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Title: INTRODUCTION TO RESERVOIR ENGINEERING


1
INTRODUCTION TO RESERVOIR ENGINEERING
  • LECTURE 1

2
CLASSIFICATION OF RESERVOIRS AND RESERVOIR FLUIDS
  • Petroleum reservoirs are broadly classified as
    oil or gas reservoirs.
  • These broad classifications are further
    subdivided depending on
  • The composition of the reservoir hydrocarbon
    mixture
  • Initial reservoir pressure and temperature
  • Pressure and temperature of the surface
    production
  • The conditions under which these phases exist are
    a matter of considerablepractical importance. The
    experimental or the mathematical determinations
    of these conditions are conveniently expressed in
    different types of diagrams commonly called
    phase diagrams. One such diagram is called the
    pressure-
  • temperature diagram.

3
Pressure-Temperature Diagram
  • Figure 1-1 shows a typical pressure-temperature
    diagram of a multicomponent system with a
    specific overall composition. Although a
    different hydrocarbon system would have a
    different phase diagram, the general
    configuration is similar.
  • These multicomponent pressure-temperature
    diagrams are essentially
  • used to
  • Classify reservoirs
  • Classify the naturally occurring hydrocarbon
    systems
  • Describe the phase behavior of the reservoir
    fluid

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5
Petroleum Geology
  • LECTURE 2

6
  1. How is petroleum formed?

Petroleum is result of the deposition of plant
or animal matter in areas which are slowly
subsiding.These areas are usually in the sea or
along its margins in coastal lagoons or
marshes,occasionally in lakes or inland
swamps.Sediments are deposited along with that at
least part of the organic matter is preserved by
burial before being destroyed by decay.As time
goes on and the areas continue to sink slowly,the
organic material is buried deeper an hence is
exposed to higher temperatures and
pressures.Eventually chemical changes result in
the generation of petroleum,a complex,highly
variable mixture lf hydrocarbons.
7
2 what is trap ?
The term trap was first applied to a
hydrocarbon accumulation by Orton stocks of
oil and gas might be reapped in the summits of
folds or arches found along their wat to higher
ground .A detailed historical account of the
subsequent evolution of the concept and etymology
of the term trap is found in Dott and
Reyonlds(1969).
8
3 where can we find petroleum ?
Hydrocarbonscrude oil and natural gasare
found in certain layers of rock that are usually
buride deep beneath the surface of the earth.
9
Basic Concepts of Origin, Accumulation and
Recovery of Hydrocarbons
  • LECTURE 3

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13
Elements of Petroleum Reservoir ---fluid content
of the reservoir
  • LECTURE 4

14
Porosity and Effective Porosity
  • LECTURE 5

15
POROSITY
  • For rock to contain petroleum and later allow
    petroleum to flow,it must have certain physical
    characteristics. Obvilusly, there must be some
    spaces in the rock in which the petroleum can be
    stored.
  • If rock has openings,voids,and spaces in which
    liquid and gas may be stored,it is said to be
    porous .For a given volume of rock, the ratio of
    the open space to the total volume of the rock is
    called porosity,the porosity may be expressed a
    decimal fraction but is most often expressed as a
    percentage.For example,if 100 cubic feet of rock
    contains many tiny pores and spaces which
    together have a volume of 10 cubic feet, the
    porosity of the rock is 10.

16
  • POROSITY
  • The porosity of a rock is a measure of the
    storage capacity (pore volume)that is capable of
    holding fluids. Quantitatively, the porosity is
    the ratio of the pore volume to the total volume
    (bulk volume). This important rock property is
    determined mathematically by the following
    generalized
  • relationship
  • where f porosity

17
POROSITY
  • As the sediments were deposited and the
    rocks were being formed during past geological
    times, some void spaces that developed became
    isolated from the other void spaces by excessive
    cementation. Thus, many of the void spaces are
    interconnected while some of the pore spaces
    arecompletely isolated. This leads to two
    distinct types of porosity, namely
  • Absolute porosity
  • Effective porosity

18
  • Absolute porosity
  • The absolute porosity is defined as the ratio of
    the total pore space in
  • the rock to that of the bulk volume. A rock may
    have considerable
  • absolute porosity and yet have no conductivity to
    fluid for lack of pore
  • interconnection. The absolute porosity is
    generally expressed mathematically by the
    following relationships
  • or
  • where fa absolute porosity.

