**۱٫ Introduction**

Gas-condensate reservoirs are vicious sources of hydrocarbon deliberate as an middle of oil and gas reservoirs. As a hydrocarbon prolongation starts, these reservoirs act as a singular proviso gas reservoir. Initial glass vigour is above a dew indicate curve, and as a outcome of fountainhead prolongation and vigour decrease, a condensate will form as a apart proviso within a reservoir. Gas-liquid ratio in gas-condensate reservoirs changes between 3200 to 150000 SCF/STB (Danesh, 1998).

Wellhead throttle is a form of valves commissioned to control a good upsurge and to strengthen aspect comforts from repairs due to vigour variation. Positive and tractable chokes are a categorical forms used on wellheads. Positive chokes has a bound cranky section, though a cranky territory of tractable chokes can be tranquil instrumentally. Fluid upsurge by chokes might be possibly vicious or subcritical.

There are fanciful and initial methods for throttle modeling. In 1949, Tangren et al. (1949) presented a initial fanciful review on two-phase upsurge opposite a restrictions like chokes. Ashford and Pierce (Ashford et al., 1975) also presented a fanciful indication for calculating vigour dump for multiphase upsurge by chokes and Sachdeva et al. (1986) extended a review of Ashford and Pierce. In 1954, Gilbert (1954) due a elementary initial association for vicious upsurge by chokes and this association became a bottom for some other researchers such as Ros (1960), Baxendell (1957), Achong (1961) and Pilehvari (1981). Al-Attar and Abdul-Majeed (Al-Attar et al., 1988) compared some throttle upsurge correlations such as Gilbert and Ashford indication with prolongation information from 155 good tests. They showed that a Gilbert indication had a smallest normal blunder within a complicated indication for upsurge calculations by chokes. Osman and Dokla (Osman et al., 1990) analyzed margin information to benefaction initial correlations for chokes in gas-condensate wells. Perkins (1993) generated equations from ubiquitous appetite equation that described isentropic upsurge of multiphase mixtures by chokes. Al-Towailib and Al-Marhoun (Al-Towailib et al., 1994) employed some-more than 3500 prolongation exam information from 10 fields in a Middle East to benefaction an initial association for two-phase vicious upsurge by chokes. Elgibaly and Nashawi (Elgibaly et al., 1998) due initial correlations for two-phase upsurge by wellhead chokes formed on information from a Middle East oil wells. Esmaeilzadeh et al. (Esmaeilzadeh et al., 2006) due opposite initial forms of throttle equation deliberation several parameters such as vigour dump and upstream heat and accurate them with information from 5 gas-condensate reservoirs in Iran. Lak et al. (2014) done a comparison between some of initial and fanciful models for good upsurge bursting calculations in a gas-condensate margin and showed that a fanciful fatalistic indication has some-more correctness in upsurge calculation.

In this paper, a Gilbert equation form is practiced for a gas-condensate fountainhead fluid. The initial information for this examine is taken from DST information conducted for several prolongation wells of this reservoir. Also, a outcome of wellhead heat on throttle calculation is investigated for Gilbert form of throttle equation.

**۲٫ The margin and cavalcade branch exam data**

The complicated gas-condensate margin is located during a Persian Gulf offshore. It includes 11 handling platforms in a complicated block. Each height contains several wells. Well prolongation streams pass by a stretchable throttle valve to revoke pressure, and afterwards they are churned together during a aspect and sent to refinery.

A set of cavalcade branch exam (DST) information were collected from opposite wells of this gas-condensate margin in a time duration from 1992 to 2013. This set of information contains wellhead vigour and temperature, throttle diameter, separator vigour and temperature, and upsurge rates of gas, condensate, and water. A schematic of aspect routine is shown in Figure 1.

**Figure 1**

A schematic of aspect process.

According to this figure, wellhead upsurge prolongation enters a exam separator after flitting opposite a throttle valve with a specific opening diameter. Gas, condensate, and H2O subdivision is achieved in a exam separator. Then, separator condensate enters a batch tank in customary conditions (60 °F and 1 atm), and condensate and gas leave a batch tank. Total gas upsurge rate (*q _{g}*) is a sum of separator gas and batch tank gas upsurge rates. Gas-liquid ratio (GLR) is distributed by dividing sum gas upsurge rate by sum glass (water and condensate) upsurge rate (

*q*+

_{c}*q*) as shown in Equation 1:

_{w}A representation of aspect DST information is given in Table 1. Totally, 864 DST datasets are collected and complicated in this work. Plot of GLR contra wellhead vigour is shown in Figure 2. As seen in this figure, wellhead vigour operation is 1580 to 4180 psi, and GLR changes between 13900 and 43300 SCF/STB. In average, H2O calm is 5% of sum glass upsurge rate. Ranges of operational variables are presented in Table 2.

