Comparison of Correlations for Estimating Product Yields from

Article pubs.acs.org/EF

Comparison of Correlations for Estimating Product Yields from Delayed Coking J. A. D. Muñoz, R. Aguilar, L. C. Castañeda, and J. Ancheyta* Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas Norte 152, 07730 Mexico, D.F., Mexico ABSTRACT: The objective of this paper is to compare the prediction capability of different correlations for calculating delayed coking yields. The evaluation was developed taking operation data reported in the literature into account for delayed coking commercial plants. The effects of pressure, feed type, and temperature on product yields were analyzed. Correlations that include the effect of operating conditions proved to be more accurate compared to those that consider only feed properties. From the calculation of yields, it is possible to conclude that an increase of 1 wt % of coke yield is obtained for each 1 wt % increase of the feed Conradson carbon residue (CCR) or for each 5 psig increase of the coke drum pressure and a reduction of 1 wt % of coke yield is achieved for each 15 °F increase of the coke drum temperature. The correlation developed by Volk et al. resulted to be the most accurate correlation to predict coke yields, while the most popular correlations (Gary-Handwerk and Maples) are the worst.

1. INTRODUCTION Delayed coking is a type of thermal cracking process used in petroleum refineries to upgrade and convert petroleum residuum (bottoms from atmospheric and vacuum distillation of crude oil) into liquid and gas product streams, leaving behind a solid concentrated carbon material, petroleum coke.1−3 The first commercial delayed coker began operation at the Whiting refinery of Standard Oil Co. in 1930. Foster Wheeler and Conoco Phillips are the mayor contributors with regard to the design, engineering, and construction of delayed coker units. Kellogg has one-third of the world’s delayed coking capacity. Lummus and Flour are the other licensors of the delayed coking process, having relatively lesser market shares.4 In the delayed coking process, the feedstock is introduced directly to the bottom of the fractionators, where it is heated, lighter fractions are removed as side streams, and the fractionator bottoms heated in a furnace with horizontal tubes are used in the process to reach thermal cracking temperatures of 485−505 °C. With short residence time in the furnace tubes, coking of the feed material is delayed until it reaches large coking drums downstream of the heater. The heated stream enters one of the pairs of coking drums, where the cracking reactions continue. For continuous operation, two coke drums are used, where one is on stream and the other is being cleaned. The physical structures and chemical properties of the produced coke determine the end use of the material, such as the fuel and feedstock for use in the aluminum, chemical, petrochemical, or steel industries. Drum overhead products go to the fractionator, where naphtha and gas oil fractions are recovered; these fractions are unsaturated and unstable and require further hydrogenation. Figure 1 shows the process flow diagram of a typical delayed coking unit.5−7 There are four process variables affecting the delayed coking plant. The temperature controls the quality of the coke produced, with a high temperature removing more volatile materials, and the coke yield decreases as the temperature increases. An increasing pressure will increase coke formation and slightly increase the gas yield. The recycle ratio is used to control the end point of the coker gas oil, because it has the same effect as the pressure. Feedstock variables are the characterization © 2013 American Chemical Society

factor and the Conradson carbon residue (CCR), which affect the product yield.4,8−10 The delayed coker is integrated with the rest of the refinery processes, and its feed originates from the crude oil supplied to the refinery. A basic scheme of a refinery, including a delayed coking unit, is shown in Figure 2. A refinery with a coker unit is sometimes called “zero-resid refinery”, which is one of the major advantages of the coking process. Another advantage is the inherent flexibility that this process has for converting a variety of feedstocks, which gives the refinery a solution to the problem of a decreasing residual fuel demand and takes advantage of the attractive economics of upgrading it to more valuable lighter products. Coking reactions are complex, and deriving a detailed kinetic model is a complicated task. The main problem with modeling a delayed coker is the ability to adequately characterize the large, multifunctional molecules involved. Xiao et al.11 developed a cracking product distribution model. It is assumed that all of the reactions are first-order reactions, the cracked products do not take part in secondary reactions, there is no consecutive process in the condensation reaction, and the condensation product is toluene-insoluble. A 12 lumped reaction model for product distribution in thermal conversion of heavy stock was developed by Zhou et al.12 They developed a predictive kinetic model for delayed coking, investigating group composition, including residua. It was concluded that a six-component approach is reasonable to be used as a lumped species for residual stock. Another reaction scheme with 11 lumps was suggested for a delayed coking unit. Results revealed that all kinetic parameters were invariant with respect to the charge feedstock compositions. Bozzano and Dente13 deal with the extension of a mechanistic approach to liquid-phase pyrolysis of hydrocarbon mixtures to delayed coking modeling and with the peculiar aspects of this process. Initially, a kinetic scheme of about 1600 equivalent Received: August 14, 2013 Revised: September 26, 2013 Published: September 27, 2013 7179

dx.doi.org/10.1021/ef4014423 | Energy Fuels 2013, 27, 7179−7190

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Figure 1. Simplified process scheme of delayed coking.25

Figure 2. Delayed coking in a scheme of petroleum refining.