19
  • Effective porosity
  • The effective porosity is the percentage of
    interconnected pore space with respect to the
    bulk volume, or
  • where f effective porosity.

20
  • One important application of the effective
    porosity is its use in determining the original
    hydrocarbon volume in place. Consider a reservoir
    with an areal extent of A acres and an average
    thickness of h feet. The total bulk volume of the
    reservoir can be determined from the following
    expressions
  • Bulk volume 43,560 Ah, ft3
  • or
  • Bulk volume 7,758 Ah, bbl
  • where A areal extent, acres
  • h average thickness

21
Permeability and Darcys Law
  • LECTURE 6

22
  • PERMEABILITY
  • Permeability is a property of the porous medium
    that measures the capacity and ability of the
    formation to transmit fluids. The rock
    permeability, k, is a very important rock
    property because it controls the directional
    movement and the flow rate of the reservoir
    fluids in the formation. This rock
    characterization was first defined mathematically
    by Henry Darcy in 1856. In fact, the equation
    that defines permeability in terms of measurable
    quantities is called Darcys Law.
  • Darcy developed a fluid flow equation that has
    since become one of
  • the standard mathematical tools of the petroleum
    engineer. If a horizontal linear flow of an
    incompressible fluid is established through a
    core sample of length L and a cross-section of
    area A, then the governing fluidflow equation is
    defined as

23
  • where n apparent fluid flowing velocity, cm/sec
  • k proportionality constant, or permeability,
    Darcys
  • m viscosity of the flowing fluid, cp
  • dp/dL pressure drop per unit length, atm/cm
  • The apparent velocity determined by dividing the
    flow rate by the cross-sectional area across
    which fluid is flowing. Substituting the
    relationship, q/A, in place of n in Equation 3-21
    and solving for q results in
  • where q flow rate through the porous medium,
    cm3/sec
  • A cross-sectional area across which flow
    occurs, cm2

24
  • One Darcy is a relatively high permeability as
    the permeabilities of
  • most reservoir rocks are less than one Darcy. In
    order to avoid the use of fractions in describing
    permeabilities, the term millidarcy is used. As
    the term indicates, one millidarcy, i.e., 1 md,
    is equal to one-thousandth of one Darcy or,
  • 1 Darcy 1000
    md
  • The negative sign in Equation is necessary as the
    pressure increases in one direction while the
    length increases in the opposite direction.
  • Integrate the above equation

25
  • Linear flow model

26
  • where L length of core, cm
  • A cross-sectional area, cm2
  • The following conditions must exist during the
    measurement of permeability
  • Laminar (viscous) flow
  • No reaction between fluid and rock
  • Only single phase present at 100 pore space
    saturation
  • This measured permeability at 100 saturation of
    a single phase is
  • called the absolute permeability of the rock.

27
  • For a radial flow, Darcys equation in a
    differential form can be written as

28
  • Intergrating Darcys equation gives
  • The term dL has been replaced by dr as the length
    term has now become a radius term.

29
Saturation
  • LECTURE 7

30
  • SATURATION
  • Saturation is defined as that fraction, or
    percent, of the pore volume
  • occupied by a particular fluid (oil, gas, or
    water). This property is
  • expressed mathematically by the following
    relationship
  • Applying the above mathematical concept of
    saturation to each reservoir
  • fluid gives


31
  • where
  • So oil saturation
  • Sg gas saturation
  • Sw water saturation
  • Sg So Sw 1.0
  • Critical oil saturation, Soc
  • For the oil phase to flow, the saturation of
    the oil must exceed a certain value which is
    termed critical oil saturation. At this
    particular saturation, the oil remains in the
    pores and, for all practical purposes, will not
    flow.

