Mahdi08 - Desalting Plant

Journal of Petroleum Science and Engineering 61 (2008) 116–123

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Journal of Petroleum Science and Engineering

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Characterization and modeling of a crude oil desalting plant by a statisticallydesigned approach

K. Mahdi a, R. Gheshlaghi b, G. Zahedi c,⁎, A. Lohi d

a Department of Chemical Engineering, University of Kuwait, Safat 13060, Kuwaitb Department of Chemical Engineering, Ferdowsi University, Mashhad, Iranc Simulation and Artificial Intelligence Research Center, Department of Chemical Engineering, Faculty of Engineering, Razi University, Kermanshah, Irand Department of Chemical Engineering, Ryerson University, 350 Victoria St., Toronto, ON, Canada M5B 2K3

⁎ Corresponding author. Tel.: +98 831 4274535; fax: +E-mail addresses: [email protected] (K. Mah

(R. Gheshlaghi), [email protected] (G. Zahedi), aloha@r

0920-4105/$ – see front matter © 2008 Elsevier B.V. Aldoi:10.1016/j.petrol.2008.05.006

a b s t r a c t

Article history:

Keywords:factorial designdesalting/dehydration processcrude oil treatment

fields is accompanied by water and dissolved salts, mainly NaCl, which can causeconsiderable operational problem. Therefore, desalting and dehydration plants are often installed in crude oilproduction units to remove water soluble salts from an oil stream. This paper investigates experimentally theeffect offive parameters (demulsifying agent concentration, temperature,washwater dilution ratio, settling timeand mixing time with wash water) on performance of the desalting/dehydration process. The performance wasevaluated by calculating the Salt Removal Efficiency (SRE) and theWater Removal Efficiency (WRE) based on thefive process parameters. In order to investigate the effect of these parameters on desalting/dehydrationefficiencies a 26−1 fractional factorial designwith five other experiments at the center of the design for analysis ofvariance was applied. Based on the statistical analysis, SRE was expressed by a model for the whole range ofvariableswhileWREwas expressedwith twomodels, each is valid in a part of variable domains. Themodelsweresatisfactorily evaluated with plant experimental data. For the SRE, the optimum values of demulsifying agentconcentration, temperature, washwater dilution ratio, settling time andmixing timewithwashwaterwere fondto be 15 ppm, 77 °C, 10%, 3 min and 9 min respectively. As a result the optimum value of 93.28% salt removalefficiency was found. This value was 94.80% and 89.57% for water removal proposed models.

© 2008 Elsevier B.V. All rights reserved.

1. Introduction

Desalting/dehydration facilities are often installed in crude oil prod-uction in order tominimize the occurrence ofwater in oil emulsions. Themainobjectives of installingdesaltingplants are:maintainingproductionrate in a field, decreasing the flow of salt content to refinery distillationfeed- stocks, reducing corrosion caused by inorganic salts and minimiz-ing energy required for pumping and transportation (Bartley, 1982).

The desalting process involves six major steps: separation by gravitysettling, chemical injection, heating, addition of less salty water(dilution), mixing and electrical coalescing. Gravity separation refers tothe primary free settling of water and is related to the residence timethat takes place in both settling tanks and desalting vessels. Thegravitational residence time is governed by the Stokes' law:

v ¼ 2πr2Δρg9μ

ð1Þ

From Eq. (1) it is clear that gravitational separation can beintensified by maximizing size of a drop (chemical injection, electrical

98 831 4274542.di), [email protected] (A. Lohi).

l rights reserved.

coalescing), maximizing density difference between two phases andminimizing viscosity of oil phase (heating, dilution). Several studieshave been done to analyze and study the affecting parameters on SREand WRE (Burris, 1978; Bartley, 1982; Anon, 1983; Agar, 2000; Al-Otaibi, 2004; Al-Otaibi et al., 2005).