Therefore, empirical modeling techniques appear to be the best approach to calculate product yields and are preferable in refining practice. Companies and consultants of petroleum industries have defined different correlations for determining delayed coker yields; however, these correlations have shortly been used to take into account the yields and product properties that are useful in preliminary studies for making a decision when a delayed coker is desired to be incorporated in an existing or new refining scheme.

reactions involving 450 equivalent components was prepared. In a second time, the reactions have been reduced to about 700. Using the structure-oriented lumping (SOL) concept, Tian et al.14,15 described the reaction behaviors of the delayed coking process. They proposed 92 types of single-core seed molecules and 46 types of multicore seed molecules to characterize the residue. A total of 7004 types of molecular lumps were generated to characterize the molecular composition of residues. These examples show the complexity of the task, as was mentioned earlier. 7180


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2.2. Maples.16 This approach also uses the residual carbon content of the feed as a single independent variable. Correlations were obtained from an extensive database collected in delayed coking plants at typical operating conditions for a wide range of feeds (Figure 3). Feed properties

One method of modeling a delayed coker is an empirical approach, which is based on the fact that the coke yield correlated very well with the CCR of the feed,16 as seen in Table 1, which Table 1. Typical Coke Yields from Delayed Coking17 carbon residue (wt %) 1 5 10 15 20 25 a

API gravity (deg)

coke yield (wt %)

a

0 8.5 18 27.5 35.5 42

NR 26 16 10 6 3.5

NR = not reported.

shows typical yields of the delayed coker for different carbon residue contents in the feedstock.17 The yields of the other products are found to correlate better with the coke yield than with the CCR. The feed American Petroleum Institute (API) gravity is only used for the mass balance, because it has been found that CCR is a better predictor than feed API gravity. The objective of this paper is to compare the prediction capability of the different correlations reported in the literature using data of coking of different vacuum residua.

2. CORRELATIONS 2.1. Gary and Hankwert.18 In the book by Gary and Hankwert,18 a series of correlations are given to obtain the yields of coke, gas (C4−), gasoline (C5−400 °F), and gas oil (400−925 °F) in weight percent and gasoline and gas oil in volume percent. They also reported a typical split of naphtha and gas oil, including the API gravity. The yield data used to develop the correlations came from commercial and pilot plants, with a coke drum pressure of 35−45 psig. The feed was a straight-run residual of less than 18° API. The correlations are

gas (wt %) = 7.8 + 0.144(CCR, wt %)

(1)

naphtha (wt %) = 11.29 + 0.343(CCR, wt %)

(2)

coke (wt %) = 1.6(CCR, wt %)

(3)

gas oil (wt %) = 100 − gas − naphtha − coke

(4)

The weight and volume percents are based on the net fresh feed to the coking unit. To transform naphtha and gas oil yields from weight to volumetric basis, the following equations are used:

naphtha (vol %) = 186.5/(131.5 + API)

(naphtha, wt %) (5)

gas oil (vol %) = 155.5/(131.5 + API)

(gas oil, wt %)

Figure 3. Maples yields of the delayed coking plant.

(6)

range between 1.4 and 21.5° API gravity and CCR content between 2.84 and 25.5 wt %. The correlations are

where API is the gravity of the feed. To split the coker naphtha into light and heavy, the authors proposed light naphtha = 35.1 vol %, 65° API

(7)

heavy naphtha = 64.9 vol %, 50° API

(8)

Similarly, to split the coker gas oil, they proposed

light gas oil (LCGO) = 67.3 vol %, 30° API heavy gas oil (HCGO) = 32.7 vol %, 13° API

(9) (10)

gas yield (wt %) = 0.2745(CCR, wt %) + 4.1264

(11)

naphtha yield (wt %) = −0.0082(CCR, wt %) + 17.025

(12)

gas oil yield (wt %) = −1.9418(CCR, wt %) + 79.225

(13)

coke yield (wt %) = 1.6755(CCR, wt %) − 0.3765

(14)

The correlations for sulfur distribution and API gravity of the products are below. Sulfur distribution:

Gary and Handwerk’s correlations do not include terms to account for the operating conditions, and the only independent variable is the CCR of the feedstock. The application of this method, in general, leads to very unpractical and inaccurate results.

naphtha (wt %) = 0.2002(sulfur in feed, wt %) 7181

(15)


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gas oil (wt %) = 0.74889(sulfur in feed, wt %)

(16)

coke (wt %) = 1.395(sulfur in feed, wt %)