32
Residual oil saturation, Sor During the
displacing process of the crude oil system from
the porous media by water or gas injection (or
encroachment) there will be some remaining oil
left that is quantitatively characterized by a
saturation value that is larger than the critical
oil saturation. This saturation value is called
the residual oil saturation, Sor. The term
residual saturation is usually associated with
the nonwetting phase when it is being displaced
by a wetting phase.
33
  • Movable oil saturation, Som
  • Movable oil saturation Som is another saturation
    of interest and is defined as the fraction of
    pore volume occupied by movable oil as expressed
    by
  • the following equation
  • Som 1 - Swc - Soc
  • where
  • Swc connate water saturation
  • Soc critical oil saturation

34
  • Critical gas saturation, Sgc
  • As the reservoir pressure declines below the
    bubble-point pressure, gas evolves from the oil
    phase and consequently the saturation of the gas
    increases as the reservoir pressure declines. The
    gas phase remains immobile until its saturation
    exceeds a certain saturation, called critical gas
    saturation, above which gas begins to move.
  • Critical water saturation, Swc
  • The critical water saturation, connate water
    saturation, and irreducible water saturation are
    extensively used interchangeably to define the
    maximum water saturation at which the water
    phase will remain immobile.

35
Capillary Pressure and Its Curve
  • LECTURE 8

36
  • Capillary pressure
  • If a glass capillary tube is placed in a large
    open vessel containing
  • water, the combination of surface tension and
    wettability of tube to water will cause water to
    rise in the tube above the water level in the
    container outside the tube as shown in Figure 3.
  • The water will rise in the tube until the total
    force acting to pull the
  • liquid upward is balanced by the weight of the
    column of liquid being supported in the tube.
  • Figure 3

37
  • CAPILLARY PRESSURE
  • The capillary forces in a petroleum reservoir are
    the result of the combined effect of the surface
    and interfacial tensions of the rock and fluids,
    the pore size and geometry, and the wetting
    characteristics of the system.
  • Any curved surface between two immiscible fluids
    has the tendency to
  • contract into the smallest possible area per unit
    volume. This is true
  • whether the fluids are oil and water, water and
    gas (even air), or oil and gas. When two
    immiscible fluids are in contact, a discontinuity
    in pressure exists between the two fluids, which
    depends upon the curvature of the interface
    separating the fluids. We call this pressure
    difference the capillary pressure and it is
    referred to by pc.
  • Capillary pressure (pressure of the nonwetting
    phase) - (pressure of
  • the wetting phase)

  • pc pnw - pw

38
  • Figure4

39
  • Transition Zone
  • The figure indicates that the saturations are
    gradually changing from 100 water in the water
    zone to irreducible water saturation some
    vertical distance above the water zone. This
    vertical area is referred to as the transition
    zone, which must exist in any reservoir where
    there is a bottom water table. The transition
    zone is then defined as the vertical thickness
    over which the water saturation ranges from 100
    saturation to irreducible water saturation Swc.

40
  • Water Oil Contact
  • The WOC is defined as the uppermost depth in the
    reservoir where a 100 water saturation exists.
  • Gas Oil Contact
  • The GOC is defined as the minimum depth at which
    a 100 liquid, i.e., oil water, saturation
    exists in the reservoir.

41
  • Figure 5

42
  • It should be noted that there is a
    difference between the free water level (FWL) and
    the depth at which 100 water saturation exists.
    From a reservoir engineering standpoint, the free
    water level is defined by zero capillary
    pressure. Obviously, if the largest pore is so
    large that there is no capillary rise in this
    size pore, then the free water level and 100
    water saturation level, i.e., WOC, will be the
    same.

43
Wettabiloity and Distribution of Reservoir
Fluids
  • LECTURE 9

44
  • WETTABILITY
  • Wettability is defined as the tendency of one
    fluid to spread on or adhere to a solid surface
    in the presence of other immiscible fluids. The
    concept of wettability is illustrated in
    Figure1. Small drops of three liquids-mercury,
    oil, and waterare placed on a clean glass plate.

45
  • The three droplets are then observed from
    one side as illustrated in Figure 3-1. It is
    noted that the mercury retains a spherical shape,
    the oil droplet develops an approximately
    hemispherical shape, but the water tends to
    spread over the glass surface.

46
  • The tendency of a liquid to spread over the
    surface of a solid is an indication of the
    wetting characteristics of the liquid for the
    solid. This spreading tendency can be expressed
    more conveniently by measuring the angle of
    contact at the liquid-solid surface. This angle,
    which is always measured through the liquid to
    the solid, is called the contact angle q.
  • The contact angle q has achieved significance as
    a measure of wettability.

