1.productivity

8/12/2019 1.Productivity

1/12


2/12

"eservoir and the reservoir fluid Process inlet pressure, and other restrictions in the process

!o predict production, it is necessary to determine the relationships between pressure and rate forthe elements above and combine them. Since the relationships depend on well design, we will

then also be able to calculate the well design that appear to give the best productivity; in otherwords, optimi#e well design and completion.

$n %hapter 1, we will use simple relations for the influ&, flow in the well and through regulationvalve. !he purpose is to show how these relations can be combined to predict production.

1.1 !o the flow

$n order for a well to produce, fluid must be drawn from the reservoir. Pressure drop in reservoirand well represent loss of energy, because of the flow resistance. !he relation between bottomhole pressure and rate is the starting point to construct a production system based on the naturalcharacteristics of the reservoir. 'e can measure this relation directly, or predict it out fromreservoir properties.

1.1.1 (inear flow characteristics Figure 1.1 indicates measured pressure and rates and personali#ed relationship between them.!he linear conte&t indicated, we can e&press that

o Rw q J 1

p p = )1 1*

+ productivity inde& )Sm-/d/bar* ( )w Ro p pq J =

p " reservoir pressure )bar* pw well potential pressure )bar*

o production )Sm - / d* $n chapter 0, we estimate productivity inde& from arcy2s law and the reservoir. 3athematicalrelationships makes it possible to predict how productivity inde& depends on the well design. 4ut

because we rarely know the conditions down in the reservoir, well, you should mathematicalestimates verified with the measurements.

Challenges 5stimate out from Figure 1.1 "eservoir and productivity indeks )answer p" 6 007 bar, + 6 07 Sm- / d*. $f we lower the production well to the 189 bar: Production of this well, when the reservoir has decreased to 077 bar:


3/12

Figure 1.1: Inflow characteristics

1.1.0 $n flow characteristics by sam production!he same well can be completed in several reservoir. 5ach reservoir will then produced inaccordance with their own inflow characteristics, so that the total flow characteristics becomes acombination of these.

$n order to uantify, we may consider 0 reservoirs, with pressures p "1 and p "0 , and productivityindices +1 and +0. $nflow characteristics from each reservoir is given by )1 1*

1

1

11

1o Rw q J

p p =

0

0

00

1o Rw q J

p p =

$f we neglect flow friction in the well between the complemented #ones, the well potentialshould be similar p w1 6 p w0 6 p w. 4y combining this and relationships above, the total inflowcharacteristic becomes

( )0101010011

1

oo

R R

w qq J J J J

p J p J

p ++++

=


4/12

$n Figure 1.0, the pressure and productivity indices considered are p "1 6 007 bar, + 1 6 07 Sm - /d;and p "0 6 0 7 bar, + 0 6 17 Sm - / d. 5 uation )1 0* gives the linear relationship between bottom

pressure and resulting total rate, as illustrated. 4ased on measurements of bottom pressure andtotal rate it may appear that the well produces from a reservoir with the pressure 00


5/12

1.0 Flow in the production pipeProduction pipe should be selected in accordance with the natural characteristics of the well. !he

basis for such selection is pressure and flow computation by the pipe flow e uation

0dxvd

f 21

vdvdx g dp 2 x =+++

)1 -*

: ?fluid density )kg/m-*v flow velocity )m / s*& length along the pipe, the flow direction )m*

g x component of gravity acceleration in the flow direction )m/s0* f the friction factor ) *

For single phase oil flow in the pipe with a constant diameter, it can be assumed that the speed isconstant, thereby neglecting vdv. !he speed depends on the flow rate and pipe diameter

4d Bqv 2 oo

= )1 *

!oo large velocity could accelerate corrosion, in e&treme cases also cause mechanical erosion.!oo small velocity could lead to accumulation of produced sand. 4y integrating )1 * along the

production pipe )length (*, we can estimate the pressure valve on the tree; peak pressure

Lvd

f L g p p xwth0

0

1 =

)1 9*

1.- !ubing head pressure characteristics !ubing head pressure characteristics specify how the pressure at the valve tree vary with rate

p th) o*. For linear the flow characteristics and single phase oil, we can predict tubing head pressure from )1 1* and )1 9*. 'e usually present tubing head pressure characteristicsgraphically, as illustrated in Fig 1.-.

Challenges5stimate out from Figure 1.-

!ubing head pressure at #ero production)answer about 87 bar*

!ubing head pressure when the well is producing 077 Sm-/d)answer about


6/12

Figure 1." #u$ing head pressure characteristics

= goal is to construct the well to achieve high production capacity. $t means to avoidunnecessary flow restriction and pressure loss. "elations above make it possible to predict theeffect of productivity inde&, pipe diameter, the friction factor, separator pressure, will have on

production capacity.