(17)

2.4. Smith et al.21 The basis of the Smith et al. correlation21 comes from Gary and Handwerk.18 They developed equations based on the feed CCR to estimate the yields of coke, gas, gas oil, and naphtha. The effect of pressure (P) was considered in the correlations as seen as follows:

API gravity:

naphtha = 0.3404(API gravity in feed) + 53.60

(18)

gas (wt %) = 7.4 + 0.1CCR + 0.8((P − 15)/20)

(31)

gas oil = 0.9131(API gravity in feed) + 10.356

(19)

naphtha (wt %) = 10.29 + 0.2CCR + 2.5((P − 15)/20)

(32)

coke (wt %) = 1.5CCR + 3((P − 15)/20)

(33)

gas oil (wt %) = 100 − gas − naphtha − coke

(34)

2.3. Castiglioni.19 Castiglioni19 proposed a graphical method to determine delayed coker yields as a function of two feed properties (API gravity and CCR) and three operation variables (combined feed rate, drum pressure, and drum temperature). The products of the delayed coker are dry gas, gasoline, gas oil, and coke. The dry gas is divided into the lighter fraction and propane, and the gasoline is divided into butanes and the C5−400 °F fraction. The method comprises three stages. In the first stage, a reference pressure (0 psig) and the actual drum pressure are considered to estimate the coke yield using the feed CCR and the operation temperature. In the second stage, a series of correction factors are determined as a function of calculated combined feed rate (CFR). In the third stage, a second series of correction factors are obtained as a function of the operation CFR. Finally, gasoline and coke factor corrections are obtained as a function of the yield of gasoline and coke, respectively. The following correlations based on these graphical methods19 were recently reported.20 Coke yield at reference and actual pressures ycoke =

22

2.5. Volk et al. Volk et al. proposed a set of linear correlations to predict the product yields as function of the microcarbon residue (MCR, in wt %), temperature (T, in °F), pressure (P, in psia), and liquid space velocity (LSV, in min−1). The range of operating conditions used to develop the correlations is 900−950 °F, 6−40 psig, and MCR from 16 to 29 wt %. The correlations are liquid (wt %) = − 1.1139MCR + 0.0419T − 0.2897P (35)

+ 1103.08LSV + 41.59

coke (wt %) = 0.9407MCR − 0.0609T + 0.1529P (36)

− 319.759LSV + 65.075

gas (wt %) = 0.1729MCR + 0.0191T + 0.13646P

(A − a1) a2

(37)

− 786.319LSV − 6.762

(20)

where

naphtha (wt %) = −0.3086MCR + 0.0137T + 0.1571P

A = b1CCR + b2

(21)

ai = f (T )

(22)

bi = f (P)

(23)

diesel (wt %) = −0.3339MCR − 0.02635T − 0.0392P (39)

+ 70.957LSV + 50.452

gas oil (wt %) = −0.4714MCR + 0.0546T − 0.4076P

CFR = − 0.2621B2 + 1.2806B − 0.0072

(24)

The authors stated that the correlations could not be used to predict yields from industrial cokers, because of the lower liquid yields obtained in the microreactor, as compared to those observed in refineries, which becomes worse at the lowest feed rate. Also, the correlations include the effects of LSV, which has a different meaning than that for commercial units. For these reasons, the following correction was proposed to derive product yields:

ycoke at operating pressure ycoke at reference pressure

(25)

Yields of gas and gasoline and the total product yield are calculated by

yi = c1ycoke 2 + c 2ycoke + c3

(26)

Factor to adjust the product yields of the delayer coker in the second step

F1i = d1CFR2 + d 2CFR + d3

(27)

Another factor employed in the last step for updating gasoline and coke yields

(i = gasoline, coke)

(28)

where

ei = f (CFR)

(29)

coke* (wt %) = 0.91coke

(41)

gas* (wt %) = 0.82gas

(42)

liquid* (wt %) = 100 − (coke* + gas*)

(43)

gasoline* (wt %) = 0.75gasoline(liquid* /liquid)

(44)

diesel* (wt %) = 0.90diesel(liquid*/liquid)

(45)

gas oil* (wt %) = liquid* − (gasoline* + diesel*)

(46)

23

2.6. Ren et al. This approach suggests that the product yields of delayed coking are dependent upon some feedstock properties and operating conditions using a quadratic polynomial with seven parameters

The final product yields, Ytotal and YG calculated in step 2 and Ycoke and YGNE calculated in step 3 can be applied to obtain the yield of gas oil by the difference between the total yield and the dry gas, gasoline, and coke yields.20

YVGO = Ytotal − (YG + Ycoke + YGNE)

(40)

+ 1851.76LSV − 25.315

where

F 2i = eiycoke + e 2

(38)

− 819.63LSV + 16.461

An equivalent CFR

Bi =

22

Y = a + bρ + cρ2 + dC R + eC R 2 + fTF + gTF2 + hTCT + iTCT 2

(30)

+ jPCT + kPCT 2 + lRe + mRe 2 + nR WO + oR WO2

Castiglioni’s charts do not allow for prediction at pressures above 30 psig or feedstocks with CCR higher than 25%; therefore, for such conditions, extrapolation is necessary, which is an important limitation of this approach.