47
  • As shown in Figure 1, as the contact angle
    decreases, the wetting
  • characteristics of the liquid increase. Complete
    wettability would be evidenced by a zero contact
    angle, and complete nonwetting would be evidenced
    by a contact angle of 180. There have been
    various definitions of intermediate wettability
    but, in much of the published literature, contact
    angles of 60 to 90 will tend to repel the
    liquid.
  • The wettability of reservoir rocks to the fluids
    is important in that the
  • distribution of the fluids in the porous media is
    a function of wettability.
  • Because of the attractive forces, the wetting
    phase tends to occupy the
  • smaller pores of the rock and the nonwetting
    phase occupies the more
  • open channels.

48
Properties of Natural Gas
  • LECTURE 10

49
PVT Behaviour
  • LECTURE 11

50
Classification of Hydrocarbon Reservoir
  • LECTURE 12

51
CLASSIFICATION OF RESERVOIRS AND RESERVOIR FLUIDS
  • Petroleum reservoirs are broadly classified as
    oil or gas reservoirs.
  • The composition of the reservoir hydrocarbon
    mixture
  • Initial reservoir pressure and temperature
  • pressure-temperature diagram

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53
Pressure-Temperature Diagram
  • Figure 1-1 shows a typical pressure-temperature
    diagram of a multicomponent system with a
    specific overall composition. Although a
    different hydrocarbon system would have a
    different phase diagram, the general
    configuration is similar.
  • These multicomponent pressure-temperature
    diagrams are essentially used to
  • Classify reservoirs
  • Classify the naturally occurring hydrocarbon
    systems
  • Describe the phase behavior of the reservoir
    fluid

54
Pressure-Temperature Diagram
  • Critical pointThe critical point for a
    multicomponent mixture is referred to as the
    state of pressure and temperature at which all
    intensive properties of the gas and liquid phases
    are equal (point C). At the critical point, the
    corresponding pressure and temperature are called
    the critical pressure pc and critical temperature
    Tc of the mixture.

55
Pressure-Temperature Diagram
  • Bubble-point curveThe bubble-point curve (line
    BC) is defined as the line separating the
    liquid-phase region from the two-phase region.
  • Dew-point curveThe dew-point curve (line AC) is
    defined as the line separating the vapor-phase
    region from the two-phase region.

56
Pressure-Temperature Diagram
  • Oil reservoirsIf the reservoir temperature T is
    less than the critical temperature Tc of the
    reservoir fluid, the reservoir is classified as
    an oil reservoir.
  • Gas reservoirsIf the reservoir temperature is
    greater than the critical temperature of the
    hydrocarbon fluid, the reservoir is considered a
    gas reservoir.

57
Types of Crude Oil
  • Low-shrinkage oil
  • Oil formation volume factor less than 1.2
    bbl/STB
  • Gas-oil ratio less than 200 scf/STB
  • Oil gravity less than 35 API
  • Black or deeply colored

58
Gas Reservoirs
  • In general, if the reservoir temperature is above
    the critical temperature of the hydrocarbon
    system, the reservoir is classified as a natural
    gas reservoir. On the basis of their phase
    diagrams and the prevailing reservoir conditions,
    natural gases can be classified into 3
    categories
  • Retrograde gas-condensate
  • Wet gas
  • Dry gas

59
Retrograde gas-condensate reservoir
  • If the reservoir temperature T lies between the
    critical temperature Tc and cricondentherm Tct of
    the reservoir fluid, the reservoir is classified
    as a retrograde gas-
  • condensate reservoir.
  • the gas-oil ratio for a condensate system
    increases with time due to the liquid dropout and
    the loss of heavy components in the liquid.
  • Condensate gravity above 50 API
  • Stock-tank liquid is usually water-white or
    slightly colored.

60
Wet-gas reservoir
  • Temperature of wet-gas reservoir
  • is above the cricondentherm of the
    hydrocarbon mixture. Because the reservoir
    temperature exceeds the cricondentherm of the
    hydrocarbon system, the reservoir fluid will
    always remain in the vapor phase region as the
    reservoir is depleted isothermally, along the
    vertical line A-B.

61
Wet-gas reservoir
  • Wet-gas reservoirs are characterized by the
    following
  • properties
  • Gas oil ratios between 60,000 to 100,000
    scf/STB
  • Stock-tank oil gravity above 60 API
  • Liquid is water-white in color
  • Separator conditions, i.e., separator pressure
    and temperature, lie within the two-phase region

62
Dry-gas reservoir
  • The hydrocarbon mixture exists as a gas both in
    the reservoir and in the surface facilities.
  • Usually a system having a gas-oil ratio greater
    than 100,000 scf/STB is considered to be a dry
    gas.

