5. Saturation Calculation: The total pore volume is then the sum of the volumes of gas, oil, and water¹. The saturation of each component is the ratio of its volume to the total pore volume. Despite being a very simple and rapid technique, the retort distillation method has certain drawbacks or disadvantages.First, the rock sample is completely destroyed, and second, high temperatures are required. Using temperatures of this magnitude results in a twofold problem or error—at such high temperature, the water of crystallization within the rock is driven off, causing the water recovery values to be greater than the pore water. Secondly, high temperatures may crack and coke the oil, causing the collected oil volume to not correspond to the volume of oil initially in the rock sample. The cracking and coking of the hydrocarbon molecules, in fact, tends to decrease the liquid volume and also in some cases may coat the internal walls of the rock sample itself.

Dean-Stark extraction

The Dean-Stark extraction method is a technique used to measure the fluid saturations in a core sample. Here’s how it works:

  1. Sample Preparation: The saturated core sample is weighed.

  2. Heating: The sample is subjected to an extraction of fluids by boiling solvent. This process causes the fluids in the sample to vaporize.

  3. Collection: The vaporized water is condensed and collected in a calibrated trap. This gives the volume of water in the sample. The solvent is also condensed, then flows back over the sample and extracts the oil.

  4. Measurement: The weight of the sample is measured before and after extraction. Then the volume of oil is calculated from the loss in weight of the sample minus the weight of the water removed from it.

  5. Saturation Calculation: Saturations are calculated from the volumes. Unlike the retort distillation method, only the water saturation can be directly determined using the Dean-Stark extraction because this is the only directly measured quantity, whereas the gas and oil saturations are determined indirectly.

Let be the wet weight of the rock sample; the dry weight after Dean-Stark extraction and drying. weight of the gas (unknown), , weight of oil (unknown), weight of the water. similarly , , and are directly measured quantities, whereas can be obtained from the sample porosity and bulk volume. using these equations we can obtain the values of and from which fluid saturations are calculated by

Interfacial Tension and Wettability

When only one fluid exists in the pore spaces of a reservoir rock, only one set of forces is considered, and that is the attraction between the rock and the fluid. In any reservoir where a single fluid is present, such as an aquifer, these forces may not be that important because porosity and absolute permeability are to some extent adequate to define the characteristics of such reservoirs. However, when more than one fluid phase is present, at least three sets of active forces need to be considered; thus, for a two-fluid system, the forces for consideration are: The first set of forces to be considered is the surface forces or the interfacial tension because wettability depends on interfacial tension and capillary pressure depends on interfacial tension and wettability, whereas relative permeabilities are dependent on interfacial tension, wettability, and capillary pressure along with some other properties. This dependence can be summarized as

Interfacial and surface tension

In petroleum reservoirs, up to three fluid phases, gas, oil, and water, may coexist. All these fluid phases are immiscible at the pertinent reservoir conditions. When these immiscible fluid phases in a petroleum reservoir are in contact, these fluids are separated by a well-defined interface between gas–oil, gas–water, and oil–water pairs. This particular interface is extremely small in thickness and is typically of the order of about 10 . The term surface tension (ST) is normally used when characterizing the gas–liquid surface forces, simply because this interface is the liquid surface. However, in the case of two immiscible liquids, the term interfacial tension (IFT) is used when describing the liquid–liquid interfacial forces.

  • However, regardless of the terminology used, the physical forces that cause the boundary or surface or interface are the same.
  • Frequently, in petroleum engineering literature, these terms are used interchangeably.
  • Technically, in a petroleum reservoir that contains all the three phases— gas, oil, and water—three different IFT or ST values are of significance: gas–oil ST, gas–water ST, and oil–water IFT. To understand the concept of interfacial tension or surface tension, consider a system of two immiscible fluids, oil and water, as shown in this figure An oil or water molecule, remote from the interface, is surrounded by other oil or water molecules, thus having a resulting net attractive force on the molecule of zero as it is pulled in all directions. However, a molecule at the interface has a force acting upon it from the oil lying immediately above the interface and water molecules lying below the interface. The resulting forces are not balanced because the magnitude of forces is different (i.e., forces from above and below) and gives rise to interfacial tension. Generally, the interfacial tension of two liquids is less than the highest individual surface tension of one of the liquids. For example, for an oil–water pair, the interfacial tension is less than that of air–water, which has the highest value.