(47)

where Y is the product yield, ρ is the feedstock density (g/cm ), CR is the feedstock carbon residue (wt %), TF is the outlet temperature of the heating furnace (°C), TCT is the temperature at the top of the coking 3

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Table 2. Coefficients of the Ren et al. Correlation23 coefficient

gas

naphtha

diesel

gas oil

coke

a b c d e f g h i j k l m n o

−1604.84 2975.15 −1535.6 −2.0776 0.0745 −2.0453 0.0022 3.2603 −0.00395 −113.08 323.99 −0.904 3.1095 −0.3115 0.0087

8204.07 −1684.88 902.68 0.6467 −0.0333 −23.9931 0.0242 −7.0614 0.00849 143.73 −430.81 8.7034 −0.6101 −0.9956 0.0826

296.17 4195.53 −2156.8 1.6932 −0.0531 −13.3962 0.0134 4.9307 −0.00581 −125.82 392.27 −10.4991 14.2094 0.4796 −0.0387

−17013.22 −4142.02 2071.01 −9.376 0.2823 75.9003 −0.0763 1.6519 −0.00216 −9.68 −5.02 −6.8568 −9.3768 1.4769 −0.1182

10217.82 −1343.78 718.71 9.1137 −0.2704 −36.4657 0.0366 −2.7814 0.00342 104.85 −280.43 9.5564 −7.332 −0.6494 0.0656

Table 3. Properties of Crude Oil and Vacuum Residues, Operating Conditions and Yields of Delayed Coking Commercial Plantsa effect of the feedstock properties effect

A

B

C

D

F

G

10.48 21.56 11.53

6.8 27.4 11.88

4.38 32.1 11.75

CCR (wt %) API gravity (deg) sulfur (wt %) viscosity at 210 °C (cSt) viscosity at 275 °C (cSt) viscosity at 305 °C (cSt)

31.00 2.3 6.08 205965

29.00 3.7 5.3 27968

22.44 7.9 2.34 4081

pressure (psig) temperature (°F) feed rate (min−1) recycle ratio

30 900 0.01 1.10

30 900 0.01 1.10

30 900 0.01 1.10

15 925 0.008 1.05

gas (wt %) naphtha (wt %) gas oil (wt %) coke (wt %)

9.05 13.50 39.80 37.65

9.00 12.50 35.51 42.99

8.59 12.30 30.00 49.11

9.2 9.21 39.80 41.79

effect of the temperature

J

L

M

H

I

8.73 26.99 11.84

7.50 29.50 11.90

5.4 31.6 NRb

5.4 31.6 NR

8.24 27.00 NR

8.24 27.00 NR

26.13 2.27 4.61 36525 1753

22.44 5.79 4.50 12117 935

15.60 10.3 2.62

15.60 10.3 2.62

19.00 5.7 2.16

19.00 5.7 2.016

120

120

703 309

703 309

15 925 0.008 1.05

15 925 0.008 1.05

15 925 0.008 1.05

15 930 0.0073 1.10

40 930 0.0073 1.10

30 900 0.014 1.10

30 930 0.014 1.10

9 8.81 35.51 46.68

8.96 8.90 32.00 50.14

8.6 9.06 30.00 52.34

8.20 17.20 56.83 17.77

12.77 21.20 43.33 22.70

5.00 14.00 59.00 22.00

6.50 15.00 58.50 20.00

Crude Oil Properties 11.83 11.24 11.00 10.82 21.24 22.36 22.81 23.15 11.70 11.75 11.77 11.79 Vacuum Residue Properties 31.00 30.04 29.05 29.00 0.1 0.713 0.778 1.4 5.15 5.01 4.97 4.85 3744000 137000 12100 85.640 46000 5340 4490 2605

CCR (wt %) API gravity (deg) characterization factor (K)

2227

E

effect of the pressure K

189 Operating Conditions 15 15 925 925 0.008 0.008 1.05 1.05 Yields 9.02 8.99 9.04 8.90 36.57 35.50 45.37 46.61

a Data A−C, Cold Lake, Arabian Heavy, and Alaska North Slope crude oil processing in refineries in the U.S.A., respectively; data D−I, Maya− Isthmus crude oils with different mix processing in refineries in Mexico; data K−M, data taken from ref 21; data J and K, paraffinic crude oil; and data L and M, naphthenic crude oil. bNR = no reported.