These studies denote that the effect of process variables is verycomplicated. Conducting experiments to evaluate and study the effectof parameters on a real plant is costly and time consuming. Specially,the governing laws usually prohibit changing parameters in a realplant and normally it is difficult due to operational limitations.Application of Fractional Factorial Design (FFD), which allowsmultiplefactors to be investigated at the same time, can address theseproblems (Box et al., 1978). Factorial design enables identification ofinteractions between factors more accurately and allows the effects ofone factor that has to be anticipated at several levels of factors studied.Compared to changing one factor at a time and keeping other factorsconstant, factorial design reduces the number of experimental runsrequired (Montgomery, 2001; Murat, 2002; Tansel and Pascual, 2004;Witchakorn and Tharapong, 2005). Consequently, time and consider-able cost of experimentation can be saved.

Experimental design is a collection of mathematical and statisticaltechniques useful for developing, improving and optimizing theprocesses and can be used to evaluate the relative significance of

Fig. 1. Schematic of crude oil desalting/dehydration plant.

Table 1Characteristics and specification of crude oil samples

Property Value

Specific gravity(60°/60°) 0.864Reid vap. pressure(Psia) 10.5Pour point (°F) b−30Average API gravity at 60 °F 31.7Viscosity, Cs (70 °F) 17.4100 °F 10.5130 °F 6.79160 °F 4.8Average sulfur content (wt.%) 2.7Asphaltenes 2.23

117K. Mahdi et al. / Journal of Petroleum Science and Engineering 61 (2008) 116–123

several affecting factors even in the presence of complex interactions.The main objective of experimental design is to determine theoptimum operational conditions of the system or to determine aregion that satisfies the operating specifications. Design of experi-ments is the most efficient approach for organizing experimentalwork. Design of experiments selects a diverse and representative setof experiments in which all factors are independent of each otherdespite being varied simultaneously. The result shows the importanceof all factors and their interactions. These models can be summarizedas informative contour plots highlighting the optimum combination offactor settings. Design of experiments is used for three primaryobjectives: Screening: Which factors are most influential and overwhat range? Optimization: how can we find the optimum settingstaking into account conflicting demands of different responses?Robustness testing: once the optimum is found, can we guaranteerobustness close to that point or do we need to change specificationsto achieve robustness? (Annadurai et al., 2002).

Experimental design reduce the number of experimental runsrequired to determine the effect of changing one process variablescompared to changing one factor at a time. The efficiency ofexperimental design increases as the number of process variablesincrease. Another benefit of design of experiments is that allows effectof one variable to be investigated at several levels of other factors(Myers and Montgomery, 2002).

The application of experimental statistical design techniques indesalting process development can result in improved product yields,reduced process variability, closer confirmation of the outputresponse to nominal and target requirements, and reduced develop-ment time and overall costs (Chen et al., 2003).

This article investigates effects of demulsifying agent concentration,temperature, wash water dilution ratio and settling time and mixingtimewith wash water for desalting/dehydration plant efficiencies using

statistic experimental design approach. To the best of our knowledge,this technique has not yet been applied for this process. In the presentstudy, first a brief description of plant is presented. Next, method ofexperimentation and experimental devices are summarized. Third partof the study discusses experimental design and approaches forobtaining models with validation of results. Finally, optimization andoptimum values of the parameters are described.

2. Materials and methods

2.1. Operating plant

Fig. 1 represents the process flow diagram of a typical desalting/dehydration plant. At point No. 1, an emulsion comprising water andoil flows to a wet tank. Such a common emulsion may contain up to25% water cut. As per design, a typical desalting/dehydration plantwould meet acceptable crude oil specifications; that is, water and saltof the crude must be reduced to 0.10% Vol and 5.0 Pounds perThousand Barrels (PTB), respectively. To remove such large quantities

Table 2Analysis of used brackish water

Property Value

Specific gravity(60°/60°) 1.009Total dissolved solids, ppm 8900Maximum oxygen content, ppm 8Conductivity, micromohs/CC 12,714Ca, ppm 801Mg, ppm 450Iron, ppm 0.25Na, ppm 1926Cl, ppm 4045SO4, ppm 1500HCO3, ppm 285F, ppm 2.5NO3, ppm 13.2NO2, ppm 6SPO4, ppm 10H2S, ppm –

