Pulsed delivery of concentrated proppant stimulation fluid

A pumping system comprising:

• one or more clean fluid pumps, wherein the one or more clean fluid pumps pump a clean fluid at a first rate and a first phasing to a location;
• one or more concentrated proppant stimulation pumps, wherein the one or more concentrated proppant stimulation pumps pump a concentrated proppant stimulation fluid at a second rate and a second phasing to the location, wherein the concentrated proppant stimulation fluid comprises a predetermined concentration of proppant;
• and
• an information handling system coupled to the one or more clean fluid pumps and the one or more concentrated proppant stimulation fluid pumps, wherein the information handling comprises a processor and a non-transitory memory coupled to the processor, the memory containing one or more instructions that, when executed by the processor, cause the processor to:
• maintain a total rate of fluid pumped to the location by controlling the first rate of the one or more clean fluid pumps and the second rate of the one or more concentrated proppant stimulation fluid pumps, wherein the fluid comprises the clean fluid and the concentrated proppant stimulation fluid pumped to the location;
• and
• control pumping of the concentrated proppant stimulation fluid to the location such that the concentration of the proppant in the concentrated proppant stimulation fluid pumped to the location simulates a square-wave.

A non-transitory computer readable medium storing one or more instructions that, when executed, cause a processor to:

• determine a decomposition of a predetermined Fourier transform, wherein the predetermined Fourier transform is based on a predetermined concentration of proppant in a concentrated proppant stimulation fluid to be pumped at pulsed intervals to a location to simulate a square-wave;
• associate one or more concentrated proppant stimulation fluid pumps to each of at least two or more orders of the decomposed predetermined Fourier transform;
• determine a first rate and a first phasing for pumping a clean fluid from one or more clean fluid pumps;
• determine a second rate and second phasing for pumping a concentrated proppant stimulation fluid from the one or more concentrated proppant stimulation fluid pumps based on the associated two or more orders of the decomposition of the predetermined Fourier transform;
• and
• wherein the determined first rate and the second rate are based on a target flow rate of a total fluid to the location, wherein the total fluid comprises at least one of the clean fluid and the concentrated proppant stimulation fluid.