The properties of the crude oil and vacuum residue, operating conditions, and yields of delayed coking units used for the correlations are shown in Table 3. To evaluate the effect of the feed properties on product yields, two data sets at different operating conditions were used: (1) columns A−C at 30 psig and 900 °F and (2) columns D−I at 15 psig and 925 °F. The effect of the pressure was examined with values of columns J−K, and the effect of the temperature was examined with values of columns L−M. 3.1. Effect of the CCR Content. In a conventional refinery scheme, the feed to delayed coker is typically vacuum residue, whose properties are a function of the type of crude fed to refinery. The main variable that affects the product yields of the delayed coker is the CCR content of the feedstock, which is why all correlations include it.

tower (°C), PCT is the pressure at the top of the coking tower (MPa), Re is the recycle ratio, RWO is the water injection/oil weight ratio, and a, b, c, d, e, f, g, h, i, j, k, l, m, n, and o are the model coefficients (Table 2) for each product. The authors reported good accuracy with average absolute error from 1 to 2.3 wt %.

3. RESULTS AND DISCUSSION The correlation proposed by Ren et al.23 was excluded from the analysis because it exhibited quite high deviations to predict the product yields with different vacuum residua. For the other correlations, the predicted values were compared to real information recovered from commercial cokers. The comparisons were performed to examine the effects of the feed properties (CCR content), pressure, and temperature. 7183


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Figure 4. Yields of the delayed coker as a function of the CCR content in the feedstock, for data set 1.

3.1.1. Data Set 1. Figure 4 illustrates a parity plot of the results obtained with the correlations for the data set 1 at constant conditions with a temperature of 900 °F and a pressure of 30 psig. The predictability of correlations can be divided in three groups: (1) Gary−Handwerk18 and Maples16 correlations showing less accurate predictions with a global average absolute error higher than 33%, which is partially due to the use of these correlations for predicting coking yields for feeds with properties out of the range of applications and the dependency of yields only upon feed CCR, (2) Smith et al.21 and Castiglioni19 correlations with a global average absolute error of 28−29%, which include the effects of the pressure and temperature, respectively, and (3) Volk et al.22 correlation providing an average relative absolute error of 5.89%, with the important error reduction in this case being because of the incorporation of the liquid space velocity as a variable and further adjustment of yields with the relationship derived from industrial data of commercial plants. In general, all correlations tend to overestimate the yields of gas, naphtha, and coke and consequently underestimate the yield of gas oil, mainly because the latter is obtained as the difference (balance) of the total yield and the remaining fraction yields. Surprisingly, the most used and well-known correlations (Gary−Handwerk, Maples, and Smith et al.) presented high errors, 20−40% for gas, 24−70% for naphtha, 27−57% for gas oil, and 20−36% for coke yields. It should be remembered that Gary and Handwerk and Maples approaches only use the feed CCR content, while Smith et al. incorporates the effect of the pressure, which slightly improves its accuracy. On the other hand, Volk et al. and Castiglioni correlations, in addition to the feed CCR content and the effect of the pressure, include the effects of the temperature and liquid space velocity. These two additions improve the accuracy of these two approaches to a great extent. Previous reports have indicated that Castiglioni correlations predict reasonably well the yields of the coking process.24 Volk et al. correlation showed the lowest errors,

0.6−8.9% for gas, 1.61−21.79% for naphtha, 3.88−5.5% for gas oil, and 0.22−6.68% for coke yields. For feedstock properties and evaluated operating conditions, the correlation of Gary−Handwerk is outside the pressure range up to 5 psig (35 psig) and the Castiglioni correlation is 60 °F lower in temperature (840 °F); however, average global errors derived from these correlations are greater than 28%, 4 times larger than the error obtained by Volk et al. (6%). In the commercial delayed coker, an increase in the coke yield from 30 to 39.8 wt % was observed when the CCR increased from 22.44 to 31 wt %. For this range, a ratio of 1 wt % increase in the coke yield is observed for each 1 wt % of CCR increase in the feed. In summary, the correlation with the best performance for calculating yields of the delayed coker was that developed by Volk et al., followed by Castiglioni, Smith et al., Maples, and Gary−Handwerk. 3.1.2. Data Set 2. The results of the predictions for the data set 2 at a constant temperature and pressure of 925 °F and 15 psig, respectively, are shown in Figure 5. The accuracy of prediction of product yields obtained from the delayed coker with the different correlations is similar to that encountered for data set 1, with the Volk et al. correlation being the best correlation. Global error for the different correlations showed, in general, an average 10% increase compared to those obtained for data set 1. The increment in error may be attributed to the different operating conditions reported for data set 2. The data set 2 comprises five different feedstocks in commercial delayed coking plants in Mexican refineries using vacuum residue from Maya and Isthmus crudes in different volume ratios (from 100% Maya to 30% Maya/70% Isthmus mixtures). The vacuum residue from Maya crude typically has a low API gravity, which is out of range for the correlations of Maples and Castiglioni. For the Gary−Handwerk correlation, 7184


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Figure 5. Yields of the delayed coker as a function of the CCR content in the feedstock, for data set 2.

