Computer Model Designs African Multiproducts Line Extension

Janusz Stuchly, Chris Kedge
SNC-Lavalin Inc.
Calgary

Design of the West Kenya pipeline extension (WKPL) in Kenya required development of a new computer model to perform the necessary steady-state hydraulic calculations.

The model addressed the increased complexity of hydraulic design when a products pipeline is a "tight" line, that is, lacking breakout tankage.

The WKPL result was a design that allows delivery of the required product volumes to each terminal while operating within the necessary hydraulic and mechanical constraints.

The model is not commercially available. Pipeline designers, however, can employ the calculation algorithm and output formats provided here to develop similar programs for similar design requirements.

WKPL is a recently constructed white-products pipeline system that transports batches of gasolines, diesel, and kerosines from the existing Kenya Pipeline Co. (KPC) terminal at Nairobi to new terminals constructed at Nakuru, Eldoret, and Kisumu, in western Kenya (OGJ, Jan. 30, 1995, p. 98).

The WKPL system was designed as a tight line: it lacks breakout tankage at the flow bifurcation point at Sinendet where the pipeline branches in two directions.

This requirement, along with the variation of pipeline capacity that occurs as product batches move through the line, presented a number of challenges during hydraulic design.

WKPL system

The WKPL system was designed and constructed by Propipe, a consortium formed by SNC-Lavalin International Inc., Calgary, and NKK Corp., Chiyoda-Ku, Japan. Construction of the system began in January 1991 and was completed in May 1994.

(Fig. 1 [39763 bytes]) provides an overview of the pipeline system and shows the locations of the pump stations and terminals. The pipeline elevation profile is shown in (Fig. 2 15199 bytes). The WKPL system begins at the KPC terminal at Nairobi and consists of:

• A 224 km, 8-in. trunk line from Nairobi to Sinendet

• A 117 km, 6-in. branch line from Sinendet to the terminal at Kisumu near Lake Victoria

• A 100 km, 8-in. and 6-in. branch line from Sinendet to the terminal at Eldoret.

Three pump stations are located on the trunk line portion of the system: at Nairobi, Ngema, and Nakuru. A fourth pump station is planned for future construction at Morendat.

A terminal is also located at Nakuru, approximately 15 km from the Nakuru pump station.

Design capacity of the system with the future Morendat station is 222 cu m/hr (5,328 cu m/day; 33,512 b/d).

A pressure-control station is installed at Sinendet on the line to Kisumu. The terminal at Kisumu lies at a much lower elevation (1,141 m) than the Sinendet bifurcation point (2,521 m).

Operational constraints

Throughputs of product pipelines in general and of the WKPL system in particular are driven by market demands for specific products. The demand for individual products is different at each terminal.

The required pipeline throughput is defined based on specific product requirements at various terminals over a specified period of time; this is known as the "batch cycle."

The batch cycle for the WKPL system has been defined as approximately 98 hr at design capacity. During one batch cycle, 21,780 cu m of the various products are transported in batches of specified volumes in a predetermined order from Nairobi to the three terminals.

At the end of one batch cycle, a new cycle is started, and this procedure is repeated continuously thereafter.

Of the three terminals, only Nakuru is on the main trunk line and receives a portion of each product as it flows past. The other two terminals are at the ends of the two branch lines starting from the bifurcation point at Sinendet.

Operators at each terminal provide the dispatcher in Nairobi with their local product requirements. At any given instant, each terminal may be receiving a different product.

Control of the pipeline operation requires that its throughput be maintained at a constant level throughout the system, and consequently, the rate of product outflow at each terminal must be adjusted each time a new product batch reaches the terminal at Nakuru.

This constraint becomes clearer considering that the sum of the product outflow rates at the three terminals must equal the rate of inflow at Nairobi.

Adjusting the outflow rate at Nakuru in response to a new product (which is necessary to ensure that the Nakuru terminal receives the required volume of the product as it flows past through the trunk line) therefore requires adjustment of the outflow rates at the other terminals to maintain this balance.

Similarly, outflows at the terminals must be adjusted when a new product batch reaches the bifurcation point at Sinendet in order to split the flow in proportion to the respective requirements for that product at the Kisumu and Eldoret terminals.

As batches of different products flow consecutively in a pipeline, some amount of mixing occurs at the boundaries between the products.

The resulting product mixture is known as "interface" and can be formed in considerable quantities, depending upon, for example, flow rate and pipeline length.

Each terminal in the WKPL system has facilities to handle the interface between different product batches. The interface is withdrawn from the line at the terminal at the same rate as the main products.

Commercial considerations resulted in selection of pipe grade and wall thickness before completion of detailed hydraulic design.