Cl2 –

NaCl, ppm 6665SiO2, ppm 30Carbonate as CO3, ppm –

NaOH, ppm –

CACO3 ppm 289

Table 4Coded parameters used in statistical analysis with their levels

Run A: X1 B: X2 C: X3 D: X4 E: X5 ηSRE

1 − − − − − 382 + − − − − 603 − + − − − 70.834 + + − − − 72.925 − − + − − 74.126 + − + − − 64.717 − + + − − 828 + + + − − 869 − − − + − 4610 + − − + − 5811 − + − + − 72.9212 + + − + − 77.0813 − − + + − 78.8214 + − + + − 67.0615 − + + + − 8216 + + + + − 91.717 − − − − + 5218 + − − − + 6819 − + − − + 77.0820 + + − − + 77.0821 − − + − + 81.1822 + − + − + 76.4723 − + + − + 8824 + + + − + 9125 − − − + + 5226 + − − + + 6627 − + − + + 79.1728 + + − + + 79.1729 − − + + + 83.5330 + − + + + 72.9431 − + + + + 8632 + + + + + 92.133 0 0 0 0 0 9534 0 0 0 0 0 95.7335 0 0 0 0 0 97.3136 0 0 0 0 0 96.137 0 0 0 0 0 95.76

Table 5ANOVA test for selected factorial model

Source Sum of squares df Mean square F-value ProbNF Note

118 K. Mahdi et al. / Journal of Petroleum Science and Engineering 61 (2008) 116–123

of water from the oil stream, a two-stage desalting system is used. Atpoint No. 2, the emulsion leaves the wet tank, where the primarywater separation takes place. At this point, emulsifier is injected into thestream before pumping through the feed pumps. After settling for aperiod of several hours, formation water or stream 13, flows out of thesystem to a wastewater treatment plant or is disposed off to a disposalpit. Point No. 3 shows emulsion flow from the wet tank to a heatexchanger, where heat is recovered from the treated crude productstream (streamNo.10). The emulsion then flows to awater bath indirectheater, raising its temperature (pointNo. 4).Water recycled from secondstage vessel (streamNo. 5) is injected into the emulsionflowcomingoutof the heater. In this system, recycling water from second stage to firststage, aims at minimizing freshwater consumption where a countercurrent flow is employed such that the dispersed brine in the crude iscontacted with freshwater streams each time. At the mixing valve (No.6), an induced shearing force agitates recycled water and emulsion. Asimple globe valve carries out the operation of a mixing valve where anoperatorwould set thedifferential pressure across thevalve to beashighas possible, ensuring bettermixing of the two fluids. StreamNo. 7 leavesthe mixing valve to enter the first stage desalter vessel. Inside the firststage vessel, the emulsion is exposed to a high voltage electrostatic field.The application of the electrostatic field causes coalescence of thedispersed water phase, and thereby due to gravity, the enlarged waterdroplets will fall and collect at the bottom of the vessel. Effluent waterfrom the first stage, stream No. 11, leaves the system to a wastewatertreatment plant or the disposal pit. This effluent water contains variousimpurities and salts that are removed from the water-in-oil emulsion.

Treatment of the emulsion is further enhanced in the second stage-desalting vessel. Stream No. 8 flows through a mixing valve at theentrance of the second stage vessel. The emulsion that has residual saltwater is further mixed with fresh water (stream No. 9). The differentialpressure across the mixing valve is usually maintained around 15 psia.

Table 3Applied levels of independent variables in the FFD

Variable Parameter Applied levels

− (low) + (high)

X1 Temperature (°C) 55 77X2 Settling time (min) 1 3X3 Mixing time (min) 1 9X4 Demulsifying agent concentration (ppm) 1 15X5 Wash water dilution ratio (%) 1 10

Then partially treated emulsion is introduced near the bottom of thesecond stage and, once more, travels upward through the electricalvoltage grids. Also at this stage, larger sizewaterdroplets are formeddueto high voltage electrostatic field and are further separated by gravity.The separatedwater is collectedat thebottomof thevessel and is recycledto the first stage desalter (stream 5), while the treated crude flows fromthe top of the vessel (streamNo.10). The latter stream (treated) continuesto pass through an analyzer (stream No.12). If the treated crude is withinthe specification, a signal is sent to the diverting valve to open the drytank, otherwise the flow is directed back to the wet tank.

