Bottom Hole Pressure Calculation

5/20/2018 Bottom Hole Pressure Calculation

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CALCULATION OF BOTTOM-HOLE PRESSURE AND SUBMERSIBLE PUMP

INTAKE PRESSURE

Ildar K. Shayhutdinov

In this article the design procedure of a bottom-hole pressure and intake pressure of submersible pump

under the fact sheet of operation of well is offered. A feature of the algorithm consists of using the given

standard field values of annulus pressure, dynamic level, flow rate and water cut. In article results of

calculations are compared to actual measured pressure at the level of pump intake. It is demonstrated, that

the applied methodology provides high accuracy of calculation for required parameters.

With artificial lift the important parameters of the oil producing wells are the bottom-hole

pressure as well as the intake pressure of the submersible pump. The definition accuracy of these

parameters is dictated by the necessity to calculate the potential well production opportunities

when selecting the appropriate pumping equipment and optimizing well performance.

Finding BH pressure thru actual well performance data can be divided in two stages:

) calculation of pressure distribution in annulus (in tubing) and definition of pressure at

the pump run-in depth;

) definition of pressure in the well bore at the interval pump intake BH and estimate

of BH pressure.

Definition of pressure at the pump intake

The hardest bit in finding the BH pressure in the producing well is calculation of pressure

at the pump run-in depth using actual well performance data. This article considers methodology

for calculation of mentioned pressure based on plotting the curve of pressure distribution in

annulus.

Fig.1 shows the diagram for producing well performance using submersible pump.

As a rule, the majority of producing wells for a more reliable pump performance are

equipped with gas separators. With gas separator the bigger part of free gas, liberated from

crude, under conditions of pump intake is directed into annulus. With absence of gas separator

(gas anchor / bottom hole separator) on the pump intake less quantity of free gas is coming into

annulus. Gas phase flow process in annulus can be characterized as gas lift operation at zero

feed/delivery mode. Theoretical and practical researches of A.P. Krylov [1] were devoted to it.

Equation for liquid-gas mixture flow in this case is presented the following way

0

0

aQ

a

gdl

dP

+=

(1)

Q - volumetric gas discharge/flow in the annulus, m3/s; - fluid density in the annulus

(presupposing that fluid in the annulus is presented by oil), kg/m3; 0a - ratio, considering

geometrical dimension of fluid passage, m3/s;g gravity acceleration, m/s2.

),(785,022

0 dDa = (2)D - production casing ID, m; d- tubing OD, m.


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Fig.1. Diagram, for calculation

of ESP performance with oil-

gas mix

Calculation of pressure distribution in annulus

is based onnumerical calculation of equation (1) with

known pressure at the pump run-in depth P . At that

the iteration procedure is implemented and actual and

calculated pressure at dynamic level P are

compared.

The algorithm for definition of pressure at thepump run-in depth is the following.

1.

The following initial data are put in:

Q - fluid flow rate under standard conditions,

m3/day; - volume ratio of water in production

under standard conditions; P - annulus pressure,

MPa; - formation pressure, K; cL - well depth

(vertical), m; H - pump run-in depth (vertical), m;

h - well dynamic level (vertical), m; d - tubing ID,

m; d- tubing OD, m; D - production casing ID, m;

- density of degassed oil under standard

conditions, kg/m3; - dynamic viscosity of

degassed oil under standard conditions, mPa s; P -

bubble point pressure at formation temperature, MPa;

0G - GOR of oil in place (gas-oil ratio) under normal

conditions, m3/m

3; - density of gas, liberated from

crude at flash liberation under normal conditions,

kg/m3; a yy , - mole fraction of nitrogen and methane in gas at flash liberation; - water

density under standard conditions, kg/m3.

Numerical calculation of equation (1) is presented as following

( )L

gdD

dDQP

=

+

)(785,0

)(785,0

22

22

(3)

P - pressure stepping, Pa; L - length delta, m.2. Pressure stepping taken and the sequential pressure values are identified for various

depths. For that the general pressure variation range )( P is divided into several intervals,

i.e. under condition

),(05,0 PPP = (4)

where P - annular pressure, Pa; - assumed pump intake-level pressure (at first

approximation is taken at random), Pa.

Accordingly recurrence relation defines the calculated pressures

=

=N

i

ii PP1

(5)

3. The temperature distribution in producing well bore is defined [2].

With known formation temperature the temperature at the pumps run-in depth

(calculation bottom-up) is calculated thru equation

=

d

hSttht 1)( (6)

To calculate the temperature distribution above the pump intake it is necessary to know

the wellhead temperature (calculation top-down):


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3

d

HSt

tHt

=

1

)( (7)

In equations (6) and (7) tt , - formation and wellhead temperatures accordingly,; h -

vertical depth, measured from bottom-hole, m; H- vertical depth, measured from wellhead, m;

St- non-dimensional Stanton number.