Figure 6. Yields of the delayed coker as function of the pressure in the drum coker.

include pressure and temperature effects tend to reproduce coking product yields with lower error. 3.2. Effect of the Pressure. Figure 6 illustrates the results obtained with the different correlations for the effect of the pressure in the coking drum at a constant temperature of 930 °F and 15.6 wt % of the CCR content in the feed. Only Volk et al., Smith et al., and Castiglioni correlations were examined because they consider the effect of the pressure. The global error in the Castiglioni correlation showed an average

the pressure is out of range at 20 psig and for the Castiglioni correlation, the temperature is below 85 °F. The average global error for Gary−Handwerk, Maples, and Castiglioni correlations was 61, 50, and 46%, respectively, 2 or 3 times greater than the error obtained by Volk et al. (17%). The effect of feed was examined with only three points for data set 1 and five points for data set 2. It is then anticipated that more information is needed for a better ranking of correlations. Despite this, it can be established that those approaches that 7185


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Figure 7. Yields of the delayed coker as function of the temperature in the drum coker.

Figure 8. Comparison of commercial and calculated yields.

is due to a negative effect of the pressure in vapor−liquid equilibrium in the coker drum; i.e., an increase of the pressure increases the gas yield, leading to higher error in correlations. The evaluated pressure range of 15−40 psig is outside the upper limit for the Castiglioni and Smith et al. correlations,

value of 20.47%, while Smith et al. and Volk et al. correlations reduced the error to 17.27 and 7.08%, respectively. Volk et al. correlation presented errors of 0.05−13.85% for gas, 4.18−5.51% for naphtha, 2.68−4.42% for gas oil, and 7.82− 18.15% for coke yields. The high error observed for the gas yield 7186


4.12 6.20

16.85 3.18

20.22 5.50

18.53 4.34

2.96 3.18

20.22 66.00

10.56 17.41

accounting for 30 and 35 psig, respectively. The average global error for these correlations is between 2 and 3 times higher than the value of the Volk et al. correlation. In commercial delayed coker, increasing the pressure from 15 to 40 psig causes an increase in the coke yield from 17.17 to 22.7 wt %. That is, an increase in the coke yield for each 1 wt % is obtained for each 5 psig increment of operating pressure in the coking drum. The ranking of correlations for the effect of the pressure based on better performance follows the order: Volk et al. > Smith et al. > Castiglioni. 3.3. Effect of the Temperature. Figure 7 shows the results with the correlations for the effect of the operating temperature in the coke drum, maintaining a constant pressure of 30 psig and CCR content in the feed of 19 wt %. Volk et al. and Castiglioni correlations showed similar global errors of 10.56 and 17.41%, respectively. The gas, naphtha, and gas oil yields were better estimated with the Volk et al. correlation, while the estimation of the coke yield was better predicted using the Castiglioni correlation. The evaluated temperature range of 900−930 °F is outside the upper limit for the correlation of Castiglioni at 840 °F. The average global error for the Castiglioni correlation was almost twice the value obtained with the Volk et al. correlation. In commercial delayed coker, increasing the temperature from 900 to 930 °F reduces the coke yield from 22 to 20 wt %. Thus, the coke yield increases 1 wt % for each 15 °F increment in the operating temperature of the coking drum. 3.4. Comparison of Correlations. The former correlations for calculating product yields of delayed coking were published at the earliest in the last quarter of the past century by Gary− Handwerk,18 Maples,16 and Castiglioni,19 while Smith et al.21 and Volk et al.22 correlations were published at the beginning of this century. The first two correlations only take into account the CCR content in the feedstock; Castiglioni also includes temperature and pressure in ranges of 800−840 °F and 0−30 psig, respectively. Smith et al.21 adds the pressure correction considering a range of 15−35 psig, Volk et al.22 appends more than all of the previous variables, evolving a broader range of the CCR content, API gravity, temperature, and pressure. Under these conditions, the following comparison was made. Figure 8 shows the comparison between calculated and commercial product yields for all of the data reported in Table 4 using all correlations. A large dispersion is observed for all cases. However, the yields predicted with the Volk et al. correlation are closer to the 45° line practically along the interval, as compared to the other correlations, which indicates better accuracy of fit. Gary−Handwerk and Maples approaches showed higher deviations virtually in the entire range, while Smith et al. correlation results are among those of Volk et al., Gary−Handwerk, and Maples. The Castiglioni correlation gave similar values as Smith et al. and Volk et al. correlations in the low yield (gas and naphtha) region, while in the high yield (oil and coke) region, in some cases, the estimated values showed larger deviations than Gary− Handwerk and Maples correlations. The average absolute error including all considered effects is in the following increasing order: Volk et al. (10.14%) < Smith et al. (27.57%) < Castiglioni (28.03%) < Maples (41.63%) < Gary− Handwerk (49%). Figure 9 shows the residual of the data points for all of the correlations. As seen, most of the residual data are negatives,

