2. sistemas de produccion 2 reservorios.pptx

8/11/2019 2. Sistemas de Produccion 2 Reservorios.pptx

1/24

PRODUCTION SYSTEMS

COURSE

DARCY LAW


2/24

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


3/24

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


4/24

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


5/24

Linear flow model


6/24

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.


7/24


8/24

Intergrating Darcys equation gives:

The term dL has been replaced by dr as the length term has now

become a radius term.


9/24

PRIMARY

RESERVOIRCHARACTERISTICS


10/24

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


11/24

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.


12/24

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:


13/24

Fluid densi ty versus p ressure for di f ferent f lu id types


14/24

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:


15/24

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


16/24

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.


17/24

Flow Regimes


18/24

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.


19/24

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.


20/24

Figure 4-1 Ideal radial

flow into a

wellbore


21/24

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


22/24

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


23/24

Figure 4-4 Hemispherical flow in a partially penetrating well


24/24

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.

2. sistemas de produccion 2 reservorios.pptx

Documents