After writing super-node KCL equation, the variable that the dependent source depends on should be written in terms of the node voltages. This pressure drop will be the sum of the pressure drops through the various components in the production system.
The solution follows Nodal analysis same steps mentioned for dependent source with an extra step. The reason is that the voltage of the node can be easily determined by the voltage of the voltage source and there is no need to write KCL equation for the node. Once the system is divided into inflow and outflow sections, relationships are written to describe the rate-pressure relationship within each section.
Alternatively, the system of equations can be gotten already in simplified form by using the inspection method.
The most common division points are at the wellhead or at the perforations, either at the reservoir sandface or inside the wellbore. This process is very useful in analyzing current producing wells by identifying flow restrictions or opportunities to enhance performance.
Method[ edit ] Note all connected wire segments in the circuit. Nodal Analysis of Electric Circuits In this method, we set up and solve a system of equations in which the unknowns are the voltages at the principal nodes of the circuit. Thus the number of nodes is 3.
The result is the following system of equations: Solving the system of equations using Gaussian elimination or some other method gives the following voltages: Note that the "pair of nodes" at the bottom is actually 1 extended node.
Then, plots of node pressure vs. The pressure in the inflow section of the system is determined from Eq. This is typical for many outflow curves, which, in some cases, will yield two intersection points with the inflow curve; however, the intersection at the lower rate is not a stable solution and is meaningless.
In this case the voltage difference across the resistance is V1 - V2 minus the voltage across the voltage source. The components upstream of the division point or node comprise the inflow section of the system, while the components downstream of the node represent the outflow section.
Non-grounded Voltage Sources Since the current of a voltage source is independent of the voltage, it cannot be used in writing KCL equations.
System C also has an intersection and would be expected to produce at a higher rate and lower pressure than System B, as indicated by the graph. If the voltage is already known, it is not necessary to assign a variable. The proper intersection of the inflow and outflow curves should be the intersection to the right of and several pressure units higher than the minimum pressure on the outflow curve.
On the other hand, if a change in a downstream component is made, then the inflow curve will remain the same and the outflow curve will change.
Here is a solved problem with a dependent current source:Nodal Analysis – Supernode Dependent Current Source When there is a dependent current source in the circuit, it should be treated as an independent current source but the variable which the current source depends on should. In electric circuits analysis, nodal analysis, node-voltage analysis, or the Nodal analysis current method is a method of determining the voltage (potential difference) between "nodes" (points where elements or branches connect) in an electrical circuit in.
Example Nodal analysis with current sources Determine the node voltages v1, v2, and v3 of the circuit in Figure 8. R1 R2 R3 Vs Is i1 i2 i3 v1 v2 v3 n1 n2 n3 Figure 8. Circuit with voltage and current source. We have applied the first five steps of the nodal method and now we are ready to apply KCL to the designated nodes.
E Analysis of Circuits () Nodal Analysis: 3 – 2 / 12 The aim of nodal analysis is to determine the voltage at each node relative to the reference node. Nodal Analysis of Electric Circuits In this method, we set up and solve a system of equations in which the unknowns are the voltages at the principal nodes of the circuit.
From these nodal voltages the currents in the various branches of. Nodal Voltage Analysis complements the previous mesh analysis in that it is equally powerful and based on the same concepts of matrix analysis.
As its name implies, Nodal Voltage Analysis uses the “Nodal” equations of Kirchhoff’s first law to find the voltage potentials around the circuit.Download