2.2. Experimental routine

Kuwait Oil Company (KOC) supplied crude oil, collected from theKuwaiti oil well. The characteristics of this crude oil are illustrated in

Model 5384.62 7 769.23 150.02 b0.0001 SignificantA 100.04 1 100.04 19.51 0.0001B 2214.78 1 2214.78 431.95 b0.0001C 1974.75 1 1974.75 385.14 b0.0001E 309.76 1 309.76 60.41 b0.0001AC 220.08 1 220.08 42.92 b0.0001BC 137.28 1 137.28 26.77 b0.0001ABC 427.93 1 427.93 83.46 b0.0001Curvature 2234.91 1 2234.91 435.88 b0.0001 SignificantResidual 143.57 28 5.13Lack of fit 140.71 24 5.86 8.22 0.0267Pure error 2.85 4 0.71 SignificantCor total 7763.10 36

Fig. 2. Normal probability plot for SRE.

119K. Mahdi et al. / Journal of Petroleum Science and Engineering 61 (2008) 116–123

Table 1. Dilution water used in the experiments was collected fromfield operation in KOC. Table 2 gives the characteristics of thefreshwater used in the experiments. The chemical used as ademulsifier in the experiment is under the trade name Servo CC3408 supplied by Servo Delden BV (Netherlands). In carrying outthe experiments, crude oil samples were first analyzed for salt result(S/R) in PTB and water cut (W/C) in volume percent. Details ofthe laboratory's instruments and experiments are given elsewhere(Al-Otaibi, 2004). Firstly, freshwater was added, followed by theaddition of demulsifier. The mixture was then heated in a water bathheater. The heated mixture was then mixed and poured into a 100-mL centrifuge tube and rotated at speed of 1000 rpm. The final stepin completing one cycle was to collect the top crude volume in thecentrifuge tube and to test it for S/R and W/C. The top volume wastaken because in the real operation process, the treated crude, aftermixing and heating comes out from the top of the desalting vessel.In a real process, an emulsion that was introduced into the systemwas subjected to freshwater injection followed by chemical dosage.The mixture, emulsion, freshwater, and chemical were then heatedto a certain temperature and then mixed together. The resultingblend was sent to a settling tank where water and salt are to bedrained off.

At thefinal stage of theprocess, dryor treated crudeoil samplesweretested and analyzed for S/R andW/C. In each cycle of the experiment, asample of crude oil to be testedwas taken in a sample tube or graduatedcylinder of about 100 mL. Then both freshwater and chemicaldemulsifier were added according to previously set ranges. Crude oil,freshwater, and chemical were next heated and thenmixed for a certaintime (min). Then, the mixture was taken to a centrifuge where it wasrotated for settling purposes. From the top of the centrifuge tube, a

Table 6Comparison of model prediction with plant experimental data for SRE

Standard order Actual value Predicted value

1 38.00 43.842 60.00 59.943 70.83 71.944 72.92 73.405 74.12 76.256 64.71 67.237 82.00 81.448 86.00 87.049 46.00 43.8410 58.00 59.9411 72.92 71.9412 77.08 73.4013 78.82 76.2514 67.06 67.2315 82.00 81.4416 91.70 87.0417 52.00 50.0618 68.00 66.1619 77.08 78.1620 77.08 79.6321 81.18 82.4822 76.47 73.4523 88.00 87.6624 91.00 93.2625 52.00 50.0626 66.00 66.1627 79.17 78.1628 79.17 79.6329 83.53 82.4830 72.94 73.4531 86.00 87.6632 92.10 93.2633 95.00 95.9834 95.73 95.9835 97.31 95.9836 96.10 95.9837 95.76 95.98

certain volume of dry crudewaswithdrawn by amicromilliliter syringeand then transferred to a test beaker. The S/R test was conducted on apartial volume of that dry crude (about 10 mL), and then 50 mL wastransferred to a centrifuge for W/C test.