63
Drives in the Reservoir(water drive and
compaction drive)
  • LECTURE 14

64
  • The Water-Drive Mechanism
  • Many reservoirs are bounded on a portion or all
    of their peripheries by water bearing rocks
    called aquifers. The aquifers may be so large
    compared to the reservoir they adjoin as to
    appear infinite for all practical purposes, and
    they may range down to those so small as to be
    negligible in their effects on the reservoir
    performance.
  • Reservoir have

    a water drive

65
Characteristics Trend
Reservoir pressure Declines very slowly (remains very high)
Gas oil ratio Little change during the life of the reservoir (remains low)
Water production Early excess water production
Well behavior Flow until water production gets excessive.
Oil recovery 35 to 75
66
  • Rock and Liquid Expansion
  • When an oil reservoir initially exists at
    a pressure higher than its bubble-point pressure,
    the reservoir is called an undersaturated oil
    reservoir.
  • At pressures above the bubble-point
    pressure, crude oil, connate water, and rock are
    the only materials present. As the reservoir
    pressure declines, the rock and fluids expand
    due to their individual compressibilities.
  • The reservoir rock compressibility is the
    result of two factors
  • Expansion of the individual rock
    grains
  • Formation compaction

67
Rock and Liquid Expansion
Both of the above two factors are the results
of a decrease of fluid pressure within the pore
spaces, and both tend to reduce the pore volume
through the reduction of the porosity. This
driving mechanism is considered the least
efficient driving force and usually results in
the recovery of only a small percentage of the
total oil in place.
68
Solution-gas Drive,Gas-cap Drive,Gravity Drive
  • LECTURE 15

69
  • The Depletion Drive Mechanism
  • This driving form may also be referred to by the
    following various
  • terms
  • Solution gas drive
  • Dissolved gas drive
  • Internal gas drive
  • In this type of reservoir, the principal source
    of energy is a result of gas liberation from the
    crude oil and the subsequent expansion of the
    solution gas as the reservoir pressure is
    reduced. As pressure falls below the bubble-point
    pressure, gas bubbles are liberated within the
    microscopic pore spaces. These bubbles expand and
    force the crude oil out of the pore space as
    shown conceptually in Figure 1

70
  • Figure 1 Solution gas drive reservoir

71
  • Gas Cap Drive
  • Gas-cap-drive reservoirs can be identified by the
    presence of a gas cap with little or no water
    drive as shown in Figure 2.
  • Due to the ability of the gas cap to expand,
    these reservoirs are
  • characterized by a slow decline in the reservoir
    pressure. The natural energy available to
    produce the crude oil comes from the following
    two sources
  • Expansion of the gas-cap gas
  • Expansion of the solution gas as it is liberated

72
  • Figure 2 Gas-cap drive reservoir

73
  • The Gravity-Drainage-Drive Mechanism
  • The mechanism of gravity drainage occurs in
    petroleum reservoirs as a result of differences
    in densities of the reservoir fluids. The effects
    of gravitational forces can be simply illustrated
    by placing a quantity of crude oil and a quantity
    of water in a jar and agitating the contents.
    After agitation, the jar is placed at rest, and
    the more denser fluid (normally water) will
    settle to the bottom of the jar, while the less
    dense fluid (normally oil) will rest on top of
    the denser fluid. The fluids have separated as a
    result of the gravitational forces acting on them.

74
Characteristics Trend
Reservoir pressure Variable rates of pressure decline, depending principally upon the amount of gas conservation.
Gas oil ratio Low gas-oil ratio
Water production Little or no water production.
Well behavior
Oil recovery Near to 80
75
  • The Combination-Drive Mechanism
  • The driving mechanism most commonly encountered
    is one in which both water and free gas are
    available in some degree to displace the oil
    toward the producing wells. The most common type
    of drive encountered,
  • therefore, is a combination-drive mechanism as
    illustrated in Figure
  • 4. Two combinations of driving forces can be
    present in combinationdrive reservoirs. These are
    (1) depletion drive and a weak water drive and
    (2) depletion drive with a small gas cap and a
    weak water drive.
  • Then, of course, gravity segregation can play an
    important role in any of the aforementioned
    drives.