Dependence of Stanton number on mass well flow rate is represented as:

,10202,0)40ln(

10763,1 44 +=

qSt (8)

where q - mass well flow rate, t/day.

If wellhead temperature data is not available the calculation of temperature distribution above the

pump intake can be done using the equation (6), taking as base for measuring the temperature at

the pump-setting depth. In this case the value of wellhead temperature is the required parameter

and is defined for c HLh = . But, in case the well is operated using centrifugal, cavity/screw

or diaphragm pump the heating of liquid gas mix passing the submersible motor will not be

considered.

Thus we are getting the temperature distribution in producing well bore.

4.

Using the data of fluid properties we find the physical properties of oil, gas, water or

water-oil mix under corresponding thermo dynamic conditions ),( ii TP [1,2].

5. The volumetric gas-liquid flow parameters Q and Q are defined in conditions of

pump intake [2].

To define gas volume, going into annulus, we need to set the gas separation ratio. For that

we recommend to use the following equations, obtained from theoretical and experimental

researches [2]:

at the level of flowing lift shoe

Fw

Q

0

0

7,01+

=

; (9)

at the sucker-rod pump intake

Fw

Q

0

0

05,11+

=

; (10)

at the electrical submersible pump intake

'75,01

0

0

fw

Q+

=

, (11)

where 0 - free gas separation ratio with zero feed/delivery mode

2

0 1

=D

d (12)

Here Q - volumetric fluid flow under conditions of pump intake, m3/s; 0w - relative

velocity of gas bubbles, m/s. Relative velocity of gas bubbles depends on the water volume ratio

in production: at w /02,05,0 0 = ; w /17,05,0 0 => ; F - cross sectional

area of production casing, m2; 'f - area of circular clearance between production casing and

submersible pump, m2.

After calculation of separation ratio the volume Q of gas flow going into annulus is

defined. In case of well operating with ESP the volume of gas flow is calculated the following

way:

QQ = (13)


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If the centrifugal gas separator is available at the ESPs intake the separation ratio is

varying within range 0,6-0,8 (it is recommended to take it as 7,0 ). If the gas anchor / bottom

hole separator is available at the SRPs intake the separation ratio is varying within range 0,4-0,6

(it is recommended to take it as 5,0 ).

6. Values of i QQ = and i = assuming there is oil-gas mix above the pump

intake, values set in equation (3) and the well depth delta 1L is found.

Hence, at the depth 11 LHh = we are having the pressure PP =1 .

7. From equations (6)-(8) the temperature 1T is defined at the depth of 1h . Usingequation (5) we calculate the sequential pressure step PPP = 12 .

The following calculations are done for the average pressure between 1P and 2P :

2

212

+= and for the temperature 1T . Here you can see that at numerical integration of

equation (1) the implemented calculations are one step behind in temperature. But it appears that

calculation error with such approximation is very minor. The volume of gas flow going into

annulus is calculated for taken i and i :

i

i

ii

TP

TP

z

zQQ = , (14)

where Q - volume of gas flow in annulus under pump intake conditions, m3/s; P , T - taken

pump intake pressure and calculated temperature correspondingly; z , iz - correspondingly the

supercompressibility ratios for the pump intake conditions and set i and i .

When calculating the density of three-phase mix in the annulus additional complications

occur due to necessity to account for dissolved gas liberating from crude.

If we presuppose there is no mass exchange/transfer between the fluid in the annulus and

the fluid going to the pump intake, then the presence of free gas phase in the annulus will be

determined only by the separation at the pumps intake. Then fluid density in equation (3)

will be equal to oil density i at set i and i .In reality there is a constant mass transfer/exchange process between the fluid in the

annulus and the fluid going to the pump intake. Accounting for fluid density change in the

annulus due to dissolved gas liberating from crude is done using the following correlation:

)1( ii += , (15)

where i - oil density in the annulus fluid at i and i , kg/m3; i - gas liquid mix density

from crude and gas liberated from it as part of the annulus fluid at i and i , kg/m3; -

volume ratio of oil degassed at i and i (without consideration for free gas phase liberated in

conditions of pump intake).

It is easy to see that

ii += )1( , (16)

( )

( ) 1),(),(

),(),(

0

000

0

000

+

=

TP

TPTPzGTPG

TP

TPTPzGTPG

i

iiiii

i

iiiii

, (17)

iii

i

TPTPz

TP

0

0..

