The Basics about Pump(s)-to-System(s)

Pumps & Systems, April 2007

In most training exercises or general discussions of pump-system interactions, great simplifications are made. The two most common examples presented are usually two pumps operating in parallel, or two pumps operating in series. Discussion rarely involves more than two pumps, and operation of a single pump against a multi-branched system is discussed even less frequently.But real installations rarely resemble such isolated and greatly simplified situations. Typically in actual practice, multiple pumps operate against multiple branches of a system, or several interconnected complex systems operate with pumps coming on and off line and valves adding multiple new branches or shutting off parts of the system.

Such multi-branched, multi-pump systems can no longer be analyzed by hand with a graph and calculator. Instead, an entire computerized network of the plant piping, tanks, and pumps that reflects proper sizes, friction, elevations, and so on needs to be carefully modeled.

However, before attempting to model the complexities of the entire plant, the fundamentals of the multi-pump, multi-branch systems that are in place must first be understood. When such an examination is reviewed, it will become clear that the entire complex network is essentially a combination of the following three cases:

1. Several pumps in parallel, against a single system
2. Several pumps in series, against a single system
3. A single pump against a two-branched system, or against a multi-branched system

Below is a simplified example exercise involving three cases that were excerpted from one of our training classes. Consider the fundamentals of three such cases as basic building blocks for an eventually more complex network:

Case (a). (2) pumps in parallel against (1) system.

 

Case (b). (2) pumps in series - against (1) system.

 

Case (c). (1) pump - against (2) system branches.

 

 

 

Cases (a) and (b) are more common, i.e. a single-branched system is considered. Case (c) is less frequently considered, but it has one pump against a multiple-branched (two in this illustration) system. Graphically, in parallel operation, (pump curves) flow is additive at constant head; in series operation, the (pump curves) head is additive at constant flow.

However, for a multiple-branched system the flow is additive (system curves) at constant head. Graphs (a), (b), and (c) below reflect the three cases above, respectively. The operating point is an intersection between the final pump curve and a final system curve, as shown with numerical examples below.

Graph (a). (2) pumps in parallel against (1) system. Method of construction of multiple (combined) pump curve: at constant head line (200-ft), double the flow (250-gpm x 2) for a point on a 2-pump curve. Repeat at several other constant head lines; for 400-ft, double the flow (200-gpm x 2). For 3-pump operation, triple the flow at constant head lines. Continue in the same fashion for more pumps. Intersections between one, two, three, or more pumps, with a given system curve, establish the operating point (resultant head and flow) for multiple pumps.

Graph (b). (2 or more) pumps (or pump stages) in series - against (1) system. Method of construction of multiple (combined) pump curve: at series of constant flows, add pump (or pump stages for multiple pumps) heads. Intersections between the resulting pump curve (stages curve) and a system curve establishes operating point (resultant head and flow).

 

Graph (c). (1) pump - against (2) system branches. Method of construction: instead of combining pump curves, add flows (at constant head) for systems (can be more then two). Intersection of the resultant system curve with a given pump curve produces the operating point (resultant flow and head).

 

Computerizing the Process

This process can be computerized, as illustrated in a simplified example of a positive displacement pump operating against two systems (two branches). Underlying programming formulas are:

1. H = h₁ + k₁ x Q₁²     - This is the general equation for a system of branch (1), including static head h₁ and friction with system friction resistance k₁
2. H = h₂ + k₂ x Q₂²     - This is the general equation for a system of branch (2), including static head h₂ and friction with system friction resistance k₂
3. Q = Q₁ + Q₂             - This is what leaves the pumps splits into branches.

Known/given: Q, k₁, k₂, h₁, h₂ (where h₁ and h₂ are static heads for the two systems, and k₁ and k₂ are friction coefficients for these systems)

Need to find: Q₁, Q₂ and pump head h.

Programming procedure:

 a. Guess h
 b. Calculate Q₁ from (1)
 c. Calculate Q₂ from (2)
 d. Calculate Q = Q₁ + Q₂ and compare with given Q
 e. If calculated flow is different than given, re-guess h and repeat the process until error is small

Only when these fundamentals of the pump(s)-to-system(s) principles are understood are you ready to take the next step - a computerized analysis of complex pumping systems.

A parting quiz: how would a procedure change if two pumps had an entirely different (the ones shown above are for identical pumps) performance curves? The best answer, as usual, will qualify you for a free ticket to attend our Pump School session.