76
  • Figure 4 Combination drive reservoir

77
Derivation of Material Balance Equation
  • LECTURE 16

78
  • When an oil and gas reservoir is trapped with
    wells, oil and gas, and frequently some water,
    are produced, thereby reducing the reservoir
    pressure and causing the remaining oil and gas to
    expand to fill the space vavated by the fluids
    removed. When the oil-and gas-bearing strata are
    hydraulically connected with water-bearing
    strata, or aquifers, water encroaches into the
    reservoir as the pressure drops owing to
    production .This water encroachment decreases the
    extent to which the remaining oil and gas expand
    and accordingly retards the decline in reservoir
    pressure.

79
  • In as much as the temperature in oil and gas
    reservoir remains substantially constant during
    the course of production, the degree to which the
    remaining oil and gas expand depends only on the
    pressure .By taking bottom-hole samples of the
    reservoir fluids under pressure and measuring
    their relative volumes in the laboratory at
    reservoir temperature and under various pressures
    ,it is possible to predict how these fluids
    behave in the reservoir as reservoir pressure
    declines.

80
  • The general material balance equation is simply a
    volumetric balance, Which states that since the
    volume of a reservoir (as defined by its initial
    limits)is a constant , the algebraic sum of the
    volume changes of the oil , free gas , water ,
    and rock volumes in the reservoir volumes
    decreases , the sum of these two decreases must
    be balanced by changes of equal magnitude in the
    water and rock volumes .

81
  • If the assumption is made that complete
    equilibrium is attained at all times in the
    reservoir between the oil and its solution gas ,
    it is possible to write a generalized material
    balance expression relating the quantities of oil
    , gas and water produced , the average reservoir
    pressure , the quantity of water that may have
    encroached from the aquifer , and finally the
    initial oil and gas content of the reservoir.

82
Steady-state and Pseudo Steady-state Flow
  • LECTURE 17

83
  • The area of concern in this lecture includes
  • Types of fluids in the reservoir
  • Flow regimes
  • Reservoir geometry
  • Number of flowing fluids in the reservoir

84
  • TYPES OF FLUIDS
  • In general, reservoir fluids are classified into
    three groups
  • Incompressible fluids
  • Slightly compressible fluids
  • Compressible fluids
  • Incompressible fluids
  • An incompressible fluid is defined as the
    fluid whose volume (or density) does not change
    with pressure. Incompressible fluids do not
    exist this behavior, however, may be assumed in
    some cases to simplify the derivation and the
    final form of many flow equations.

85
  • Slightly compressible fluids
  • These slightly compressible fluids exhibit
    small changes in volumeor density, with changes
    in pressure.
  • It should be pointed out that crude oil and water
    systems fit into this category.
  • Compressible Fluids
  • These are fluids that experience large changes in
    volume as a function of pressure. All gases are
    considered compressible fluids.

86
  • FLOW REGIMES
  • There are three flow regimes
  • Steady-state flow
  • Unsteady-state flow
  • Pseudosteady-state flow
  • Steady-State Flow
  • The flow regime is identified as a steady-state
    flow if the pressure at every location in the
    reservoir remains constant, i.e., does not change
    with time. Mathematically, this condition is
    expressed as
  • (4-1)

87
  • The above equation states that the rate of change
    of pressure p with respect to time t at any
    location i is zero. In reservoirs, the
    steady-state flow condition can only occur when
    the reservoir is completely recharged and
    supported by strong aquifer or pressure
    maintenance operations.
  • Unsteady-State Flow
  • The unsteady-state flow (frequently called
    transient flow) is defined as the fluid flowing
    condition at which the rate of change of pressure
    with respect to time at any position in the
    reservoir is not zero or constant.
  • This definition suggests that the pressure
    derivative with respect to time is essentially a
    function of both position i and time t, thus
  • (4-2)

88
  • Pseudosteady-State Flow
  • When the pressure at different locations in the
    reservoir is declining
  • linearly as a function of time, i.e., at a
    constant declining rate, the flowing condition is
    characterized as the pseudosteady-state flow.
    Mathematically, this definition states that the
    rate of change of pressure with respect to time
    at every position is constant, or
  • (4-3)
  • It should be pointed out that the
    pseudosteady-state flow is commonly referred to
    as semisteady-state flow and quasisteady-state
    flow.
  • Figure shows a schematic comparison of the
    pressure declines as a function of time of the
    three flow regimes.

