2. Sistemas de Produccion 2 Reservorios.pptx
Transcript of 2. Sistemas de Produccion 2 Reservorios.pptx
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PRODUCTION SYSTEMS
COURSE
DARCY LAW
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PERMEABILITY
Permeability is a property of the porous medium that measures the
capacity and ability of the formation to transmit fluids. The rockpermeability, 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 calledDarcys 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
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where n = apparent fluid flowing velocity, cm/seck = 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 thecross-sectional area across which fluid is flowing. Substitutingthe relationship, q/A, in place of n 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
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One Darcy is a relatively high permeability as the permeabilities of
most reservoir rocks are less than one Darcy. In order to avoid theuse of fractions in describing permeabilities, the term millidarcyis 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 pressureincreases in one direction while the length increases in theopposite direction.
Integrate the above equation
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Linear flow model
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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 singlephase is
called the absolute permeability of the rock.
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Intergrating Darcys equation gives:
The term dL has been replaced by dr as the length term has now
become a radius term.
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PRIMARY
RESERVOIRCHARACTERISTICS
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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
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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 flowequations.
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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 intothis category.
Compressible Fluids
These are fluids that experience large changes in volume as afunction of pressure. All gases are considered compressible
fluids.
The isothermal compressibility coefficient c is described
mathematically by the following two equivalent expressions:In terms of fluid volume:
In terms of fluid density:
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Fluid densi ty versus p ressure for di f ferent f lu id types
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FLOW REGIMESThere 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 thepressure at every location in the reservoir remains
constant, i.e., does not change with time.
Mathematically, this condition is expressed as:
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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
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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
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 asa function of time of the three flow regimes.
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Flow Regimes
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Ideal Steady-State Flow Equation - Radial Flow
The steady-state flow equations are based onthe following assumptions:
1. Thickness is uniform, and permeability is
constant.
2. Fluid is incompressible.
3. Flow across any circumference is a constant.
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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 FlowDepending 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 couldresult 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
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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.