This, in combination with the pipeline's elevation profile (particularly the large change of elevation occurring along the branch line to Kisumu terminal), imposed additional constraints which had to be taken into account.

Batch hydraulics

A single-product pipeline will have a different maximum flow rate (or capacity) that can be achieved without violating various constraints (such as maximum or minimum operating pressure) anywhere in the line, depending on what product is being transported.

Each product has a unique combination of viscosity, density, and vapor pressure which affects the pipeline capacity.

Because of these property differences, the hydraulic characteristics of a multiproduct batch pipeline differ significantly from those of a single-product pipeline.

If a pipeline transports a batch of one product, followed by a batch of a different product, the maximum capacity of the line at any instant will generally fall somewhere between the values that correspond to each product individually.

It follows that as one product is displaced in the line by another, the maximum capacity must vary between limits corresponding to the individual product capacities.

In order to change from one limit to another continuously, the instantaneous capacity will necessarily vary as a function of the position of the interface between the two products. This capacity variation becomes more complex when more products are present in the line.

The variation of the maximum capacity over one batch cycle for a portion of the WKPL system is shown in (Fig. 3 [12813] bytes).

Because of this capacity variation, the hydraulic design procedure must focus on ensuring that the time-averaged product throughput over the batch cycle will meet the delivery requirements of product volumes at the terminals.

If one is to maintain a constant flow rate in the line, then for certain batch positions, this may result in violation of the constraints of minimum or maximum pressure somewhere in the system.

This can be shown on a plot of hydraulic gradient, which conveniently illustrates the effect of frictional pressure drop (or equivalently, frictional head loss) along the line independently of the effects of the pipeline elevation profile.

Hydraulic gradient is defined as the sum of elevation and pressure head and, under static (nonflowing) conditions, would be constant everywhere in the line. It then follows that for steady-state flow, the difference in the hydraulic gradient between two given locations would be due solely to frictional losses.

(Fig. 4 [24455 bytes]) shows the calculated hydraulic gradient profile for a portion of the WKPL system for a single product flowing in the line.

For a single product, the calculated profile appears as a straight line on this graph (assuming constant values for density and viscosity of each product, as discussed presently).

Fig. 5 [25074 bytes] shows the profile which would result for four different products flowing in the line, in which case the profile still consists of straight lines but with different slopes for different product batches.

The figure shows that for the instantaneous batch positions shown, the capacity is limited because the minimum pressure constraint would be violated at the inlet to the Eldoret terminal if the flow rate were at all increased.

Computer model

Hydraulic design of the WKPL system required a computer model which would properly account for the variation of the pipeline capacity as the product batches move through the line.

Commercially available software programs were unable to model the operation of the WKPL pipeline system correctly. As a result, a new computer model called the Batch Tracking Model (BTM) was developed.

Essentially, the model performs calculations at successive time steps over an entire batch cycle, adjusting the positions of the product batches by a small amount at each time step and performing iterative steady-state hydraulic calculations for the instantaneous batch positions to determine the maximum flow which does not violate the imposed pressure constraints.

While the model was mainly intended for the design of the WKPL system, its overall structure and assumptions were developed to be applicable to any products pipeline.

The main function of the model is to determine continuously the maximum capacity of the pipeline as a function of time over a specified batch cycle.

Alternately, the user can specify a flow rate to be maintained constant over the batch cycle, and the model will determine if this flow exceeds the maximum capacity at any time during the cycle.

For both modes, the time required to transport an entire batch cycle is computed, allowing the average flow rate over a cycle to be calculated.

Following are the major capabilities of the model:

• Calculations can be performed for products with different vapor pressures by defining product-specific minimum operating pressures and minimum pump station inlet pressures.

• The limitations of the installed or proposed pumping units can be accounted for by specifying a flow vs. head relationship for each pump. If these data are unknown, a constant pump discharge pressure can be specified.

• Minimum and maximum operating-pressure constraints are continuously accounted for in the calculations during the batch-cycle simulation, throughout the entire pipeline system.

• The model can monitor and adjust the take-off flows at each terminal, when required, to satisfy the nominated deliveries of specific products to each terminal.

For the purpose of hydraulic modeling, the pipeline is divided into several hypothetical pipe segments, connected at points called nodes.

The nodes may represent points of physical significance, such as terminals, pump stations, or pressure regulators, or may simply represent points along the pipeline where the elevation is known or where the pipe diameter or wall thickness changes.

The fundamental structure of the hydraulic calculations carried out at each time step is based on the approach commonly used in steady-state hydraulic models, using a finite-difference approximation for the solution of the appropriate formulations of the continuity and momentum equations.

