For the sentence in your question,
As the process proceeded, these values became lower. The reason for
this is/was that they are/were highly dependent on the
resources which are/were consumed as the process
proceeds/proceeded.
you can use consistent 'past tense' or consistent 'present tense'. e.g.
As the process proceeded, these values became lower. The reason for
this is that they are highly dependent on the resources which are
consumed as the process proceeds.
As the process proceeded, these values became lower. The reason for
this is that they were highly dependent on the resources which were
consumed as the process proceeded.
As the process proceeded, these values became lower. The reason for
this was that they were highly dependent on the resources which were
consumed as the process proceeded.
The reason for this is the specialness of the "be" verb. Used alone "be" states things in simple truth versions. In "There was an .." the verb "be" is talking about a state of things that was in the past, and is no longer in the present. In "..became lower..", the state of things became that state of things and it still is in the present.
This sentence
As the process proceeded, these values became lower. The reason for
this is that they are highly dependent on the resources which
were consumed as the process proceeded.
is also grammatically correct. You can separate the two clauses "The reason for this is that they are highly dependent on the resources" and "which were consumed as the process proceeded.". You can use "is" or "was" with reason provided the reason has "not expired"(the reason is no longer valid). If the reason is no longer valid, you have to use the past tense.