Tests of a pilot pipeline, built to mirror conditions of an operating Egyptian pipeline, have confirmed the validity of commonly available equations for calculating length and quantity of interfacial mixing.N. O. Shaker, R. MansourEgyptian Petroleum Research Institute

Cairo

The research investigated the possibility of using the Shokeir-to-Assiout pipeline (Fig. 1 [108,959 bytes]) for batching crude oil and LPG with no physical barrier despite the density difference between pumped products.

The research paid specific attention to minimizing losses from interfacial mixing and to operational philosophy. The work began by checking the validity of available equations for calculating length and quantity of interfacial contamination with data of another active pipeline, Suez to Mostorod.

Then, a pilot pipeline was built to simulate the operating conditions of the Shokeir-to-Assiout pipeline and to investigate the flow of batches on this line. Included were calculations of loses and contamination and their mathematical treatment for prediction.

The results indicated batched pumping to be economically and environmentally feasible.

### Unconventional flow

Pipelines are the most economical means for transporting oil, natural gas, and petroleum products overland and subsea. Nevertheless, the search continues for more-efficient pipeline design and construction approaches to operational and maintenance problems.For the last two decades, energy consumption, market dynamics, and the high cost of new pipeline construction have necessitated unconventional flow in which LPG is batch-transported through pipelines with other products or crude oil.

The major problem we are dealing with originates with the Petroleum Pipelines Co. regarding the transportation of crude oil and LPG from Shoukeir (Gulf of Suez) to Assiout (Upper Egypt) through a single pipeline.

Solving problems in fluid flow requires determining the variation of pressure with velocity from point to point throughout the flow line in three dimensions as well as such other factors as friction. In addition to losses from wall friction in a piping system, there are also losses of mechanical energy and pressure from flow through valves or fittings.

Furthermore, unless accurate means of interface detection and control system are used, the problem of mixing one product with another in the storage tank may ruin the entire stored quantity.

Because the current problem is too complicated to solve analytically, experimental studies would then be the only means for evaluating fluid flow.

Therefore, the approach to solving the problem was to construct experiments by pumping both materials (crude oil and LPG) and calculating the interface (experimentally and theoretically).

The necessary analysis on certain samples may be then performed to evaluate and assess the results.

The pilot investigation consisted of two parts:

- Check the validity of a set of equations for calculating length and quantity of interface (contamination). To realize this goal, the operating Suez-Mostorod pipeline was chosen.
- Construct a pilot pipeline that almost simulates the conditions of Shoukeir-Assiout pipeline (the main target).

### Validity check

First, the analytical data and specifications of four pumped materials (LPG, benzene, kerosine, and diesel) were studied (Table 1 [26,183 bytes]).Then the validity of the available equations for calculating the lengths of interface and the possible quantities of interfacial contamination caused by batch interference were compared with actual data resulting from pumping of successive different batches.

These equations, which were obtained via the Institute of Mechanical Engineering, and prototype calculation procedures are given in the accompanying box.

The trajectory of Suez-to-Mostorod (East of Cairo) has two portions: the first is 10-in. OD, 89-km long; the other is 12-in. OD, 51-km extension.

Interface quantities of different pumping scenarios through this line are given in Table 2 [41,564 bytes], while Table 3 [38,450 bytes] summarizes the actual measured interface quantities vs. calculated.

Table 3 clearly indicates the validity of the equations supplied for interface measurements and may therefore be considered a good basis for dealing with the current problem.

### Pilot construction; sampling

A pilot pipeline 775 m long was designed to have two different segments of 12 and 16 in. OD but having the same wall thickness. The first segment of smaller diameter was of 200 m long; the second, 575 m (Fig. 2 [99,216 bytes]).The arrangement of the pipeline was constructed at Petroleum Pipelines Co., Mostorod-Cairo, in order to simulate (as closely as possible) the flow of crude and LPG through the Shokeir-Assiout pipeline.

The pilot unit was fitted with a digital 10-6 g/cc precision density meter near its outlet in order to detect the interface that was formed by the pumping of crude oil and LPG. Flow rates were 160 cu m/hr and 200 cu m/hr for LPG and crude oil, respectively.

The experimental procedures and the operational philosophy employed through the experimental work are the following:

- Calculating the possible length and quantities of interfaces as a result of crude oil and LPG flow in the pilot unit.
- Conducting a set of experiments on the flow of both liquids through the pilot unit; measured data of interface were compared with calculated ones.
- For forecasting, mathematically fitting data.

^{1}

A liquid sample was transferred from the source into a sample container to fill up to 80% of its capacity.^{2-4} Crude oil, LPG, and interface samples were collected and analyzed.

Analyses of interface samples provided residue determination in LPG by weathering at 36° F. (ASTM-D), and gas chromatographic analysis of the residue present in LPG after heating at 36° F. (method ASTM-D 2163-82).^{3-6} One of the important functions in liquid pipelines, especially those in which more than one product is shipped, is to record passage of the interface between two products, or batches. This capability is necessary to provide accurate measurement of the volume of each product shipped.

In products pipeline, for example, the difference in properties between two products may be small, and inter-phase detectors must be quite sensitive (OGJ, Nov. 30, 1981, p. 80).

Densitometers have been used widely for interface detection; the present case used an automatic densitometer connected to dispatching control center.

### Predicting

With the results of the five runs, prototype analysis of which is given in Table 4 [55,885 bytes], another phase of data processing was started for forecasting.The investigated process, i.e., the relationship between time (t) and density (p), varies from one higher asymptote (crude-oil density) to another lower asymptote (LPG density; Fig. 3 [46,968 bytes]).

Such a relationship is better described by exponential functions. The fitting step has yielded a unique mathematical model for all five runs that presents high level of fit.

The model has the form of the following equation: r = (a + b * *f* (t)) ^{-1} in which a and b are constants; *f* (t) is a time function: *f* (t) = (1 + exp (c - d * t )) ^{-1} in which c and d are constants.

The regression coefficient of mode^{1} (R^{2} = 0.985) shows almost absolute accuracy of the fitting, which in turn leads to reliable calculations.

The extrapolation of this formula (Fig. 4 [51,546 bytes]) illustrates the fact of two asymptotes: the constancy of both densities with time as only one fluid flows. The negative time to the left of the x-axis means the time period behind the start of the experiment. This figure confirms the correct choice of the model.^{1}

To have a complete set of information, the fitting process continues to produce the composition (Y) and its relationship with density, so that one can predict by time vs. density the fluid composition at interface.

This phenomenon, density-composition-relationship, happens between 100 vol % of one fluid to the complete absence of it and the presence of 100 vol % of the other fluid through a time period of interface contamination.

To fit this relationship to a mathematical form, the authors chose the following model:

Y = (a + c * p)/(1 + b * p) in which a, b, and c are constants; RIn finding the limits of the model,^{2}= 0.99.

^{3}by dividing both the numerator and dominator by p, supposing p = ( (i.e., one fluid density-no contamination), we get (p

^{(infinity)}= (c/b), which is a constant value almost equaling 100%. Fig. 5 [51,261 bytes] illustrates both measured and model data.

### References

- ASTM Standards Methods D 1265-82 of Sampling of Liquefied Petroleum (LP) Gases.
- Annual Book of ASTM Standards, Vol. 05.01.
- Annual Book of ASTM Standards, Vol. 05.02.
- Annual Book of ASTM Standards, Vol. 05.03.
- ASTM Standards Methods D 2163-82, "Analysis of Liquefied Petroleum (LP) Gases and Propane Concentrates by Gas Chromatography," p. 95.
- Annual Book of ASTM Standards, Vol. 05.05.

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