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Wells performance is evaluated by IPR curves that show the relationship between bottomhole pressure and inflow rate. This curve and its outcome equation can be applied for production schedule and maintenance management of well and reservoir. But, the measuring of bottomhole pressure to approach these curves needs much time and high expenses and also running special tools in wells. In these operations, the probability of catastrophic failure such as well damage or well complete lost may exist. However, these difficulties in offshore wells like production platform in the South Pars gas field that are installed tens kilo meters far from lands are harder than any places. Therefore, nowadays by considering these difficulties, there is a high tendency for using wellhead test data that are very inexpensive as well as these data are less accurate than in well data. Moreover, pressure drop due to the existence of gas condensate in well fluid causes the flow regime to be more complicated. Wide researches have been applied to two-phase flow pressure drop in the wellbore and a lot of equations are considered. Anyhow, these equations and their accuracy should be studied in each special case. In this study that is on the south Pars gas condensate field wells, widespread of equations are utilized for calculation of pressure drop in the tubing and they are applied for tubing performance curve as well. In the south pars field wells, the well data of bottomhole pressure are not being measured during production. In this paper, we try to calculate bottomhole pressure by using PIPESIM software and simulating reservoir fluid and wellbore. For calculating this pressure, with the combination of effective conditions, the best equation of flow regime in that well will be selected. Eventually, by simulation of the reservoir fluid, different parameters like in well performance and proper tubing size is calculated.

Well performance equations are written based on the well bottomhole pressure and flow rate, but measured bottomhole pressure required time, cost and great equipment. This graph is applied to estimate the well production and production planning for the wells and reservoir management. The main challenge to obtain this graph or inflow performance relation (IPR) is well bottomhole pressure measurement which deals with some main problems.

Pressure drop due to the gas condensate in wells causes complexity of the gas condensate wells flow.

Extensive research on two-phase flow pressure drop in the well column is done and some equations are proposed in this case. However, these equations and their accuracy must be checked for any special case. The study is done on the wells of South Pars gas condensate field. A wide variety of these equations that applied in calculating the pressure drop in the tubing is applied to obtain tubing performance curve.

One of the important parameters in the design of multiphase flow pipeline is determining the number of phases in the system while the process of transmission and distribution, respectively. To investigate and describe multiphase fluid phase behavior, we need to accurately understand and recognize hydrocarbon’s phase diagrams (multi-component systems). So that the incorrect results of predicting multiphase fluid phase behavior cause the unacceptable design of the transfer system, separation system, and other multiphase flow operation.

Normally, when a mixture of oil and gas in a flow pipeline, due to lower density and viscosity of the gas phase than the liquid phase, the gas phase will navigate more quickly. In two-phase flow due to retardation or slow-moving liquid phase to the gas phase is called slippage [

Some quantities at the two-phase flow due to the difference in speed between the two phases may have retardation which is a point function. In general, retardation of liquid is called hold up which defined as the ratio of the volume occupied by the fluid (including the volume of liquid and gas) to the total tube volume.

Consultants for expression of physical properties of a fluid based on pure components, the compositional fluid model is applied. So the separation of fluid phase equilibria and homogeneous properties by blending properties of its components, are determined. The accuracy of this model depends on the accuracy in determining the properties of pure components constituting the fluid.

The most important characteristic of two-phase flows is the interface between the gas and liquid phases with the common different shapes. There is the possibility of the existence of an infinite range of different interfaces between two phases. But generally, the effect of surface tension between two phases leads to the creation of curved interfaces that ultimately all of them are into spherical shapes (such as drops and bubbles). There are several flow regime or flow pattern in vertical, horizontal or inclined flow such as bubble or slug flow.

Many relations were applied to predict two-phase flow pressure drop in flow lines in the last decades. The only correct way to predict empirical evaluation of the two-phase pressure drop is compared the predicted pressure drop with measurement or practical pressure drop (in fields). Evaluation of empirical equations of pressure drop was conducted by several researchers. All of these comparative studies are generally preferred method proposed by researchers.