),(

= (18)

Here - volume ratio of gas, liberated at i and i (without consideration for free gas

phase liberated in conditions of pump intake); - density of gas additionally liberated fromcrude at i and i , kg/m

3; G 0 - specific volume of gas liberated in conditions of pump


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intake, modified to normal conditions, m3/t; ),(0 TPG - specific volume of gas liberated at i

and i , modified to normal conditions, m3/t; .. - density of gas dissolved in crude in

conditions of pump intake, modified to normal conditions, kg/m3.

Note: when determining the density i no free gas accounted liberated in conditions

of pump intake.

Determining parameter presents a hard task. Based on actual data processing we

received the following empirical dependence:

5587,0

.

.

=

Q

QQ , (19)

where Q - volumetric gas flow in the annulus in conditions of pump intake, m3/day; Q . -

volumetric oil flow in conditions of pump intake, m3/day; Q - volumetric gas liquid mix

flow in conditions of pump intake, m3/day.

Acquired values iQ and are placed in equation (3) and delta is determined 2L .

Value 212 Lhh = is calculated with 2P .

Sequential pressure step is taken PPP = 23 ,

2

323

+= etc.

Thus the sequential/step-by-step calculation is implemented till the vertical depth ih is

decreases or equalizes the value of well dynamic level h , i.e. i hh .

Pressure iPat the last calculation sequence/step is defined for certain depth ih , and not

for h . To determine pressure

P directly at the dynamic level we are using the following

correlation

ii

iiii

hh

PPhhPP

=

1

11

))(( (20)

8. Pressure P at dynamic level is calculated assuming the pump intake pressure is equal

, taken at random at first approximation. Pressure at the pump intake is corrected based

on comparison of calculated P and actual

P pressures at dynamic level.

Actual pressure P at dynamic level is determined by known barometric equation [1]:

zT

h

PP

03415,0

= , (21)

where - average temperature in the interval from the wellhead to dynamic level; z -

supercompressibility ratio at P pressure and temperature.

To correct the pump intake pressure the following procedure is used:

if %5%100||

PPP and PP < , then the pump intake pressure taken at first

approximation is excessive, and it has to be lowered, for example, take it equal to

95,0= ;

if %5%100||

P

PP and

PP > , then the pump intake pressure taken at first

approximation underrated, and it has to be increased, for example, up to value of

05,1= .

9. Calculation thru points 2-8 is repeated till condition %5%100||

P

PP is

fulfilled.


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During the implementation of iteration procedure the situation might occur when as a

result of numerical integration of equation (1), at the depth significantly lower than dynamic

level the calculated value of pressure appears to be close to atmospheric and lower. It happens

when initially setting the overrated pressure value at the pump intake level. In this case the

assumed initial pump intake pressure is lowered.

Note: if setting incorrect initial data the proposed iteration procedure doesnt always

match. Hence it is recommended to use the closest solution of equation giving the minimal

accuracy error.

Also keep in mind that the algorithm proposed to determine the pump intake pressuredoesnt consider the foaming leading to data corruption of measuring the dynamic level in

annulus.

Calculation examples

Thru proposed calculation algorithm for submersible pump intake level pressure using

Visual ++ Borland the software has been created called Well analyst. Initial data for

calculations are given in tables 1 and 2. Calculation results are given in table 3.

Physical properties of oil-in-place and degassed crude

Table 1Oil in place Degassed crude and single degassing gasField,

formation f, f, MPa b, MPa G, m3/t bo . ,

mPa*s

. ,

kg/m30. ,

kg/m3

0. ,

mPa*s

0. ,

kg/m3

N2, %

Varyogan,

formation 28

345 21,4 15,6 175,1 1,49 0,5 785 832 4,1 1,168 1,4

Samotlor,formation11

333 17,1 11,8 97,8 1,27 1,5 755 844 5,0 0,86 0,2

Samotlor,formation1-2

333 16,5 9,4 76 1,18 1,42 735 844 5,0 0,86 0,2

Samotlor,formation 8

349 21,19 13,5 135 1,26 1,15 735 843 7,0 1,13 3,84

Samotlor,formation1 349 24,4 11 119 1,24 1,03 735 844 6,6 0,955 3,2

VKY, formation21

349 25 20,6 236 1,45 0,42 808 832 5 0,85 0,75


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Initial data for calculation of pump intake pressure and actual values