The pipeline system is assumed to be isothermal, and accordingly, no temperature calculations are performed. Similarly, the products are assumed to be incompressible, and changes in flowing velocity resulting from changes in pressure are not calculated.

These two simplifying assumptions introduce no appreciable errors into the calculations. The viscosity of refined products is low, and temperature has only a minor effect on frictional pressure drop.

Similarly, changes in product density resulting from changes in operating pressure also have a very minor effect on pressure drop. Using these simplifying assumptions allows for ease in adjusting batch positions when a small amount of product is introduced into the line at each time step.

Calculation modes

The first mode of calculation defines the maximum pipeline capacity continuously over the batch cycle, using the following algorithm:

1. Initial line fill is established in the line consistently with the known sizes and sequence of product batches as defined by the terminal operators' nominations, or by design data for the pipeline.

2. Pressure-drop calculations are first carried out for a user-specified initial flow rate.

Successive pressure drop calculations are then carried out iteratively, either increasing or decreasing the flow rate until the difference between the flow which can be transported by the pipeline without violating any of the constraints, and the flow which violates one or more of the constraints, is less than a specified tolerance.

3. A user-defined volume of product (usually a small amount, for example 10 cu m) is introduced into the pipeline and the same volume of product is removed from the line at the terminals.

The volumes removed at the terminals correspond to the user-specified ratio of product allocation between these terminals.

4. Positions of the batches are adjusted accordingly and iterative pressure-drop calculations are again carried out, as described above in Step 2.

Once the new maximum line capacity for the specific positions of batches of different products is established, the user-defined volume of the product is again introduced to and removed from the line as required to adjust the positions of batches, and the calculations are repeated.

5. The calculations are carried on until the volume of products corresponding to the full batch cycle has been moved from the starting terminal to the delivery terminals.

The second calculation mode allows the user to define a set flow rate, which is held constant unless the changing batch positions cause the capacity to fall below the specified rate.

When this happens, the calculation sequence is as previously described, until the line capacity rises to exceed the specified flow rate.

This mode of calculation is useful to determine if pumping the product at a desired rate (the design flow rate of the pumps, for example) would result in constraint violations at some time during the batch cycle, and if so, whether the required average flow rate can still be achieved.

For input data, the model requires a physical description of the pipeline system, maximum line pressures, product properties and minimum allowable pressures, product batch volumes and sequence, and product delivery volumes at terminals over the batch cycle.

Model output

As the BTM algorithm requires many repetitive calculations, a vast amount of information is generated during its operation.

It is desirable for the user to have access to the calculation output in some form, not only at the end of the run, but while the model is running as well. For these reasons, a graphical form was selected to display the program output, both on-screen and as "snapshots," which can be saved at any time step during program execution for hard-copy printing.

Program output is presented graphically in the following forms:

• Head profile (hydraulic gradient) for the entire pipeline.

• Superimposed on this graph are the pipeline elevation profile, the minimum allowable head profile, the maximum allowable head profile for normal operating conditions, and the maximum head profile for upset conditions (pressure-surge conditions, for example).

• Pressure profile for the entire pipeline.

• Superimposed on this graph are the minimum operating pressure along the line, the maximum operating pressure for normal operation, and the maximum operating pressure for upset conditions.

• Batch position profile of different products in the line.

• This output also shows at each time step the cumulative volume of each product that has been delivered to each terminal, the total volume of products remaining at the initiating terminal, and the time elapsed since the beginning of the batch cycle. (At the end of the run, the final value corresponds to the duration of the cycle, which can be used to calculate the average flow over the cycle.)

In addition, the following data are presented as functions of time and can be viewed or printed only after the program has finished executing:

• Product flow rate at the initiating and delivery terminals

• Pump head profiles for all of the pump stations.

WKPL hydraulic design

The WKPL pipeline has been designed to transport four types of products:

• Regular gasoline (MSR)

• Premium gasoline (MSP)

• Diesel fuel (AGO)

• Kerosine (DPK).

As noted previously, product properties were represented by constant values. The values of product properties used for the design are shown in (Table 1 [4211 bytes].)

Product batch volumes used for hydraulic design were as shown in (Table 2 [6983 bytes]).

The ultimate capacity of the line was defined at 222.0 cu m/hr. The actual throughput of the line, however, was expected to increase gradually from approximately 140.0 cu m/hr at the start of operation to 222.0 cu m/hr over a period of 20-25 years.

Control philosophy

Hydraulic design of a product pipeline requires development of a control philosophy for the system. Design of the WKPL system as a "tight" pipeline restricted the number of options available for this control philosophy.

In order to satisfy the operating constraint that the system must be able to deliver specified volumes of products to each of the delivery terminals, the flow rate into the line has to be maintained constant.