**Figure 2**

Values of GLR contra wellhead vigour of DST data.

The information presented in Tables 1 and 2 uncover that a H2O upsurge rate is available as 0 in 231 information entries or 26.7% of all a data. It is due to a doubt of H2O flowmeter since infrequently a upsurge conductor does not work scrupulously and formula in a H2O upsurge rate of 0 in recording DST data. This creates a meant comprehensive blunder of 5% in a measuring of sum glass proviso upsurge rate.

**Table 1**

A representation of aspect DST data.

**Table 2**

Ranges of operational variables in DST data.

**۳٫ Choke modeling**

As mentioned before, a wellhead chokes are commissioned to control a good upsurge or downstream pressure. If upsurge quickness by a throttle is rebate than a sound speed, it is called subcritical flow. Otherwise, upsurge in a throttle is vicious when issuing quickness is larger than a sound speed. In a vicious flow, a upsurge rate is not contingent on downstream conditions. For a compressible fluid, a upsurge rate increases when vigour ratio decreases. Once vicious vigour ratio has been reached during a sonic velocity, a upsurge becomes choked and a upsurge rate stays consistent (Holland et al., 1995).

Several initial models have been grown for vicious throttle upsurge modeling. The ubiquitous form of these models is presented in Equation 2 that is formed on Gilbert investigations on chokes (Guo et al., 2007).

where, *C*, *m*, and *n* are initial constants associated to glass properties in this equation. Gilbert distributed a values of 10, 0.546, and 1.89 for *C*, *m*, and *n* respectively on a basement of prolongation information from a 10 territory margin in California (Gilbert, 1954).

Other values for a constants were due by other researchers such as Ros (1960), Baxendell (1957), Achong (1961), and Pilehvari (1981). These values are presented in Table 3. The optimized values of a constants are not unique, and there is rather a vast movement in a constants, mostly for *C*, and to a rebate border for *m* and *n*.

**Table 3**

Empirical parameters of Equation 2.

Because of opposite ranges of operational parameters such as upsurge rate, pressure, and GLR, a optimized constants of a certain dataset can't be used to make predictions from another dataset, and this can lead to a substantial error. For example, if a strange Gilbert equation (Gilbert, 1954) is used to envision wellhead vigour for representation aspect DST information of Table 1, a meant comprehensive blunder (ME%) of 28.2% will be resulted, as shown in Table 4. The relations blunder and meant comprehensive blunder percent are distributed from Equations 3 and 4.

**Table 4**

Wellhead vigour calculations with strange Gilbert (Gilbert, 1954) equation (*C*=10.00, *m*=0.546, and *n*=1.89).

Standard flaw from a meant comprehensive blunder is discernible by Equation 5. This parameter shows a apportionment of blunder values around a meant error.

Mean comprehensive blunder is distributed for a whole DST information with a mentioned models. The calculation formula are presented in Table 5.

**Table 5**

The meant comprehensive blunder of models for a whole DST data.

As these calculations show, a blunder of a complicated models is between 18.5 to 85.1%. Respectively, Achong and Pilehvari have a smallest and limit errors between these models. Also, a parameter *C* of a throttle Equation 2 is smallest and limit for these dual models (respectively 3.82 and 46.67). Generally, it appears that high *C* values means a aloft blunder in throttle calculations for this gas-condensate fluid. In other words, reduce values of *C* should be used for a displaying of wellhead chokes in this gas-condensate reservoir.

**۴٫ Method of DST information regression**

In Gilbert equation and identical equations, parameters such as gas-liquid ratio and throttle distance seem in energy form. Therefore, after holding logarithm, equation translates to a linear equation to obtain constants with a minimization of a calculation error.

Taking logarithm from both sides of Equation 2 formula in Equation 6:

The blunder of vigour calculation for a given indicate (*e _{i}*) and a sum of block of errors (

*S*) are discernible as Equations 7 and 8:

Then, *S* is discernible as a summation of blunder squares:

Parameter *S* will be minimized supposing that all prejudiced derivatives are equal to zero. In other words:

Writing a equations for 3 derivatives leads to a set of equations with *C*, *m*, and *n* as unknowns. These equations are shown with Equations 10 to 12.