5.29 9.15

7.08 17.27 20.47 18.15 31.68 42.05 0.05 4.58 4.07 12.98 25.64 20.89 18.15 31.68 27.31 7.82 19.60 14.46 3.55 5.78 21.24 4.42 6.98 34.09

61.23 17.03 49.75 35.74 45.65 141.06 60.54 90.55 82.63 143.80 19.68 0.51 19.61 11.75 2.35 28.00 9.22 32.95 20.00 35.57 31.43 13.94 36.60 23.22 52.01 19.68 5.99 24.07 12.20 29.16 52.69 4.34 47.58 32.50 13.70 61.20 6.35 54.46 37.76 37.72

41.56 5.89 33.51 29.71 28.60 69.90 21.79 49.46 43.72 60.00 19.68 0.22 19.75 19.25 1.20 24.99 2.51 29.80 23.67 24.50 30.67 6.68 35.77 28.84 52.67 19.68 0.22 24.07 19.70 2.00 46.71 4.85 41.19 35.79 22.39 56.94 5.50 49.46 42.14 46.45

12.40 20.00 8.28 10.67 9.25 43.77 7.01 21.54 Volk et al. Castiglioni

11.49 66.00

5.51 22.03 15.09 4.18 22.00 4.07 6.95 15.64 30.17 0.05 9.27 18.29 Volk et al. Smith et al. Castiglioni

13.85 22.00 42.05

141.06 60.54 90.55 82.63 143.80 109.57 39.05 82.09 63.11 66.56 31.90 5.12 31.52 13.74 21.72 28.27 0.51 19.61 11.75 2.97 Gary−Handwerk Volk et al. Maples Smith et al. Castiglioni

34.43 7.78 37.35 15.34 33.67

69.90 21.79 36.92 43.72 60.00 54.37 1.61 24.23 35.39 45.93 32.33 5.28 31.22 21.01 15.13 35.51 8.90 39.62 22.65 19.34 28.42 0.60 19.75 19.25 8.27 Gary−Handwerk Volk et al. Maples Smith et al. Castiglioni

max min average max min

max

average

min

max

average

min

max

average

min

coke gas oil naphtha gas

Table 4. Percentage of Absolute Relative Error for Yield Fractions for All Correlations

Article

Feed Effect, Set 1 62.22 30.61 10.94 3.88 31.81 27.41 38.38 24.27 52.38 1.20 Feed Effect, Set 2 132.32 34.89 49.45 3.10 86.94 31.89 76.72 19.91 111.63 2.35 Pressure Effect 4.84 2.68 22.02 4.58 9.58 8.39 Temperature Effect 10.34 2.96 15.33 3.25

global

average

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Figure 9. Residual values.

Table 5. Statistical Analysis intercept

slope

Gary−Handwerk Volk et al. Maples Smith et al. Castiglioni

9.91 1.53 7.47 4.59 3.20

0.5514 0.9126 0.6697 0.7686 0.8665


17.40 1.89 12.40 8.53 9.48

0.3263 0.8942 0.4980 0.6278 0.5870


14.45 3.41 11.51 6.61 7.44

0.2926 0.8978 0.4125 0.6836 0.7749


18.16 5.14 16.54 11.05 −0.47

0.4755 0.8323 0.5566 0.7133 0.978


13.87 2.26 10.86 6.95 4.56

0.4452 0.9095 0.5654 0.7221 0.8174

residual (+) Gas 1 3 1 2 4 Naphtha 2 9 2 4 6 Gas Oil 4 7 4 5 7 Coke 2 7 2 2 9 Global 9 26 9 13 26 7188

residual (−)

maximum absolute error (%)

8 10 8 9 9

138.87 43.82 85.60 80.29 143.80

7 4 7 7 7

138.81 48.33 88.62 80.90 138.19

5 6 5 6 6

141.06 54.99 90.55 82.63 141.26

7 6 7 9 4

109.57 60.54 85.88 63.11 66.56

27 26 27 31 26

141.1 60.5 90.5 82.6 143.8 dx.doi.org/10.1021/ef4014423 | Energy Fuels 2013, 27, 7179−7190