A group of researchers including Brill-Lawson and Vohra et al., examined nine empirical relations using field data from 726 wells follows as below: 1―Poettmann, Carpenter [

It should be noted that all these researchers have applied the same empirical relations to predict and calculate phase properties in all these methods. For comparison the results of this study, the parameters of the mean deviation (APD) and standard deviation (SD) are applied as follows:

A P D = ∑ i = 1 n e i / n (1)

S D = [ ∑ i = 1 n ( e i − A P D ) 2 / n − 1 ] 0.5 (2)

In the above relations, “n” is the total number of data related to pressure drop and deviation, “e_{i}” can be determined by the following equation:

e = 100 ( Δ P 1 − Δ P 2 Δ P 1 ) (2)

According to

For gas condensate reservoirs usually, the Duns and Ros [

One of the applications of well performance modeling is related to well’s cement performance as Carey et al. [

Standard deviation | Mean deviation percent | Method |
---|---|---|

195.7 | −107.3 | Poettmann, Carpenter |

195.1 | −108.3 | Baxendell, Thomas |

36.1 | −5.5 | Fancher, Brown |

50.2 | −15.4 | Duns, Ros |

26.1 | −1.3 | Hagedorn, Brown |

35.7 | −8.6 | Orkiszewski |

27.6 | −17.8 | Beggs, Brill |

34.7 | +8.2 | Aziz et al. |

43.9 | +42.8 | Chierici et al. |

well cement with 30 years of CO_{2} exposure from the SACROC Unit, West Texas, USA was obtained. Related to hydraulic fractured wells, Fan and Thompson [

In this paper, the best tubing equation compatible with the empirical data has been chosen as the Tubing-Performance-Relation (TPR). Also, the Rawlins and Schellhardt inflow equation compatible with the empirical data has been chosen as the IPR. By applying the sensitivity analysis on the most effective parameters, the best coupled IPR-TPR model has been proposed as a semi-empirical model to optimize the flow equation through the gas condensate wells.

This simulation steps are carried out as follows.

1) Getting the required data for the simulator run.

2) Plot pressure gradient through the well based on the different pressure gradient relations.

3) Plot pressure gradient through the well based on the measured pressure gradient data obtained from the PSP.

4) Compare the pressure gradient curves obtained from steps 2 and 3.

5) Select a best or accurate relation has the best fit on PSP data as the optimum

pressure gradient relation.

6) Calculate the bottomhole pressure from the selective optimum pressure gradient relation.

7) Calculate the well head pressure from the corresponding calculated bottomhole pressure.

8) Plot the IPR and Tubing-Performance-Relation (TPR) curves and obtain the required parameters including optimum production rate.

9) Change some parameters in order to see their impact on bottomhole pressure.

Simulation of reservoir fluids properties is usually the most accurate method for analysis of reservoir fluids characteristic, especially in the wet gas systems, condensate, and volatile oil. So, in any case to accurate whether information about reservoir fluids is low available for production engineers, equation of state is the best choice. The ideal gas low is accurate for gas systems in low pressure and or high temperature. But for some gas systems, such as gas condensate reservoirs with high pressure and temperature, it is so inaccurate. As a result, more accurate equations of state of gases and condensate have been developed. The equations that are applied in the simulation study are Viscosing equation of state, multi flash, and sis flash. Sis flash test includes two and three parameter Peng-Robinson (PR) equation of state. Multi flash test also includes PR, BWRS, SRK, standard PR, and standard SRK. In this paper we utilize the multi flash equations of state, PR equation of state, which are more flexible than other groups. Also, in viscosity calculation by two LBC and Pedersen method, Pedersen method is used because of lower sensitivity to used equation of state than LBC

Group equations | ||||
---|---|---|---|---|

Relation groups | Bja | Ansari | Beggs & Brill original | Beggs & Brill revised |

Duns & Ros | Govier Aziz & Fogarasi | Gray (modified) | ||

Gray(original) | Hagedorn & Brown | Hagedorn & Brown, Duns & Ros map | ||

Mukherjee & Brill | No Slip Assumption | Orkiszewski | ||

Tulsa University Fluid Flow Projects (TUFFP) | ||||

Tulsa | Beggs & Brill | Duns & Ros | Govier, Aziz | |

Hagedorn & Brown (Revised) | Hagedorn & Brown (original) | Mukherjee & Brill | ||

Orkiszewski | ||||

Shell Flow Correlation | SRTCA two-phase | SRTCA three-phase (standard) | SRTCA three-phase (with WO dispertion-experts only) | |

Shell SRTCA & Artificial slug correlations (version 1.1 1999) | SRTCA two-phase | SRTCA two-phase slugging | SRTCA two-phase slugging & slug DP | |

SRTCA three-phase | SRTCA three-phase & water-oil dispertion | |||

Shell SIEP correlations August 2000 | GZM-NEWPRS oil systems | GZM-CO_{2}PKG CO_{2} rich systems | GZM-GASPKG gas/condensate systems | |

MMSM-Moreland Mobil Shell Method | SHELLFLO-Harmonized WTC/SRTCA |

method. In 55% - 70%water production is called the cutoff point. The emulsion viscosity is calculated by volume ratio method.

