# CALCULATIONS ALLOW PROGRAM TO DESIGN PIPELINES FOR WAXY CRUDE

T. F. Al-Fariss, S. E. M. DesoukyKing Saud University

Riyadh, Saudi Arabia

Calculations have been derived which will permit writing of a computer program for design of a pipeline handling Newtonian, pseudoplastic, or yield-pseudoplastic crudes.

Rheological characteristics of six types of Saudi waxy oils were measured with a Haake Rotovisco Model RV-11 rotational viscometer at 9, 12, 15, 18, 21, and 24C. The relative amount and molecular distribution of wax content in Saudi oils directly affect their Theological behavior.

At an elevated temperature (e.g., 40 C.), wax dissolves in the oil to form a homogeneous fluid. When the temperature is decreased, wax crystals separate out with adsorbed resin, and the rheological behavior of Saudi oils is changed from a Newtonian fluid into pseudoplastic and yield-pseudoplastic successively.

This change in Theological behavior, due to the thermal and shear histories and weight percentage of wax, strongly affects the design calculations of a pipeline handling such Saudi oils.

Statistical analysis was used to find out the variation of Theological behavior with operating temperatures and wax content in various Saudi oils. The evaluation was carried out at a statistical confidence level of 95%.

Experimental data were correlated with respect to power-law and Herschel-Bulkey law. The pipeline design calculations were carried out through a computer program.

The friction factor was determined from Torrance's correlation and Dodge and Metzner correlation for yield-pseudoplastic and pseudoplastic fluids, respectively. The frictional pressure drop was calculated from Darcy-Weisbach equation.

### RHEOLOGICAL BEHAVIOR

An extensive investigation of the rheological characteristics of waxy oils is necessary for optimizing the energy consumption and emphasizing the safety of the designed thickness in a pipeline handling such oils.1

The relative amounts of wax content in Saudi oils directly affect their Theological behavior in the pipeline under either normal operating conditions or after shutdown. This change in Theological behavior was observed at different temperatures as well as different weight percentages of wax.

At an elevated temperature, Saudi oils behave as Newtonian fluids. With a continuous lowering of the temperature, they Theologically exhibit pseudoplastic and yield-pseudoplastic behavior successively.

Although several studies had reported significant effect of temperature on Theological behavior of waxy oils, no agreement had emerged on a general interpretation of such effects for different types of waxy oils.1-4 All the developed rheological equations, which relate the shear stress to the shear rate and temperature cannot be employed in the pipeline design calculations because their applications are limited within a specified temperature range.1 4 5

Because the temperature and rheological behavior of waxy oils vary along the pipeline, there is a need for rheological models which are applicable in a wide range of temperatures.

The t-test is used to investigate the effect of both temperature and weight percentage of wax on rheological behavior of Saudi waxy oils and determine the proper rheological models which correlate the measured data best.6 7 These rheological models should be substituted in the Rabinowitsch-Mooney equation8 to derive the relations which couple wall shear stress (?w) and flow function (8 V I/D).

The derived relations are used to determine the values of n' and k' employing the generalized approach developed by Metzner and Reed.9

For specified pipeline characteristics such as diameter, thickness, length, and flow rate, the friction factor for pseudoplastic oil under turbulent flow conditions is determined from the Dodge and Metzner correlation.10 in case of pumping yield-pseudoplastic oils, the friction factor is determined from Torrance's correlation.8

The frictional pressure drop is determined from Darcy-Weisbach equation.8

All the results obtained are employed in a computer program to carry out the pipeline design calculations. The safety of the pipeline thickness is checked at the end of the design calculations.11

### EXPERIMENTS

Six types of Saudi waxy oils (3 and 6 wt % wax concentration with 43 C. melting point, 3 and 6 wt % wax concentration with 49 C. melting point, and 3 and 6 wt % wax concentration with 60 C. melting point) were tested experimentally.

The Theological characteristics were measured with a Haake Rotovisco Model RV1 1 rotational viscometer at temperatures 9, 12, 15, 18, 21, and 24 C.

In a typical experiment, the sample of the oil to be tested was placed in the viscometer and held at the specified test temperature for 12 hr before the measurements were made. This duplicates the aging time in flow equipment. Then the yield stress was measured at the lowest rotational speed.

Next, the rotational speed was increased and the corresponding shear stress and shear rate values were recorded.

In our experiments, 36 sets of the measured data were obtained. These data were plotted in Figs. 1 and 2.

When these data are correlated as a function of temperature, six Theological models are enough, while 30 rheological models are needed when temperature is not included as a parameter.1 3-5 Thus statistical analysis was helpful to reduce the number of Theological models to be used in pipeline design.

Both temperature and wax effects can be thoroughly studied by carrying out the t-test.6 10 Usually, the t-test is used to check if there is a statistical difference between two sets of data.

This test is carried out by calculating the value of tc from Equation 1 6 7 (box) in which s is expressed by Equation 2. There, U and s are the mean and the standard deviation of n data points, respectively.

The value of tc is then compared with the so called t-tabulated (tt) which can be determined from statistical tables at specified confidence levels and degrees of freedom (df).7

The degree of freedom is calculated from Equation 3.

If tt is greater than tc, it explicitly means that there is no statistical difference between two sets of data at the specified confidence level. Consequently, the two sets of data can be treated as one set.

Before carrying out t-test, it might be advisable to classify the experimental data into yieldless oils and yield oils data. The classification is given in Table 1 from which it can be observed that 13 sets of data comprise yieldless oils, and 23 sets of data represent yield oils.