Theperformanceof thedesalting/dehydrationprocesswasevaluatedby calculating the SRE and WRE. These efficiencies were obtained fromcorrelationsusing the collected experimental data. These efficiencies aretherefore expected to depend on the demulsifying agent concentration,temperature, wash water dilution ratio, settling time and mixing time.The SRE (ηSRE) was calculated from Eq. (2), whereas WRE (ηWRE) wascalculated from Eq. (3), respectively:

ηSRE ¼ 1−ZoutZin

ð2Þ

ηWRE ¼ 1−Xout

Xinð3Þ

where Zout is the outlet salt result (PTB); Zin is the inlet salt result(PTB); Xout is the outlet water cut (%); and Xin is the inlet water cut (%).Calculations of the salinity and water cut efficiencies at differentexperimental conditions were evaluated to determine the effect of thevarious parameters on the performance of the desalting/dehydrationprocess. The objective of next section is to illustrate a way forminimum experimentation based on experimental design methods toinvestigate correlations, which will be able to estimate SRE and WREdepending on process parameters.

2.3. Experimental design

The statistical analysis of the results was performed with DesignExpert version 6.0.4 statistical software (Stat- Ease Inc. Minneapolis,MN). The Fractional Factorial Design FFD was used to investigatefactors that had a significant effect on the SRE and WRE. Theadvantage of FFD is that it allows testing additional factors withoutincreasing the number of experimental runs (Gheshlaghi et al.,2005).

Proper analysis will identify the insignificant factors and will keepthem away from design. In this study, the Analysis Of Variance(ANOVA) combined with F-test has been used to evaluate non-significant terms (p≤0.05). The predictor variables were expressed in

Fig. 3. Residual versus predicted response for SRE.

Table 9Prediction of Eq. (6) and experimental plant data for WRE

Standard order Actual value Predicted value

1 18.75 23.952 37.50 39.063 9.68 14.64 61.29 58.225 33.33 31.296 53.33 55.857 37.5 39.788 77.5 73.969 31.25 31.7510 56.25 56.3111 35.48 31.8412 64.25 66.0213 53.33 48.5414 66.67 63.6615 50 47.5816 87.5 91.217 38.75 34.9118 53.13 51.119 61.29 60.6120 70.97 67.1921 34.67 42.2522 66.67 67.8923 87.5 85.7924 87.5 82.9225 43.75 42.7126 68.75 68.3427 74.19 77.8628 74.19 74.9929 63.33 59.530 73.33 75.6931 93.75 93.632 93.75 100.1733 21.88 21.7234 28.57 21.7235 28.21 21.7236 15.63 21.7237 14.29 21.72

120 K. Mahdi et al. / Journal of Petroleum Science and Engineering 61 (2008) 116–123

the terms of coded variables. The relations between the coded variablexi and its natural variable Xi is defined as:

xi ¼Xi− Xi;high þ Xi;low

� �=2

Xi;high−Xi;low� �

=2ð4Þ

Mixing time, demulsifying agent concentration, temperature, washwater dilution ratio and settling time were assessed for experimentaldesign. The range and the levels of the variables are given in Table 3. A25 fractional factorial design with five replicates at center point foranalysis of variance was carried out.

3. Results and discussion

3.1. Fractional factorial design

The quantitative statistical analysis for effects of the factors onWRE and SRE was performed in this section. The factorial experi-

Table 7Domain division for obtaining WRE

Factors First part Second part

Low High Low High

X3 1 5 5 9X4 1 8 8 15

Table 8ANOVA test for obtaining WRE at first domain

Source Sum of squares df Mean square F-value ProbNF Note

Model 14275.93 10 1427.59 66.80 b0.0001 SignificantA 3321.74 1 3321.74 155.44 0.0001B 2338.43 1 2338.43 109.43 b0.0001C 2115.59 1 2115.59 99.00 b0.0001D 1255.13 1 1255.13 58.73 b0.0001E 3040.25 1 3040.25 142.27 b0.0001AE 647.19 1 647.19 30.29 b0.0001BC 140.83 1 140.83 6.59 0.0166BE 511.76 1 511.76 23.95 b0.0001ABE 726.66 1 726.66 34.00 b0.0001ABCD 178.37 1 178.37 8.35 0.0079Curvature 5723.83 1 5723.83 267.85 b0.0001 SignificantResidual 534.25 25 21.37Lack of fit 352.89 21 16.80 0.37 0.9414 Not significantPure error 181.36 4 45.34Cor total 20534.01 36

mental design and experimental results for SRE are summarized inTable 4.