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90
  • RESERVOIR GEOMETRY
  • For many engineering purposes, however, the
    actual flow geometry may be represented by one
    of the following flow geometries
  • Radial flow
  • Linear flow
  • Spherical and hemispherical flow
  • Because fluids move toward the well from all
    directions and coverage at the wellbore, the
    term radial flow is given to characterize the
    flow of fluid
  • into the wellbore. Figure 4-1 shows idealized
    flow lines and iso-potential lines for a radial
    flow system.

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  • Figure 4-1 Ideal radial
    flow into a wellbore

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  • Linear Flow
  • Linear flow occurs when flow paths are parallel
    and the fluid flows in a
  • single direction. In addition, the cross
    sectional area to flow must be
  • constant. Figure 4-2 shows an idealized linear
    flow system.
  • Figure 4-2 Ideal linear flow
  • into vertical
    fracture

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  • Spherical and Hemispherical Flow
  • Depending upon the type of wellbore completion
    configuration, it is possible to have a spherical
    or hemispherical flow near the wellbore. A well
    with a limited perforated interval could result
    in spherical flow in the vicinity of the
    perforations as illustrated in Figure 4-3. A well
    that only partially penetrates the pay zone, as
    shown in Figure 4-4, could result in
    hemispherical flow. The condition could arise
    where coning of bottom water is important.
  • Figure 4-3 Spherical flow due to limited entry

94
  • Figure 4-4 Hemispherical flow in a partially
    penetrating well

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  • NUMBER OF FLOWING FLUIDS IN THE RESERVOIR
  • There are generally three cases of flowing
    systems
  • Single-phase flow (oil, water, or gas)
  • Two-phase flow (oil-water, oil-gas, or
    gas-water)
  • Three-phase flow (oil, water, and gas)
  • The description of fluid flow and subsequent
    analysis of pressure data becomes more difficult
    as the number of mobile fluids increases.

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Horizontal Wells
  • LECTURE 18

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  • Since 1980, horizontal wells began capturing an
    ever-increasing share of hydrocarbon production.
    Horizontal wells offer the following advantages
    over those of vertical wells
  • Large volume of the reservoir can be drained by
    each horizontal well.
  • Higher productions from thin pay zones.
  • Horizontal wells minimize water and gas zoning
    problems.
  • In high permeability reservoirs, where
    near-wellbore gas velocities are high in
    vertical wells, horizontal wells can be used to
    reduce near-wellbore velocities and turbulence.
  • In secondary and enhanced oil recovery
    applications, long horizontal injection wells
    provide higher injectivity rates.
  • The length of the horizontal well can provide
    contact with multiple
  • fractures and greatly improve productivity.

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  • The actual production mechanism and reservoir
    flow regimes around the horizontal well are
    considered more complicated than those for the
    vertical well, especially if the horizontal
    section of the well is of a considerable length.
    Some combination of both linear and radial flow
    actually exists, and the well may behave in a
    manner similar to that of a well that has been
    extensively fractured.
  • Assuming that each end of the horizontal well is
    represented by a vertical well that drains an
    area of a half circle with a radius of b, Joshi
    (1991) proposed the following two methods for
    calculating the drainage area of a horizontal
    well.

99
  • Method I
  • Joshi proposed that the drainage area is
    represented by two half circles of radius b
    (equivalent to a radius of a vertical well rev)
    at each end and a rectangle, of dimensions L(2b),
    in the center. The drainage area of the
  • horizontal well is given then by
  • Figure 5-1

100
  • (5-1)
  • where
  • A drainage area, acres
  • L length of the horizontal well, ft
  • b half minor axis of an ellipse, ft

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  • Method II
  • Joshi assumed that the horizontal well drainage
    area is an ellipse and given by
  • (5-2)
  • with
  • (5-3)
  • where a is the half major axis of an ellipse.
  • Joshi noted that the two methods give different
    values for the drainage area A and suggested
    assigning the average value for the drainage of
    the horizontal well. Most of the production rate
    equations require the value of the drainage
    radius of the horizontal well, which is given by

102
  • (5-4)
  • Where
  • reh drainage radius of the horizontal well, ft
  • A drainage area of the horizontal well, acres

103
Natural Flow Recovery
  • LECTURE 19

104
  • A thorough understanding of the flowing well is
    necessary prior to placing it on artificial lift
    . There are two surface conditions under which a
    flowing well is produced , that is , it may be
    produced with a choke at the surface or it may be
    produced with no choke at the surface. The
    majority of all flowing wells utilize surface
    chokes . Some of the reasons for this are safety
    to maintain production allowable to maintain
    an upper flow rate limit to prevent sand entry
    to produce the reservoir at the most efficient
    rate to prevent water or gas coning and
    others.