### TEMPERATURE EFFECT

The results of t-test to investigate the effect of temperature on the Saudi waxy oils are given in Table 2, from which the following points can be observed:

- For yieldless oils, the values of tc are less than the value of tt at a confidence level 95% for Type I, Type III, or Type IV.
This means that the experimental data of each type are statistically not different at the specified confidence level.

In other words, it statistically means that the changes in temperatures were not affected by the rheological behavior of each type.

Hence, the 13 sets of yieldless oil data can be reduced to four sets.

These sets of data are all data of Type I, data of Type II which were measured at temperature of 24 C., data of Type III which were measured at temperatures of 15, 18, 21, and 24 C., and data of Type IV which were measured at temperatures of 21 and 24 C.

- For yield oils, the values of tc for Type II, Type IV, Type V, or Type VI were less than the value of tt. Thus, the experimental data of each type were statistically not different at confidence level 95%.

Hence the 33 sets of yield oil data can be reduced to 5 sets. These sets of data are: all data of Type II except those measured at temperature 24 C.; data of Type III which were measured at temperatures 9 and 12 C.; data of Type IV which were measured at temperatures 9, 12, 15, and 18 C.; and all data of both Type V and Type VI.

### STUDIES WITH WAXY OILS

In an attempt to quantify the effect of wax content in Saudi oils on their Theological behavior, t-test was also carried out for the experimental data of both yieldless and yield oils.

The evaluation is given in Table 3, from which the following can be observed:

- For yieldless oils, a statistical difference between data of Type I and those of Type II, Type III, and Type IV exists. Thus the data of yieldless oils can be divided into two sets: Set 1 and Set 2.
Set 1 includes all data of Type I, and Set 2 consists of the other data which were outlined in Table 1.

- For yield oils, the data of Type VI were statistically different from those of Type II, Type III, Type IV, and Type V.

This means that the data of Type VI can be combined with Set 3, while the other data can be grouped together and named as Set 4.

### DETERMINING MODELS

As has been discussed, the number of data sets became four and involved all the experimental data of Saudi waxy oils at different temperatures.

Because power-law and Herschel-Bulkey models were commonly used in design calculations,1 3-5 9-10 they are employed in the present research work.

Data of yieldless oils (Set 1 and Set 2) were correlated with power-law model: Equation 4 for Set 1 and Equation 5 for Set 2.

In case of yield oils, data of Set 3 and Set 4 were correlated with Herschel-Bulkey model: Equation 6 for Set 3 and Equation 7 for Set 4.

Hence, Saudi waxy oils were time-independent at the specified temperatures, at which their Theological behaviors confirmed to Newtonian (Equation 4), pseudoplastic (Equation 5), or yield-pseudoplastic fluids (Equations 6 and 7).

### DESIGN CALCULATIONS

In order to design a pipeline handling Newtonian, pseudoplastic, of yield-pseudoplastic oils, the design calculations must be based on the Theological properties of yield-pseudoplastic oils. The main reason for this is probably that pumping yield-pseudoplastic oils in a pipeline required higher pressure than those of yieldless oils whether at normal operating conditions or after shutdown.1 4

For a pipeline handling yield-pseudoplastic fluids under turbulent-flow conditions, the design calculations should involve the following:

- Determination of the pressure required to maintain the desired flow rate under normal operating conditions.
- Calculation of the pressure required to restart and maintain the desired flow rate after shutdown.
- Ensuring the safety of the pipeline thickness under maximum operating pressure.

Under normal operating conditions, the pressure required to maintain the desired flow rate is calculated from Equation 8.8

There Pf, PSH, and PKE are the pressures equivalent to friction and static heads and kinetic energy, respectively. The frictional pressure drop can be determined from Darcy-Weisbach equation (Equation 9.)8

In Equation 9, the friction factor is calculated from Torrance's equation (Equation 7).

After shutdown, the frictional pressure required to initiate flow is estimated from Equation 11. This equation is only used when the restarting temperature is higher than the pour point.

In addition, the safety of the pipeline thickness must be checked by using Equation 12.11

The proposed computer program is summarized in Fig. 3. It is capable of handling both laminar and turbulent-flow conditions.

Under laminar-flow conditions, the program computes the pressure drop and designed pipeline thickness and reverts to stop-command. In case of turbulent flow, the program computes friction factor, frictional pressure drop, operating pressure drop, and designed pipeline thickness.

The program can be set up for design purposes with the design procedure shown in Fig. 3.

For such setting up, n = 1 and yield stress 0 for Newtonian oils, and yield stress 0 for pseudoplastic (power law) oils.

The proposed program was executed for an existing pipeline which handles Saudi waxy oils. The pipeline characteristics, waxy oils' properties, and pumping pressures are given in Tables 4 and 5.

### REFERENCES

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- Uhde, A., and Kopp, G., "Waxy Crudes in Relation to Pipeline Operations," Journal of the Institute of Petroleum Vol. 57, No. 554, pp. 63-73, 1971.
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- Metzner, A.B., and Reed, J.C., "Flow of Non-Newtonian Fluids-Correlation of the Laminar, Transition and Turbulent Flow Regions," AlChE Journal, Vol. 1, No. 4, p. 434-440, 1955.
- Dodgo, D.W., and Metzner, A.B., "Turbulent Flow of Non-Newtonian Systems," AICHE Journal, Vol. 5, No. 6, pp. 189-204, 1959.
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