Given the earlier definition of surface or interfacial tension, it has the dimensions of force per unit length usually expressed as or and commonly denoted by the Greek symbol . Some other commonly used definitions of interfacial or surface tension include:

  • A quantitative index of the molecular behavior at the interface between gas and liquid or two immiscible liquids
  • Measure of the specific surface free energy between two immiscible phases having different composition
  • The boundary tension at an interface between a gas and liquid or between two immiscible liquids Unlike other common specific properties of fluids, such as density, boiling and freezing points, viscosity, and thermal conductivity that are properties of the main body or bulk of the fluids, interfacial tension or surface tension is the best known property of fluid interfaces.
Effect of pressure and temperature on interfacial tension and surface tension:

  • with the increase in pressure, surface tension of liquids decreases.

  • With the increase in temperature, surface tension of liquids decreases. Based of the following equation, with the increase in temperature the entropy of the surface is increased, and the tension decreased. where is the surface entropy temperature pressure surface tension

  • When IFT is 0, the forces between two liquids are the same and the liquids are miscible.

  • At pressures above the bubble point () because of all the gas being in solution, there won’t be any surface tension (ST). But the interfacial tension (IFT) between water and oil would be at its maximum value.

Laboratory measurement of interfacial tension

The experimental techniques that are used for measuring interfacial tension or surface tension are essentially identical, that is, an apparatus or experimental setup used for measuring the interfacial tension between two liquids, generally, can also be employed for conducting surface tension measurements. A variety of experimental techniques are available for the measurement of IFT or ST values and are referred to as tensiometers. In the petroleum industry, the most commonly used technique for measurement of IFT or ST of petroleum reservoir fluids is the pendant drop method. The pendant drop method involves suspending a droplet of the liquid in the companion or second-liquid phase (e.g., a droplet of heaviest liquid in the surrounding light–liquid phase) for IFT determination, whereas a liquid droplet is suspended in a companion gas or vapor phase for ST measurements. The liquid droplet is allowed to hang from a narrow tube, spout, or a syringe from its tip. The shape and size of the liquid droplet is mainly a function of the prevailing IFT or ST between the given fluid pairs. With this method, the IFT or ST values are determined from the profile (image) of the static pendant drop for a given density difference between the gas–liquid phases or the liquid–liquid phases. A video system is generally used to capture the image of the drop, subsequently dimensioned by image analysis. The IFT or ST values are calculated from the following equation: where: is the density difference between the two immiscible phases (e.g., gas–liquid or oil–water) in is the acceleration due to gravity in is the equatorial or maximum horizontal diameter of the unmagnified (or magnification corrected) droplet in is the drop-shape factor as a function of and the diameter of the droplet measured at a distance above the tip of the droplet or defined as the diameter in a selected plane. When the earlier units are used, the calculated value of will be in

Wettability

In dealing with petroleum reservoir fluids in a reservoir system, it is necessary to consider not only the surface and interfacial tension between immiscible fluid phases but also the forces that are active at the interface between the liquids and the solids (reservoir rock surface). The consideration of the interface between the liquids and the solid assumes a significant importance in reservoir engineering, simply because the petroleum reservoir fluids are ubiquitously in contact with the solid (reservoir rocks) until they are brought to the surface as part of the production process. It is the combination of all the active forces that determines the wettability of reservoir rocks. Wettability is a key parameter that affects the petrophysical properties of reservoir rocks.