Table 2Well # Field,

formationPump setdepth, m

Dynamiclevel, m

Annularpressure,

Mpa

Fluid flowrate,

m3/day

Watercut,%

Boreholedeviation,degrees

Pumpintake

pressure,Mpa

Pump type

1587 350 0,9 144,0 80,0 30 8,45-

160-1750

1587 785 2,3 144,0 80,0 30 7,15-

160-17501263

1587 842 2,45 144,0 80,0 30 6,85-

160-1750

883

Varyogan,formation 28

1610 106,5 0,84 82,4 0,0 29 5,85-80-1700 withgas separator

1200 530 0,8 33,0 0,0 0 4,8 7476

Samotlor,formation11

1200 344 0,66 36,0 0,0 0 6,5

29866Samotlor,

formation1-

2

1528 1266 1,6 58 28 0 2,95-30-

1800 with gas

separator

61503Samotlor,

formation 81683 403 2,2 222 5 0 11,9

5-

400-1250

29970Samotlor,

formation 82011 633 1,2 81 5 0 9,7

-5-60-

1700 with gasseparator

21109Samotlor,

formation 82029 564 1,4 114 5 0 9,5

5-160-1750 withgas separator

61803Samotlor,

formation 81808 701 1,8 440 5 0 5,2

5-500-1250 withgas separator

Samotlor,

formation1

1987 1513 1,4 36 5 0 3,45-50-


51118 Samotlor,formation1

2182 1313 1,6 36 10 0 6,75-50-


594VKY,

formation21

2200 270 1,4 226 5 0 6,1DN-1750 withgas separator

550VKY,

formation21

2030 135 0,8 146 48 0 6DN-1300 withgas separator

Comparison of calculated and actual pressures for reviewed wells

Table 3

Calculated pressure (MPa) and divergence from actual (%) at (MPa)Well

1263 883 7476 29866 61503 29970 21109 61803 51118 594 550

Actualpressure,

MPa8,4 7,1 6,8 5,8 4,8 6,5 2,9 11,9 9,7 9,5 5,2 3,4 6,7 6,1 6

Calculatedpressure,

MPa8,28 7,27 7,04 5,69 4,68 5,89 3,41 12,03 9,69 8,96 5,36 4,16 6,87 6,19 6,43

Absolutedivergence,

MPa0,12 -0,17 -0,24 0,11 0,12 0,61 -0,51 -0,13 0,01 0,54 -0,16 -0,76 -0,17 -0,09 -0,43


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As seen from results, given in table 3, divergence of calculated from actual pressures

does not exceed 0,76 MPa, it shows relatively high accuracy of proposed methodology. Besides

the degree of reliability of individual initial datum leaves much to be desired.

Application of Well analyst software allows to implement a fairly correct estimate of

well potential when selecting the downhole equipment, as well as using the more correct

calculated BH pressure values when adapting 3D hydrodynamic models.

Bottom-hole pressure calculation

Lets now review the peculiarities of calculating the pressure distribution within the

interval pump intake bottom-hole, as well as BH pressure.

Calculation methodology is based on numerical calculation of the following differential

equation for gas liquid mix flow, assuming the negligibly small inertial loss,

dH

dPg

dH

dP

+= , (21)

wheredH

dP- summarized (total) pressure gradient during flow of gas liquid mix in lift, Pa/m;

- density of gas liquid mix, kg/m3;

dH

dP

- frictional loss gradient, Pa/m.

Numerical calculation of equation (21) is not presenting extra complexity from

methodology point of view and is implemented thru one of the methods shown in details [1,2].

The necessary correlations stated above are to be considered as well.

Conclusion

The proposed algorithm for determination of BH pressure and pump intake level pressure

has the most applicable degree of accuracy comparing with existing approaches.

The peculiarity of given calculation algorithm for determination of BH pressure and

pump intake level pressure is that for its implementation sufficient are the reliable data for actualwell operation, content and properties of produced fluid. This, particularly, will allow, when

adapting 3D reservoir models, a more qualified application of previous multiple metering data

for dynamic levels and other well parameters. This aspect particularly, for the most part,

predetermined the statement of corresponding researches.

Literature

1. Reference guide to design the development and operation of oil fields, edition by Sh.K.

Gimatutdinov, Moscow, Nedra, 1983

2.

Mischenko I.T., Calculations in oil production, Moscow, Nedra, 1989

3.

Michael Lissuk, Analysis of existing methodology for determination of annular pressurewith ESP well operation, journal Technique and process of oil production, 2, 2000

Author/Credits

Ildar K. Shayhutdinov

E-mail: [email protected]

Documents

Bottom Hole Pressure Calculation