Based on the experimental values statistical testing was carried outusing Fisher statistical test. The regression model obtained gives SREas a function of different variables as:

ηSRE ¼ 73:25þ 1:77x1 þ 8:32x2 þ 7:86x3þ 3:11x5−2:62x1x3−2:07x2x3 þ 3:66x1x2x3 ð5Þ

The model contains four linear and three interaction terms plusone block term. According to Eq. (5), all terms have positive effectsexcept the interactions between temperature-mixing time (x1 and x3)and interaction between settling time-mixing time (x2 and x3). It isinteresting that demulsifing agent concentration does not have strongeffect on SRE. The advantage of the model can be checked by several

Table 10ANOVA test for WRE at the second part of X3 and X4 domain

Source Sum of squares df Mean square F-value ProbNF Note

Model 8954.97 6 1492.49 26.45 b0.0001 SignificantB 1878.23 1 1878.23 33.29 b0.0001C 4870.85 1 4870.85 86.33 b0.0001E 1210.57 1 1210.57 21.46 b0.0001AC 278.48 1 278.48 4.94 0.0343BC 379.36 1 379.36 6.72 0.0148ABE 337.48 1 337.48 5.98 0.0208Curvature 6093.78 1 6093.78 108.01 b0.0001 SignificantResidual 1636.2 29 56.42Lack of fit 1392.38 25 55.7 0.91 0.6191 Not significantPure error 243.82 4 60.96Cor total 16684.9 36

Fig. 4. Normal probability plot and Studentised residual for WRE based on Eq. (7).

Fig. 5. Response surface for SRE in two cases.

121K. Mahdi et al. / Journal of Petroleum Science and Engineering 61 (2008) 116–123

criteria. The fit of the model was expressed by the coefficient ofdetermination, R2, which was found 0.9672, emphasis that 96.72% ofthe variability in the response can be obtained by the model. Thismeans the model does not explain only 3.28% of the total variation.The value of adjusted determination coefficient is 0.9675, which alsois high to advocate for high significance of the model. Excellentcorrelation between independent variables is indicated by high valueof correlation coefficient (R=0.9740).

Table 11Optimum values of desalting/dehydration process for WRE and SRE

Model Optimumtemperature(°C)

Optimumsettling time(min)

Optmix(mi

SRE(Eq. (5)) 77 3 9WRE(Eq. (6)) 77 3 9WRE(Eq. (7)) 55 3 1

The corresponding ANOVA is tabulated in Table 5. Statistical testingof the model has been done by Fisher's statistical test for analysis ofvariance. The F-value in this table is the ratio of mean square error dueto regression to the mean square of the real error. If a model is a goodpredictor of the experimental data, consequently the calculated F-value should be as big as possible. Themodel F-value of 150.02 impliesthe model is significant. There is only a 0.01% chance that F-value thislarge could occur due to noise. Adequate precisionmeasures the signalto noise ratio. A ratio greater than 4 is desirable. For our proposedmodel, the ratio is 46.687, which indicate an adequate signal, and soforth the model can be used to navigate the design space.

p-value less than 0.05 indicate model terms that are significant atthe probability level of 95%. In this case, x1, x2, x3, x4, x1x3, x2 x3 and x1x2 x3 are significant model terms. Values greater than 0.1, indicate thatthe model terms are not significant. The curvature F-value of 435.88implies that there is significant curvature (measured by differencebetween the range of center points and the average of the fractionaldesign) in the design space. There is 0.01% chance that a curvature F-value with a large value could occur due to the noise. The F-value of8.22 indicates that the fit is significant.