If it were desired to take advantage of the increased line capacity that occurs as the batches of product move through the line (that is, fully to use the maximum capacity of the line), the flow setpoints at the receiving terminals would have to be modified continually.

This type of operation was not considered viable or practical.

The control philosophy that was selected was to maintain a constant flow rate of product into the pipeline at the Nairobi terminal for the duration of the batch cycle.

A series of hydraulic calculations determined the impact of this control philosophy on the pipeline operation.

While the selected philosophy negatively affected the average throughput of the pipeline (the average flow being lower than if the input flow were continuously varied to match the time-varying capacity), the calculation confirmed that the line could achieve the required ultimate average capacity of 222 cu m/hr.

(Fig. 6 [18910 bytes])shows the flow rate out of the Nairobi terminal over the batch cycle.

During a short period between approximately 37 and 40 hr elapsed time, the pipeline capacity falls below the specified flow rate of 222.17 cu m/hr, briefly reaching a minimum value of approximately 216.3 cu m/hr at an elapsed time of 37.9 hr.

Operating the pipeline at a flow rate of 222.17 cu m/hr compensates for the brief capacity reduction and ensures that the required average value of 222 cu m/hr is met.

The recommended control philosophy and resulting restrictions in pipeline capacity were discussed extensively with KPC and its engineering consultant.

BTM and its ability to provide intermediate snapshots of pressure and head profiles helped in illustrating the need of selecting the chosen control philosophy.

BTM was used extensively during hydraulic design to analyze the pipeline operation under a variety of operating conditions, not only at design capacity, but also for earlier phases of operation at lower flow rates.

Also, BTM was used to define power demand profiles for the pump stations over the batch cycle for different pipeline throughputs over several years of pipeline operation.

Examples of the results of hydraulic calculations carried out by BTM during hydraulic design have been included here for illustration. In these examples, the pipeline operates at its design capacity.

The data shown represent instantaneous profiles of pressure, hydraulic gradient, and product-batch position, occurring at an elapsed time of 37.9 hr from the beginning of the batch cycle.

(Fig. 7 [21667 bytes]) shows the pressure profile from Nairobi to Eldoret. The corresponding hydraulic gradient (head) profile from Nairobi to Eldoret is shown in Fig. 5.

It can be seen clearly from both Figs. 5 and 7 that the instantaneous system capacity is limited by the constraint of minimum pressure at the inlet to the terminal at Eldoret.

Similar figures showing the Nairobi-Sinendet-Kisumu pressure and hydraulic gradient profiles were prepared during hydraulic design as well. (Fig. 8 [21872]) shows the positions of the product batches at the instant under consideration.

At the Nairobi pump station, changes in head occur only when the product being pumped changes, since the discharge pressure is maintained constant during the batch cycle and the products have different densities.

For the other three pump stations, however, changes in head occur not only for this reason, but also because the suction pressures at the pump stations change as functions of batch positions in the pipeline when the flow rate is held constant.

Since the pump discharge pressures are also maintained constant during the cycle, a change in the suction pressure changes the differential head across the pump. This is illustrated for the pump station at Ngema in (Fig. 9 [18036 bytes]) which shows pump head requirements as a function of time over the entire batch cycle.

(Fig. 10 [20009 bytes]) shows the variation of product outflow rate over the batch cycle for the terminal at Eldoret.

As previously mentioned, the product outflow rate at Nakuru terminal must be changed each time a different product flows past, in order to meet the nominated delivery requirements.

Outflow rates at Eldoret and Kisumu terminals must be changed not only when the outflow rate is changed at Nakuru (to maintain a constant flow from Nairobi), but also when a new product reaches the bifurcation point at Sinendet as well (to reflect the different split of flow between Eldoret and Kisumu for each product).

This can be seen for the Eldoret terminal in Fig. 10.

Performance test

The contract between Propipe and KPC required that following construction and commissioning of the WKPL system, a performance test be carried out to demonstrate that the pipeline would meet the contractual throughput requirements.

The contract specified a 72-hr test during which both the flow and pressure at critical points in the line were to be monitored to verify the compliance with the approved test procedure.

BTM was used to develop the test procedure.

The model was used to define the expected variation of the pipeline pressure profile for the specified initial line fill, anticipated flow rate, and types of products to be used for the test.

The test was carried out in June 1994. Test results showed close agreement between the predicted values of pressure change over time for the specified flow rate.

Acknowledgments

The authors wish to thank Bill Ho, previously of SNC-Lavalin but now with Greenpipe Industries Ltd., Calgary, and Alex Huddleston, SNC-Lavalin Inc., Bangkok, for their important contributions to this work.