By elucidate this set of equations, a best values for parameters *C*, *m*, and *n* are calculated.

In sequence to examine a outcome of heat on throttle calculations, Gilbert equation was altered and wellhead heat was deliberate in a equation, as follows:

Taking derivatives of Equation 14 with honour to constants *n*, *m*, *C*, and *k* formula in set of Equations 15 to 18:

**۵٫ Results and discussion**

In this study, a calculations are achieved for dual sets of DST data. The initial dataset includes all 864 information points. The second dataset involves those points for that H2O upsurge rate is available; this set includes 633 information points. The formula are presented in Table 6.

**Table 6**

Regression results.

Figure 3 compares a distributed contra reported wellhead vigour for all a data. The 45° line is also shown for improved comparison. The reported wellhead vigour contra a distributed wellhead vigour for information with a specified H2O upsurge rate is shown in Figure 4.

**Figure 3**

The reported wellhead vigour contra a distributed wellhead vigour for all a data.

**Figure 4**

The reported wellhead vigour contra a distributed wellhead vigour for a information with a specified H2O upsurge rate.

According to a results, information but a H2O upsurge rate are sparse during a tip of a graph. Uncertain information have a meant comprehensive blunder of 8.6%, while a blunder of a remained information is 3.9%; a meant comprehensive blunder is 5.1% for all a data. It is between dual mentioned errors. In this case, for 38% of a capricious data, a meant comprehensive blunder is some-more than 10%, that indicates that these information are a vital means of a error. In other words, capricious information boost a retrogression blunder of all a data.

The formula uncover that a retrogression for a information containing H2O upsurge rates is some-more accurate with a meant comprehensive blunder of 3.0%. In this case, 3% of a sum information has some-more than 10% error. Better retrogression is due to a rejecting of a capricious data. In other words, 5% blunder of a glass proviso upsurge measurement, that includes 26.7% of all a data, means an boost of 2.1% in a blunder of calculations. This implies that a rejecting of capricious information causes a substantial rebate of blunder in calculations, and stealing capricious information in information filtering will outcome in some-more accurate calculations. The parameters performed from this retrogression can be used for a throttle calculation of gas-condensate glass with correct accuracy.

Therefore, nonetheless a water-condensate ratio is not high, and in normal H2O forms 5% of a sum glass phase, throttle calculation correctness decreases due to neglecting H2O upsurge rate.

The formula of a retrogression of Equation 13 for information with a specified H2O upsurge rate are shown in Table 7. Also, a wellhead vigour distributed by Equation 2 contra a wellhead vigour distributed by Equation 13 for this retrogression is shown in Figure 5.

**Table 7**

Regression formula for Equation 13.

**Figure 5**

The wellhead vigour distributed by Equation 2 contra a wellhead vigour distributed by with Equation 13.

The retrogression formula for Equation 13 uncover that a meant comprehensive blunder of 3.0% does not change, and there is not a substantial disproportion between a wellhead pressures distributed by Equations 2 and 13. Therefore, deliberation a wellhead heat in a Gilbert equation form has no discernible outcome on throttle calculation accuracy.

**۶٫ Conclusions**

In this work, vicious upsurge calculations by chokes were complicated formed on DST information from a gas-condensate reservoir. The H2O upsurge rate of 26.7% of these information was 0 since of doubt in H2O flowmeter. Therefore, DST information was divided into dual sets; a initial dataset contained all a data, and, in a second, a capricious information was eliminated. The bottom form for throttle calculation was Gilbert model. Using DST data, a equation parameters was modified.

The formula showed that doubt in H2O upsurge rate decreases a correctness of regression. Uncertain information had a meant comprehensive blunder of 8.6%. The meant comprehensive blunder was 5.1% for all a information and 3.0% for information with a specified H2O upsurge rate. This shows that a rejecting of capricious information causes a conspicuous rebate in error.

For study a outcome of wellhead heat on calculations, heat was deliberate in a calculation equation, and specified information and parameters were mutated again. The formula showed that a meant comprehensive blunder is 3.0%, and there is no poignant disproportion between a wellhead vigour values distributed by a new equation and those distributed by Gilbert form equation. Therefore, wellhead heat has no substantial outcome on throttle calculation.

**Nomenclature**

Article source: http://ijogst.put.ac.ir/article_50694_5204.html