Fundamental concepts of wettability

To understand the fundamental concept behind wettability, we first introduce its definitions. Wettability has been variously defined in the literature, but can be essentially summarized as:

  • The relative ability of a fluid to spread on a solid surface in the presence of another fluid, for example, water spreading more than the oil or vice versa.
  • The tendency of surfaces to be preferentially wet by one fluid phase, for example, water or oil preferentially wetting.
  • The tendency of one fluid of a fluid pair (oil–water) to coat the surface of a solid spontaneously. Considering all these definitions, it is clear that whichever way wettability is addressed, it basically means that in a multiphase situation, one of the fluid phases (oil or water) has a greater degree of affinity toward the solid surface of the reservoir rock. Thus, the tendency of a fluid phase to spread over the surface of a solid is an indication of the wetting characteristics of the fluid for the solid. The spreading tendency of a fluid can be expressed more conveniently as adhesion tension, , Adhesion tension is a function of the interfacial tension and determines the wetting tendencies of a fluid–rock system. the adhesion tension is defined by: where is the interfacial tension between the solid and the lighter fluid phase (oil in this case). is the interfacial tension between the solid and the denser fluid phase (water in this case).

The angle of contact, (measured through the denser liquid phase, water in this case), at the liquid–solid surface is also shown in this figure Obviously, the value of will range from to . By definition, the cosine of the contact angle is

combining the previous equations:

Classification of wettability

  1. Water wet In this wettability state, all pore surfaces of the rock have preference for the water phase rather than the hydrocarbon phase, and as a result of this condition, the gas and oil are contained in the centers of the pores.
  2. Oil Wet This wettability state is exactly the opposite of the water-wet state, that is, the relative positions of the hydrocarbons and water are reversed. It is believed that surface-active asphaltenic components of the oil phase cause this wetting state.
  3. Intermediate Wet The definition of intermediate wettability state from a pore level standpoint is somewhat vague in that there is some tendency for both phases (oil and water) to have preference for the rock surface; however, if that tendency is equal, then this may be termed as neutral-wetting state or considered as a special category of intermediate wettability.
  4. Fractional Wettability has been variously characterized as Dalmatian, speckled, or spotted because some of the pores are water wet, while others are oil wet, or, in other words, a portion of the rock is strongly water wet, while the rest is strongly oil wet.
  5. Mixed Wettability was proposed by Salathiel in 1973, referring to a special type of fractional wettability in which the oil-wet surfaces form continuous paths through the larger pores. Salathiel, however, states that mixed wettability he introduced should be distinguished from the fractional wettability

Measurement of Reservoir rock wettability

Reservoir wettability can be evaluated by two different groups of methods: qualitative and quantitative.

  • In qualitative methods, wettability is indirectly inferred from other measurements, such as capillary pressure curves or relative permeability curves. However, relative permeability curve methods are suitable only for discriminating between strongly water-wet and strongly oil-wet cores.
  • Quantitative methods are direct measurement methods, where the wettability is measured on actual rock samples using reservoir fluid samples and wettability is reported in terms of a certain wettability index, signifying the degree of water, oil wetness, or intermediate wetness. These direct quantitative methods include:
  • contact angle measurement (Sessile drop method)
  • the Amott test (Amott-Harvey method)
  • USBM (Centrifuge method) The contact angle measures the wettability of a specific surface, while the Amott and USBM methods measure the average wettability of a core sample.
Contact angle measurement

The determination of reservoir wettability from contact angle measurements by the sessile drop method is simple in concept. A drop of water is placed on a mineral surface in the presence of reservoir oil, and the angle through the water phase is measured. If the water drop spreads over the mineral surface, the surface is water wet and the contact angle is low; if the water drop beads up, the contact angle is high and the surface is oil wet. This situation can also be reversed, that is, a drop of oil placed on a mineral surface in the presence of formation water. A photograph of the system is subsequently taken for accurate measurement of the contact angle.

