INTRODUCTION TO NODAL ANALYSIS

After a well is drilled and  completed, itrequires a great effort to transport or flow fluid through the reservoir until the piping system and ultimately flow into a separator for gas-liquid separation which are placed on the surface. the movement of these fluids requires energy to overcome friction losses and to lift the products. The pressure drop in the total system at any time will be the initial fluid pressure minus the final fluid pressure. This pressure drop is the sum of the pressure drops occurring in all of the components of the system. The selection and sizing of the individual component varies with producing rate.

The final desing of a production system cannot be separated into reservoir performance and piping system performance and handle independently. The amount of oil and gas flowing into well from the reservoir relies more on the pressure drop in the piping system, and the pressure of the piping system depends on the amount of fluid flowing through it. Therefore; the entire production system must be analyzed as a unit.

 SYSTEMS ANALYSIS APPROACH

The systems analysis approach, often called NODAL ANALYSIS has been applied for many years to analyse the performance of systems composed of interacting components (Electrical circuits, complex pipeline networks and centrifugal pumping systems are all analyzed using this method. The procedure consists of selecting a division point or node in the well and dividing the system at this point. All components upstream of the now comprise the inflow section, whereas the outflow section consists of all the components downstream of the node. A relationship among flow rate and pressure drop must be available for each component in the system. The flow rate through the system can be determined once the following requirements are satisfied:

• Flow into the node equals flow out of the node,
• Only one pressure can exist at a node.

The average pressure of the reservoir (Pavg) and the pressure of the system outlet called separator pressure ( Psep) are not functions of flow rate. Nevertheless, if the Psep is under control by a choke, it could be the Wellhead pressure (Pwh).

Once the node is selected, the node pressure is calculated from both directions starting at the fixed pressures.

Inflow to the node:

Pr – AP ( Upstream componets) = Pnode.

Ouflow from the node:

Psep + AP ( downstream components) = P node.

The pressure drop, AP, in any component varies with flow rate, Q. For that reason, a plot of node pressure versus flow rate will produce two curves, the intersection of which will give the conditions satisfying requirements (Flow into the node equals flow out of the node, and Only one pressure can exist at a node). That is illustrated as follows:

The effect of a change in any of the components can be analyzed by recalculating the node pressure versus flow rate using the features of the component that was changed. If a change was made in an upstream component, the outflow curve will remain unchanged.

Nevertheless, if either curve is changed, the intersection will be shifted, and a new flow capacity and node pressure will exist. The curve will also be shifted if either of the fixed prcssures is changed. which may occur with depletion or a change in separatioll conditions.

The effect on the flow capacity of changing the tubing size is shown as follows , and so does the effect of a change in flowline size.

The effect of increasing the tubing size, as long as the tubing is not too large, is to give a higher node or well-head pressure for a given flow rate, because the pressure drop in the tubing will be decreased. This shifts the inflow curve upward and the intersection to the right. A large flowline will reduce the pressure drop in the flowline, shifting the outflow down and the intersection to the right. The effect of a change in any component in the system can be isolated in this manner. Also, the effect of declaning reservoir pressure or changing separator pressure can be determined.

A more frequently used analysis procedure is to select the node between the reservoir and the piping system. This node does divide   the well into a reservoir system component and a piping system component.

The effect of a change in tubing size on the total system producing capacity when Pwf is the node pressure is illustrated above. An increased in production rate achieved by increasing tubing size is illustrated às well. however, if tubing is too large, the velocity of the fluid moving up the tubing may be too low effectively lift the liquids to the surface. This could be caused by either large tubing or low production rates.

A producing system may be optimized by selecting the combination of component characteristics that will give the maximum production rate for the lowest cost. Although the overall pressure drop available for a system, Psep, might be fixed at a particular time, the producing capacity of the system  relies more on where the pressure drop happens. If too much pressure drop occurs in one particular component or module, there may be insufficient pressure drop remaining for efficient performance of the other modules. Even though the reservoir may be capable of producing a large amount of fluid. If too much pressure drop occurs in the tubing , the well performance suffers.

For this type of well completion, it is obvious that improving the reservoir performance by stimulation would be a waste of effort unless larger tubing were installed.

A case in which the well performance is controlled by the inflow is shown. In this case, the exessive pressure drop could be caused by formation damage or inadequate perforations. It is obvious from the plot that improving the performance of the piping system or outflow or placing the well on artificial lift would be fruitless unless the inflow performance were also improved.