Based on flow data analysis for a large number of gas wells have been obtained from Rawlins and Schellhardt (1936), a relationship between gas flow rate (Q_{SC}) and squared pressure drop, reservoir pressure (P_{R}) and well flow pressure (P_{wf}), that can be expressed as follows: [

Q S C = C ( P R 2 − P w f 2 ) n (4)

The variable “n” represents the excessive fluid pressure drop due to high gas velocity or turbulence effect and may range from 1 to laminar flow and to 0.5 for turbulent flow and variable “C” in the above equation related to reservoir rock properties, reservoir fluid properties, and reservoir geometry.

In gas condensate reservoirs, the annular-mist flow regime is more common. In this paper the Turner drops model is applied for the simulation of condensate drops flow around and within the well. Within the well, gas velocity causes a drag force acting on the drops. If drag force resulted by gas velocity is equal to gravity force of drop, gas velocity is called critical gas velocity. In velocity lower than critical velocity, drops fall and we can see liquid loading phenomenon in the wellbore, and in velocity higher than critical velocity, drops rise.

The information needed to build a simulation model in the software environment should be investigated.

The measured depths of facilities in the simulated well N1 are considered as 309.67, 2061, and 2725 for SSSV, tubing, and liner, respectively.

For simulation, PVT properties of the reservoir fluids which are showed in

Finally, relations in the software is used to calculate pressure drop with the help of main required input data for the well pressure drop simulation as

At first

According to the above figures, it is obvious that Hagedorn & Brown (original) relation has the best fit or the lower error (

Varying the friction factor and the holdup factor parameters are to reduce the error of the Hagedorn & Brown (original) pressure gradient relation that this relation is not sensitive to these two parameters.

Pwf (Psia) | Twh (F) | Pwh (Psia) | Q (MMSCFD) | Depth (m) |
---|---|---|---|---|

4378 | 181.04 | 3440 | 82 | 2725 |

4424 | 179.96 | 3525 | 57 | 2725 |

4488 | 139.46 | 3624 | 33 | 2725 |

Well Fluid Composition | Comp. | Mole % | Molecular Weight | Specific Weight |
---|---|---|---|---|

H_{2}S | 0.2 | 34.076 | ||

CO_{2} | 2.2 | 44.01 | ||

N_{2} | 3.0 | 28.013 | ||

C_{1} | 78.9 | 16.043 | ||

C_{2} | 7.2 | 30.07 | ||

C_{3} | 3.4 | 44.097 | ||

IC_{4} | 0.1 | 58.124 | ||

NC_{4} | 0.4 | 58.124 | ||

IC_{5} | 0.318 | 72.151 | ||

NC_{5} | 0.8882 | 72.151 | ||

C_{6} | 0.5975 | 84 | 0.685 | |

FR_{1} | 1.3471 | 107.34 | 0.73937 | |

FR_{2} | 0.8904 | 146.11 | 0.78182 | |

FR_{3} | 0.5588 | 222.47 | 0.8431 | |

Reservoir Pressure-P_{r} (Psia) | 4555.39 | |||

Reservoir Temperature-T_{r} (F) | 215 | |||

Well Performance Model or Reservoir Model | Fetkovitch | |||

Well Completion Model | Cased-hole | |||

Well Direction Model (m) | Actual Depth = 2725 Measured Depth = 2725 No Inclination Vertical Well | |||

Temperature Gradient Model | Hagedorn & Brown (original) | |||

Bottomhole Facilities Model | Packer, Production Casing, Tubing, … | |||

Pressure Drop Calculation Optimum Model | Plot Pressure vs. Depth |

Er % | Math Correlation | Gas Rate (MMSCFD) | WHP from Correlation (Psia) | WHP from PSP (Psia) | Well Number |
---|---|---|---|---|---|

0.1 | Hagedorn & Brown (original) | 82 | 3443.6 | 3440 | #1 |

1.3 | Hagedorn & Brown (original) | 57 | 3570.8 | 3525 | #1 |

1.1 | Hagedorn & Brown (original) | 33 | 3663.7 | 3624 | #1 |

WHP from Pipesim (Psia) | Hold up Factor | Friction Factor | Q (MMSCFD) | Math Correlation |
---|---|---|---|---|

3443.6 | 1 | 1.5 | 82 | Hagedorn & Brown (original) |

3443.6 | 1.5 | 1 | 82 | Hagedorn & Brown (original) |

3443.6 | 1.5 | 1.5 | 82 | Hagedorn & Brown (original) |

After the choice of the optimum relation, the optimum bottomhole pressure is calculated with the help of Hagedorn & Brown (Original) and Gray (modified) pressure gradient relations. At first,

Now bottomhole pressure can be calculated by Hagedorn & Brown (Original) pressure gradient relation at the various wellhead pressures and flow rates.