Energy & Fuels

Article

increase of 5 psig pressure in the coke drum. (3) A reduction of 1 wt % of the yield of coke for each increase of 15 °F in the temperature of the coke drum.

which mean that the models have the tendency to underpredict commercial values. Available data yields by fraction or global were applied to determine the intercept and the slope of the linear equation between commercial and predicted yields for each correlation. The intercept, slope, number of positive and negative residuals, and maximum absolute error are reported in Table 5. The intercept and slope of the Volk et al. correlation in the five cases (gas, naphtha, gas oil, coke, and global) are nearest to 0 and 1, respectively, indicating a better agreement with the real data compared to the other correlations. The negative and positive residual data in the global analysis are balanced, representing a random distribution. However, in the fraction cases, the gas fraction accounts for more negative residuals and naphtha fraction accounts for more positive residuals, indicating a tendency to underpredict and overpredict values, respectively. The Castiglioni correlation behavior is similar to that of the Volk et al. correlation. The gas fraction predicts greater values, and the coke fraction predicts smaller values; however, the positive and negative residuals are globally balanced. The intercept (between −0.47 and 9.48) and slope (between 0.5740 and 0.978) values are very different to 0 and 1, respectively, indicating predictions with the greatest errors. Smith et al., Maples, and Gary−Handwerk correlations have the tendency to underpredict values for all of the fractions. Currently, delayed coking plants have increased severity in operating conditions to obtain higher yields of products, such as naphtha and gas oil, and only the Volk et al. correlation shows a wide range of validity in the pressure and temperature, which leads to more accurate calculations of product yields from the delayed coker. The characterization factor value indicates that crude oils are naphthenic−paraffinic-type. The trend is seen that the more paraffinic crude is (higher characterization factor value), the higher the coke yield is obtained because of the cracking reaction of paraffinic hydrocarbons.

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AUTHOR INFORMATION

Corresponding Author

*Fax: +52-55-9175-8429. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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4. CONCLUSION There are few correlations reported in the literature to calculate product yields of the delayed coker. Some correlations are based on the content of CCR in the feedstock, while others include pressure and temperature effects. Correlations that include the effect of operating conditions proved to be more accurate compared to those that consider only feed properties. The Volk et al. correlation exhibited the highest accuracy for the estimation of the delayed coker yields, probably because this correlation uses the CCR content in the feed, pressure, temperature, and liquid space velocity as variables and a correction to improve the prediction of commercial yields. Castiglioni and Smith et al. correlations show less accuracy than the Volk et al. correlation, because these correlations use CCR, P, and T for Castiglioni and CCR and P for Smith et al. Gary−Handwerk and Maples correlations account for the highest deviation because they are based only on the content of CCR in the feedstock. Correlations that only include feed properties underestimate the commercial values of gas, gasoline, and coke yields. The gas oil yield is neither overestimated nor underestimated. Gas oil yield prediction showed the highest error in most of the correlations, because it is obtained as the difference (balance). From the evaluation of different effects, the following ratios arise for the considered range of operating conditions: (1) An increase of 1 wt % of coke yield for each increase of 1 wt % of CCR in the feed. (2) An increase of 1 wt % of coke yield for each

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NOMENCLATURE A = factor in the delayed coker model in eq 20 ai = parameter in eq 20, where i = 1 and 2; parameter in eq 22, where i = 0, 1, and 2 a, b, c, d, e, f, g, h, i, j, k, l, m, n, and o = model coefficients (Table 2) for each product API = gravity of the feed (deg) B = factor in the delayed coker model in eq 24 bi = parameter in eq 21, where i = 1 and 2; parameter in eq 23, where i = 0, 1, and 2 CR = feedstock carbon residue (wt %) CCR = Conradson carbon residue CFR = equivalent combined feed rate ci = parameter in eq 26, where i = 1, 2, and 3 di = parameter in eq 27, where i = 1, 2, and 3 DC = delayed coker ei = parameter in eq 28, where i = 1 and 2 F1i = factor for product “i” of the delayer coker model in eq 27 F2i = factor for product “i” of the delayer coker model in eq 28 LSV = liquid space velocity (min−1) MCR = microcarbon residue (wt %) P = pressure PCT = pressure at the top of the coking tower (MPa) Re = recycle ratio RWO = water injection/oil weight ratio T = temperature TCT = temperature at the top of the coking tower (°C) TF = outlet temperature of the heating furnace (°C) Ttotal = total yield Y = product yield yi = yield of product “i” ycoke = coke yield Ycoke = yield of coke YG = yield of dry gas ygasoline = gasoline yield YGNE = yield of gasoline YVGO = yield of gas oil ρ = feedstock density (g/cm3) REFERENCES

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Comparison of Correlations for Estimating Product Yields from

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