The phrase "process during which" is correct and usable in written English.
You can use it when you are describing a process that takes place over a period of time. For example: "This study looked at the process during which students acquire knowledge of the subject."
Muscle regeneration is a dynamic process during which cell state and identity change over time.
Every Balanchine ballet is a dramatic process during which we see the world onstage change and change again.
He described an exhaustive process during which, he said, Mr. Coleman had the chance to air all of his arguments.
Musical performance, step in the musical process during which musical ideas are realized and transmitted to a listener.
It is a complicated chemical process during which fuel goes through pyrolysis, oxidation and reduction stages.
In addition, there is the so-called foley process during which foley artists add sound effects that synchronize with the on-screen action, like footsteps or rustling clothes.
The settlement followed a thorough pre-litigation process during which further investigations into the claim took place including the commissioning of expert independent reports.
It came at the end of a 10-year process during which Einstein pursued the ambitious project of "generalising" his special theory of relativity, formulated in 1905.
Workouts can lead to debt-for-equity conversions and fresh loans from lenders, a process during which current shareholders usually see their investments written down.
Sabine begins to realize the rippling social and ecological effects of her smallest choices: an exhilarating but exhausting process, during which she loses her two best friends.
Traditionally, sculptors working in metal made wax versions of a piece as a step in the casting process, during which the wax would melt away.