Challenge 5stimate, according to Figure 1.-

Production by reducing the separator pressure from 07 to 17 bar )answer about 8-7 Sm- / d*

1. "ate regulation


7/12

!o regulate the rate of individual wells, we use the choke valves mounted after the valve tree.Pressure reduction is acieved leading a fluid Aet into a wider pipe cross section. 4y this, thevelocity energy is dissipatdby turbulence between the Aet and the fluid around it. Pressure lossdue to the wall friction will usually be negligible. Figure 1. illustrates the simplest constructionof such a valve

Figure 1.% Flow through simple nozzle

!he behavior can be uantified by combination of the 4ernoulli2s e uation and %arnotrelationship. 4ernoulli2s law describes the pressure until the end no##les. For incompressiblefluid, this gives

( )000

1thcthc vv p p =

)1


8/12

!he first term of the relation aabove provides the pressure reduction due to acceleration throughthe no##les )4ernoulli*. !he second term provides pressure recovery after the outlet )%arnot *.'e assume little compressible fluid and e ual pipe si#e before and after the no##les, so that thevelocites will be the same v th 6 v s. !he pressure reduction can be e&pressed

2

c

2c

2

c sth A

Q21

A A

1 AQ

21

p p

= )1 8*

!he simplifying indicated above )1 8* assumes the opening through the valve is much smallerthan the pipe cross section =c BB=. $n valves designed for pressure reduction, this will usually

be the case

Figure 1.& #he production rate controlled $y the regulation al e

!oday choke valves are often designed such that Aets rays collide with each other. Cpenings areoften adAustable.

$n Denturi no##les, the cross section changes gradually. !his limits the turbulence, so that mostof the velocity energy is reclaimed as pressure and 4ernoulli2s law applies. !hen the pressureafter the no##les is almost the same as the upstream pressure. Such no##les will not substantiallyaffect the rate.

1.9 Future production


9/12

'ith time, the reservoir conditions will change, depending on production and inAection. Suchchanges affect

Future production and income Eow different production decisions will affect future production

Future pressure and fluid composition are usually forecasted by numerical reservoir simulation.4elow a reservoir model is simplified sufficiently to be analytical solvable. %ombining this withwell flow relation provides fundamental insight into the dynamics of field production.

1.9.1 "eservoir model'e will assume that the reservoir is producing by e&pansion, uantify by the compressibilitye uation

dpdV

V c

1=

c fluid compressibility, under reservoir conditionsD fluid volume in the reservoir dp pressure reductiondD additional fluid volume, because of the pressure reduction

"eservoir fluids fill the pore space. !hus, additional fluid volume corresponds to production.From the compressibility e uation, we can relate production to change in reservoir pressure

oo R Bq

cV dt dV

cV dt dp 11 ==

>umerical reservoir simulation solve the relationship e uation above in - dimentions. Eere, wewill ignore pressure gradient in the reservoir. =ssuming constant pore volume and constant fluidcompressibility, the relationship above provides pressure change due to production

= t

t oo Ro R

o

dt BqcV 1

)t ( p )t ( p )1 @*

p " average reservoir pressureo production rate

5 uation )1 @* can be viewed as a simple reservoir model. 4y solving for different assumptionsabout the flow and production, we will be able to predict future production. !his is shown below

1.9.0 Plateau Processing capacity op, may initially limit the production. 'ith production rate e ual

processing capacity, we can solve )1 @*. !his shows that under these assumptions, the reservoir pressure declines steadily with time


10/12

( ) t qcV B

pt p opo

Ri R = )1 G*

'ith reservoir pressure declining, the well pressure will also decline, as illustrated by figure 1.


11/12

appro&imately constant. $t then follows from )1 1* that the rate change must then correspond tothe change in reservoir pressure

Ro pd J dq =

Setting this into the reservoir relation )1 @* and integrate, predict the production profile after the

plateau period

( ) ( ) po t t cV

B J

opo eqt q

=)1 11*

Hnder the assumptions above, production would decline e&ponentially, as illustrated in Figure1.8 below. 5 uation )1 11* also makes it possible to predict how changes in the reservoir and

production conditions will affect the immediate and future production.

Figure 1.- )eclining production

=t the plateau reservoir will fall linearly with time, as shown above. 'ith declining production,reservoir pressure will fall more slowly and approach the well pressure. 4y combining )1 11*and )1 G*, we can uantify this

( ) ( )( ) ( ) po t t

cV B J

t s Rp Rp p R e p p p1 pt t p

= )1 10*

!here p "p reservoir pressure at the end of the plateau

Figure 1.@ illustrates the pressure over time, based on relationships and conditions above


12/12

Figure 1. Future pressures* according to the simple reser oir model

1.8 (iterature Iilbert, '5 : Flowing and /as0 ift ell (erformance Paper =.P.$. @71 -7E. Presented at the spring meeting of the Pacific %oast istrict, ivision ofProduction, =P$, (os =ngeles 3ay < 8, 1G9

Iolan, 3., and 'hitson, %.E. ell (erformance $E" %, 1G@

1.productivity

Documents