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  • In particular , flowing wells utilize a choke in
    their early stages of production . As time
    progresses , the choke size may have to be
    increased and eventually removed completely in
    order to try to optimize production .
  • The second condition that we are concerned
    with is producing the flowing well with no
    restrictions at the surface except normal
    Christmas tree turn , bends, etc . Even these may
    be streamlined in order to obtain the maximum
    flowing rate possible .

106
  • In order to analyze the performance of a
    conventionally completed flowing well , in is
    necessary to recognize that there are three
    distinct phases , which have to be studied
    separately and then finally linked together
    before an overall picture of a flowing wells
    behavior can be obtained . These phase are the
    inflow performance , the vertical lift
    performance , and the choke (or bean
    )performance.
  • The inflow performance , that is , the flow of
    oil , water , and gas from the formation into the
    bottom of the well , is typified , as far as
    gross liquid production is concerned , by the PI
    of well or , more generally , by the IPR .
  • The vertical lift performance involves a study
    of the pressure losses in vertical pipes carrying
    two-phase mixtures(gas and liquid).

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Mechanical Recovery(rod system)
  • LECTURE 20

108
  • Oil well pumping methods can be divided into two
    main groups
  • Rod systems.Those in which the motion of the
    subsurface pumping equipment originates at the
    surface and is transmitted to the pump by means
    of a rod string.
  • Rod less systems.Those in which the pumping
    motion of the subsurface pump is produced by
    means other than sucker rods.
  • Of these teo groups,the first is represented by
    the beam pumping system and the second is
    represented by hydraulic and centrifugal pumping
    systems.

109
  • The beam pumping system consists essentially of
    five parts
  • The subsurface sucker rodfriven pump.
  • The sucker rod string which transmits the surface
    pumping motion and power to the subsurface
    pump.Also included is the necessary string of
    tubing and/or casing within which the sucker rods
    operate and which conducts the pumped fluid from
    the pumpto the surface.
  • The surface pumping eauipment which changes the
    rotating motion of the prime mover into
    oscillatinf linear pumping motion .
  • The power transmiddion unit or speed reducer.
  • The prime mover which furnishes the necessary
    power to the system.

110
Fomation Damage Control
  • LECTURE 22

111
  • Skin Factor
  • It is not unusual for materials such as
    mud filtrate, cement slurry, or clay particles
    to enter the formation during drilling,
    completion or workover operations and reduce the
    permeability around the wellbore.

112
Skin Factor
This effect is commonly referred to as a wellbore
damage and the region of altered permeability is
called the skin zone. This zone can extend from a
few inches to several feet from the wellbore.
Many other wells are stimulated by acidizing or
fracturing which in effect increase the
permeability near the wellbore. Thus, the
permeability near the wellbore is always
different from the permeability away from the
well where the formation has not been affected
by drilling or stimulation. A schematic
illustration of the skin zone is shown in Figure
4-5.
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  • Those factors that cause damage to the formation
    can produce additional localized pressure drop
    during flow. This additional pressure drop is
    commonly referred to as Dpskin. On the other
    hand, well stimulation techniques will normally
    enhance the properties of the formation and
    increase the permeability around the wellbore, so
    that a decrease in pressure drop is observed.
  • Figure 4-5

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  • Positive Skin Factor, s gt 0
  • When a damaged zone near the wellbore exists,
    k-skin is less than k and hence s is a positive
    number. The magnitude of the skin factor
    increases as k-skin decreases and as the depth of
    the damage r skin increases.
  • Negative Skin Factor, s lt 0
  • When the permeability around the well k-skin is
    higher than that of the formation k, a negative
    skin factor exists. This negative factor
    indicates an improved wellbore condition.
  • Zero Skin Factor, s 0
  • Zero skin factor occurs when no alternation in
    the permeability around the wellbore is observed,
    i.e., k-skin k.

115
Revision
  • LECTURE 2324

116
FINAL TEST
LECTURE 25
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