Introduction to Nodal Analysis

Introduction to Nodal AnalysisInstructional Objectives1.Explain the concept of Nodal Analysis.2.List 4 segments in the reservoir/well system where pressure loss occurs.3.Define the following terms: inflow performance curve, outflow performance curve, system graph, solution node.

Pressure Losses in Well SystemPwh

Nodal AnalysisPwh

Inflow Performance Curve

Outflow Performance Curve

System Graph2111 STB/D1957.1 psi

Solution Node At WellheadPwh

System Graph - Wellhead Node2050 STB/D500 psi

References

Introduction to Nodal AnalysisIntroduction to Nodal AnalysisUpon completion of this section, the student should be able to:1.Explain the concept of Nodal Analysis.2.List the four major segments between the reservoir and the separator where pressure loss occurs.3.Give definitions for each of the following terms:Inflow performance curveTubing performance curveSystem graphSolution nodeIntroduction to Nodal AnalysisFluid flows from the reservoir to the stock tank because of the pressure gradients within the system. The total pressure drop from the reservoir to the separator is the sum of the individual pressure drops through four different segments: in the reservoir, across the completion, up the wellbore, and through the flowline.It is relatively straightforward to calculate the pressure drop for each of these segments, if we know the flow rate and either the upstream or downstream pressure, and the physical properties of the segment. But we do not know the flow rate - that is what we are trying to find. How do we calculate the flow rate, knowing the reservoir and separator pressures? This is the central question of Nodal Analysis.Given the reservoir pressure and the separator pressure, along with the physical properties of each segment, what is the flow rate at which the well will produce?Introduction to Nodal AnalysisHow do we determine the right flow rate? We know the separator pressure and the average reservoir pressure.We start in the reservoir at the average reservoir pressure, pr, and assume a flow rate. This lets us calculate the pressure just beyond the completion, pwfs. We can then calculate the pressure drop across the completion, and the bottomhole pressure pwf. This pressure is valid only for the assumed flow rate.Or, we may start at the separator at psep, and calculate the pressure drop in the flowline to find the wellhead pressure, pwh. Then we can calculate the bottomhole pressure pwf. Again, this pressure is valid only for the assumed flow rate. The two calculated bottomhole pressures will probably not be the same. If not, then the assumed rate is wrong.Nodal analysis refers to the fact that we have to choose a point or node in the system at which we evaluate the pressure - in this case, the bottom of the wellbore. This point is referred to as the solution point or solution node.Introduction to Nodal AnalysisLets assume that the well is completed open hole, and that the well is neither damaged nor stimulated. In this case, the pressure drop across the completion is zero.For the moment, we ignore the wellbore and the flowline.If the flow rate is 0, the bottomhole pressure pwf will be the same as the average reservoir pressure, pr. As we increase the flow rate, the pressure drop in the reservoir segment increases - causing the bottomhole pressure pwf to decrease. When we graph the flowing bottomhole pressure as a function of flow rate, the result is a curve intersecting the y-axis at the initial reservoir pressure, and intersecting the x-axis at the maximum rate the well would produce if opened to the atmosphere at the perforations.This curve is usually referred to as the inflow curve or the reservoir curve.Until we take into account the pressure drop within the wellbore, this curve tells us very little about the rate at which the well will produce for a given wellhead pressure.Introduction to Nodal AnalysisNow lets assume that the separator is so close to the wellhead that we may ignore the pressure drop through the flowline.At some low flow rate, perhaps 200 STB/D, the flowing bottomhole pressure may be 1500 psi. In order to increase the flow rate without changing the surface pressure, we have to raise the flowing bottomhole pressure.(At extremely low flow rates, the bottomhole pressure actually falls with increasing flow rate. This is a real phenomenon, and we will address it at some length later in the course. For now, note that the bottomhole pressure for a shut-in well filled with oil is actually higher than the bottomhole pressure for a well flowing a mixture of oil and gas at low rates.)This curve is usually referred to as the outflow curve or the tubing performance curve.Until we take into account the reservoir behavior, this curve also tells us almost nothing about the rate at which the well will produce.Introduction to Nodal AnalysisThe inflow curve describes the relationship between the bottomhole pressure and the flow rate for the reservoir. The outflow curve describes the relationship between the bottomhole pressure and flow rate for the wellbore. When we graph these two curves on the same graph, we refer to this as the system graph. The intersection of the inflow curve and the outflow curve gives the one unique flow rate at which the well will produce for a specified set of reservoir and wellbore properties. The point of intersection will also give the unique bottomhole pressure at which this rate will occur.If we had chosen a different point as our solution node, the shapes of the curves would have been different. The y-coordinate of the intersection of the inflow and outflow curves would have given the pressure at the new solution node. The flow rate at which the curves intersect, however, will be the same no matter where the solution node is taken. Calculated intersection points may differ slightly because of numerical errors.Introduction to Nodal AnalysisWhat if we take the solution node at the wellhead? Again, we know the separator pressure and the average reservoir pressure.As with the bottomhole node, we start in the reservoir at the average reservoir pressure, pr, and assume a flow rate. This lets us calculate the pressure just beyond the completion, pwfs. We can then calculate the pressure drop across the completion, and the bottomhole pressure pwf. Finally, we calculate the pressure drop up the wellbore to find the wellhead pressure pwh. This pressure is valid only for the assumed flow rate.Or, we may start at the separator at psep, and calculate the pressure drop in the flowline to find the wellhead pressure, pwh. Again, this pressure is valid only for the assumed flow rate. Graphing inflow and outflow curves for a range of assumed rates allows the solution flow rate and wellhead pressure to be obtained from the intersection of the curves.Introduction to Nodal AnalysisIn general, the inflow curve describes the relationship between the pressure at the solution node and the flow rate into the node. For this case, with the solution node at the wellhead, the inflow curve represents the combined performance of the reservoir and tubing system.The outflow curve describes the relationship between the pressure at the solution node and flow rate out of the node. Here, with the solution node taken at the wellhead, the outflow curve is horizontal - we have fixed the wellhead pressure at 500 psi in our input data.The intersection of the curves gives the flow rate (2050 STB/D) and the wellhead pressure (500 psi). The slight discrepancy between this value and the 2111 STB/D calculated using a bottomhole node should not be of concern.Introduction to Nodal AnalysisReferences

1.Mach, Joe, Proao, Eduardo, and Brown, Kermit E.: A Nodal Approach for Applying Systems Analysis to the Flowing and Artificial Lift Oil or Gas Well, paper SPE 8025, 1979.