Finally, with the help of the calculated bottomhole pressure and according to the log-log plot “(P_{ws}^{2} − P_{wf}^{2}) vs. Q”, the parameters n (−), and c (MMSCFD/Psi^{2}) can be predicted as 0.73395466 and 0.0025888781, respectively. Also, the flow turbulency can be investigated.

The wellhead pressure as well as the flow rate is applied as input data.

Also,

Er % | WHT from Pipesim (F) | WHT (F) | Gas Rate (MMSCFD) | Math Correlation |
---|---|---|---|---|

11.44 | 201.7 | 181 | 82 | Hagedorn & Brown (original) |

11.27 | 200.3 | 180 | 57 | Hagedorn & Brown (original) |

11.64 | 196.5 | 176 | 33 | Hagedorn & Brown (original) |

Pwf (Psia) | Pwh (Psia) | Q (MMSCFD) with +5% |
---|---|---|

3930.4 | 2958.5 | 103.28 |

3913.9 | 2912.1 | 109.48 |

3900 | 2866.2 | 115.55 |

3892.5 | 2841.6 | 118.62 |

Pwf (Psia) | Pwh (Psia) | Q (MMSCFD) with −5% |

3879.7 | 2958.5 | 93.44 |

3856.5 | 2912.1 | 99.06 |

3835.5 | 2866.2 | 104.55 |

3824.2 | 2841.6 | 107.32 |

Pwf (Psia) | Pwh (Psia) with +5% | Q (MMSCFD) |

4068.5 | 3106.425 | 98.36 |

4045.1 | 3057.705 | 104.27 |

4023.9 | 3009.51 | 110.05 |

4012.4 | 2983.68 | 112.97 |

Pwf (Psia) | Pwh (Psia) with −5% | Q (MMSCFD) |
---|---|---|

3740.1 | 2810.575 | 98.36 |

3724.3 | 2766.495 | 104.27 |

3710.9 | 2722.89 | 110.05 |

3703.7 | 2699.52 | 112.97 |

effect on the bottomhole pressure. Moreover, by increasing the wellhead pressure, the calculated bottomhole pressure increases.

The Hagedorn & Brown (original) pressure gradient relation has the best fit or the lower error in prediction of bottomhole pressure in this gas condensate well study. Therefore, this relation can be applied in other cases with close characteristic and can be replaced with the high time and cost operation. Also, this relation at the higher flow rate has an accurate results in the pressure gradient prediction.

Hagedorn & Brown (original) pressure gradient relation at every flow rate is not sensitive to the friction factor and the holdup factor parameters. Therefore, in any quantities of these parameters or any effects, causing an increase or decrease, doesn’t effect on this relation ability to predict the bottomhole pressure.

Hagedorn & Brown (original) pressure gradient relation can be applied to predict the wellhead temperatur. However, at 57 MMSCFD flow rate, the predicted wellhead temperature is more accurate.

Two-phase flow in the gas condensate well can be formed in the well column at a higher flow rate. At a lower flow rate two-phase flow in the gas condensate well can be formed in the well column at a higher depth. In this case, two-phase flow can be formed for 33 MMSCFD flow rate at 2682 meters.

The bottomhole pressure can be easily and low-costly obtained by this relation with a high accuracy, because of the elimination data points which at these points the wellhead pressure and the flow rate data sets are not valuable.

The well performance curve can be plotted and “n” and “c” parameters are obtained. “n” quantity shows an intermediate laminar-turbulent well flow in this case. Also, the calculated “n” parameter that is between 0.5 and 1 is a reason for acceptable analysis by this method.

The sensitivity analysis is done and shows that the flow rate variation has a low effect on the bottomhole pressure with the at acceptable results at any flow rate.

The sensitivity analysis is done and shows that the wellhead pressure variation has a considerable effect on the bottomhole pressure. Additionally, by increasing the wellhead pressure, the calculated bottomhole pressure increases.

Finally, this relation shows so good results as mentioned previously. So, this is usable to construct TPR and IPR curves and obtain the optimum flow rate in this case.

The authors are grateful to the south Pars gas Company for supporting this research’s data.

Ejraei Bakyani, A., Rasti, A., Qazvini, S. and Esmaeilzadeh, F. (2018) Gas Condensate Wells Simulation to Optimize Well Flow Performance Using Tubing Equations Coupled with Inflow-Performance-Relation (IPR) Curve. Open Access Library Journal, 5: e4590. https://doi.org/10.4236/oalib.1104590