by KermitE. Brown,Dale R. Doty,Carl Granger, LewisLedlow, Joe Mach, Eduardo Proafro, Zelimir Schmidt, A. PaulSzilas and
4.1 INTRODUCTION The objective of nodal systemsanalysis is to combine the various components of the oil or gas well in order to predict flow rates and to optimize the various compG. nents in the system. This approach was discussed by Mach,Proafro, and Brown and is given here essentially the same as in the original paper (copyright SPE of AIME):r An approach is presented for applying systems analysis to the complete well system, from the outer boundary ofthe reservoir to the sand face, acrossthe perforations and completion sectionto the tubing intake, and up the tubing string, including any restrictions and downhole safety valves, thesurface choke, the flow line and separator. Figure 4.1 shows a schematic of a simple producing system. This system consists of three sections or modules: (1) flow through porous medium (2) flow through vertical or directional conduit (3) flow through horizontal pipe or inclined flow line Figure 4.2 shows the various pressure lossesthat can occur in the more complex system from the reservoir tothe separator. Beginning from the reservoir, these are noted as: AP1: P, - P*. : pressure loss in porous medium AP2: P*r" - P6: pressurelossacrosscompletion AP3: Pu* - Po*: pressure loss across regulator, choke, or tubing nipple APa: Pusu- Posv: pressure loss across safety valve APs: P*r, - Posc: pressure loss across surface choke AP6: Posc Pspp: pressureloss in surface flow line AP7: P*r - P*n:total pressure loss in tubing string, which includes APa and APn Aa: P*h - Prpp: total loss in surface flow line, including surface choke 87
The various well configurations may vary from the very simple system of Figure 4.1 to the more complex system of Figure 4.2 or any combination thereof, and presentday completions more realistically include the various configurations of Figure 4.2 (especiallyofl shore). This chapter will discuss the manner in which to interrelate the various pressure losses. In particular, the ability of the well to produce fluids will be interfaced with the ability of the piping system to handle these fluids. The manner in which to treat the effect of the various components will be shown by a nodal concept. In order to solve the total-producing-system problems, nodesare placed to segment the portion defined by different equations or correlations. Figure 4.3 has been prepared showing locations of the various nodes. This figure is the same asi Figure 4.2 except only the node positions are shown. A node is classified as functional when a pressure differential exists across it and the pressure or flow-rate response can be represented by some mathematical orphysical function. More realistically, we will refer to a node at the bottom of the well, at the top of the well, etc., as a solution node. These two solution positions were discussedby Brown and Beggs.2 Node I represents the separator pressure, which is usually regulated at a constant value; however, some separator pressures do change with rate and should be properly accounted for. There are twopositions whereby the pressures are not functions offlow rates. These are P, at node 8 and PsBpat node 1. For this reason,any trial-and-error solution to the total system problem must be started at node 1 (Rep), node 8 (P,), or both node 1 and 8 if an intermediate node such as 3 or 6 is selectedas the solution node. Once the solution node is selected, the pressure drops or gains from the startingpoint are added until the solution node is reached. Example problems are worked to show the nodal system approach. For example, the flow rate possible can be determined by utilizing node 8 (P,), node
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Complete Producing System
Figure 4.3 Location of VariousNodes (after Mach,...