The SRE predicted by the model with the corresponding observedvalue are given in Table 6. Comparing the model prediction and the

imuming timen)

Optimum demulsifyingagent concentration(ppm)

Optimum wash waterdilution ratio(%)

15 105.0001 101 10

Fig. 6. Response surface for WRE based on Eq. (6).

Fig. 7. Response surface for WRE based on Eq. (7).

122 K. Mahdi et al. / Journal of Petroleum Science and Engineering 61 (2008) 116–123

experimental values shows that there is an excellent agreementbetween the model and experimental data.

The normal error distribution was confirmed by plotting thenormal probablity plot of the student residual for the model (Fig. 2).

Constant variance assumption at different levelswere checked at Fig. 3by plotting the studentized residual vs. predicted response as obtainedfrom the model. A constant variance was observed through theresponse range.

The samemethodlogy and analysis used for evaluating the SREwasapplied for the WRE prediction. The study reveals that the predictedresults using the model for the whole range is not satisfactory forWRE. To overcome this drawback the prementioned levels at Table 3for X3 and X4 were divided into two sections to explain WRE. Table 7shows this analysis. Table 8 represents ANOVA test for first section.

Reffering to Table 8, WRE equation for first part of the domain interms of coded factors is expressed by the following equation:

ηWRE ¼ 58:1þ 10:19x1 þ 8:55x2 þ 8:13x3 þ 6:25x4þ 9:75x5−4:5x1x5 þ 2:1x2x3 þ 4x2x5−4:77x1x2x5þ 2:36x1x2x3x5 ð6Þ

In Eq. (6) all linear terms and more concentration terms appear.The equation indicates at lower levels of X3 and X4, interactionbetween parameters is very high. This can be a reason for the failure ofour earlier attempt in expressing the WRE with one equation forwhole range of variables. The model is able to predict the efficiency asshown in Table 9.

The same analysis have been adopted for second range of X3 andX4. ANOVA analysis for this part of study is tabulated in Table 10. Thecorresponding model is expressed as below:

ηWRE ¼ 59:68þ 7:66x2−12:34x3þ 6:15x5−2:95x1x3−3:44x2x3−3:25x1x2x5 ð7Þ

Comparing to Eq. (7) to Eq. (5) one can notice that the temperaturelinear effect is not significant in WRE calculation at higher levels of X3

and X4. Normal probablity chart and studentised residual for thismodel has been shown in Fig. 4 (a) and (b).

123K. Mahdi et al. / Journal of Petroleum Science and Engineering 61 (2008) 116–123

In this study a full scale optimization for process and variables wasrequired. The obtained models were optimized using Matlab program-ming language. The optimal values of the process parameters were firstobtained in coded units and then converted to uncoded units by Eq. (4).The optimumvalues of the process variables for the maximum removalefficiency are shown in Table 11. (Fig. 5) displays the reponse of SRE as afunction of two selected process variables (this means effect of other 3variables has been considered constant). The WRE, based on twoproposed models, have been illustrated in (Figs. 6 and 7).

4. Conclusions

This article explains studies made on the effect of demulsifyingagent concentration, temperature, wash water dilution ratio, settling/mixing time with wash water on desalting/dehydration processefficiency. In order to investigate correlations for SRE and WRE withminimum experimentation FFD were carried out. In this case,minimum experimentation was performed to obtain the correlationsthat led to minimum cost and time of experimentation. A 25 FFD withfive other experiments at the center of the design for analysis ofvariance was conducted. A single model for the whole range ofvariables expressed the SRE, while the WRE was expressed with twomodels, in two different ranges. The models were successfully testedand all confirmed with experimental data. By implementing optimi-zation routines, optimum values of variables to maximize WRE andSRE were determined.

Nomenclaturev Stock's velocity, m/sr droplet radius, mΔρ density difference between two phase,kg/m3

g gravity acceleration, m/s2

μ fluid viscosity, Kg/m sp probabilityη efficiencyZ salinityX water cut, %Xi independent variable real valueXi o variable value at the center pointΔXi step change valueA,B, C, D, E significant model constantsxi coded variable

Subscripts and superscriptsSRE salt removal efficiencyWRE water removal efficiencyin inputout outlet

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