Amott Test

The Amott wettability test is the most commonly and routinely used test in core analysis for the determination of average wettability of core samples. The determination of wettability is based on the displacement properties of the oil–water–rock system. The Amott test basically comprises natural and forced displacement of oil and water from a given core sample. The test begins with a residual oil saturation in the core sample obtained by forced displacement of the oil by water. Subsequently, the test measures the average wetting characteristics of the core sample using a procedure that involves four displacement operations:

  1. Immersion of the core sample in oil to observe the spontaneous displacement of water by oil.
  2. Forced displacement of water by oil in the same system by applying a high displacement pressure.
  3. Immersion of the core sample in water to observe the spontaneous displacement of oil by water.
  4. Forced displacement of oil by water. The volume of water and oil released in the spontaneous and forced displacement steps are recorded. let:
  • be the volume of water spontaneously displaced by oil.
  • the volume of water released by forced displacement of water by oil.
  • the volume of water from spontaneous ad forced displacements.
  • the volume of oil spontaneously displaced by water
  • the volume of oil released by forced displacement of oil by water
  • the volume of oil from spontaneous and forced displacements

Based on these steps, the test results are expressed as displacement by oil ratio, , and displacement by water ratio, , respectively, defined by the following equations:

Modification of the Amott Test (Amott–Harvey Test)

Other investigators used a modification of the Amott wettability test called the Amott–Harvey relative displacement or wettability index. Unlike the Amott test, this procedure begins with oil flooding of the core sample to achieve irreducible water saturation, which is generally carried out in a centrifuge. The sequence of displacements used in the original Amott test is reversed in this case; the core sample containing irreducible water saturation is first subjected to the spontaneous and forced displacement of oil by water and then is followed by the spontaneous and forced displacement of water by oil. Based on the recorded volumes, the displacement by water and displacement by oil ratios are then calculated by the Amott method. Using these ratios, the Amott–Harvey wettability index is calculated as: This equation combines the two displacement ratios into a single wettability index that varies from +1 for complete water wetness to −1 for complete oil wetness

USBM method

The USBM test is also one of the most popularly used methods to determine the wettability of a core sample. The entire wettability test is conducted in a centrifuge apparatus. This figure shows a cross-section of the arm of a centrifuge or the centrifuge tube setup used to house the core sample, displacing fluid, and the collection of displaced fluid. The test begins by establishing the irreducible water saturation in the core plug sample. Once the sample is prepared at irreducible water saturation, wettability determination begins with the first step in which cores are placed in brine and centrifuged at incrementally increasing speeds until an effective pressure (difference between the two phase pressures) of −10 psi is reached. During the course of this first step, effective pressure and water saturation are determined at each constant speed of the centrifuge. the average water saturation is computed from the amount of oil displaced. it should be noted that the effective pressures for the brine drive are indicated by negative pressures. This distinction is made by considering that these effective pressures are the phase pressure differences between the nonwetting phase and the wetting phase, that is, in the case of brine drive, if water is considered as a wetting phase, Then , yielding a negative value. In the second and final step, the core is placed in oil and centrifuged. During this oil-drive step, oil displaces brine from the core. The water saturation and the effective pressures are calculated at each incremental centrifuge speed in a manner similar to the first step. The second step is terminated when effective pressure of +10 psi is reached. The effective pressure in this case is indicated by positive values because , again considering water as the wetting phase. After completion of these two steps, the effective pressures for both the brine drive and the oil drive are then plotted against the water saturation, identified as curve I and curve II, respectively, in this figure. In each case, the curves are linearly extrapolated or truncated if the last pressure is not exactly +10 psi. The USBM wettability index is then calculated from the ratio of the area under the two effective pressure curves according to the following equation: where: is the USBM wettability index is the area under the oil curve is the area under the brine curve

if , the core is water wet if , the core is oil wet if , the core is neutrally wet

  • The areas under the oil and the brine curves represent the thermodynamic work required for the respective fluid displacements. For instance, the displacement of a nonwetting phase by a wetting phase requires less energy than displacement of a wetting phase by a nonwetting phase.

Factors affecting wettability

Reservoir wettability is almost entirely dependent on the characteristics of the fluids involved and the lithology of the rock in question.

  • Composition of the reservoir oil
  • Composition of the brine
  • Reservoir pressure and temperature
  • Depth of the reservoir structure

Capillary pressure