The document discusses the principle of superposition theorem and its applications in reservoir engineering. The principle states that the total pressure drop at any point in a reservoir is the sum of the pressure drops caused by each individual well. It applies to linear systems and allows engineers to model complex reservoir responses by combining simple models. The theorem can be used to account for the effects of multiple wells, changing production rates, boundaries, and pressure on transient flow solutions, aiding in pressure transient test analysis.

1. Name : Hishmat Rai
Roll no: 16PG46
Topic : Principle of Superposition Theorm and its application
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2. Superposition
• It is fundamental tool of pressure transient test analysis
and reservoir engineering.
• It should be noted that principle of superpostion hold
only for linear system (in mathematical sence)
• It makes us to contruct reservoir response function in
complex situation ( boundaries, variable rate , varaible
pressure production) using only simple basic model for
constant pressure solution 2

3. Principle of superposition theorm
• It state that, “ The total
pressure drop at any point
in the reservoir is the sum
of pressure drop at that
point caused by flow in
each wells in the
reservoir”.
• (Pi-Pwf)total at any point
=(pi-p)due to well 1 +(pi-
p)due to well 2+(pi-p)due
to well 3. 3

4. Criteria for Linear equation
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• All derivates of presure with repect to time or space and
time varaible in the first power
• No product derivates
• All cofficient of derivate idependent of the solution, which in
pressure transient analysis
Forms of Superposition Theorm:
1. Supperposition in space
2. superposition in time

5. 1. Superposition in space
• Consider two well in infinite system then the
pressure change at the observation point.
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6. 2.Superposition of Time
• Superposition in time
applies for single well
systems with varying flow
rate . The single well with
following production rate
as shown in fig.
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7. Application of Principle of superposition Theorm
Superposition concept can be applied to account for
the effects on the transient flow solution
 Effects on multiple well
Effects on rate change
Effects on the boundary
Effects of pressure change
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8. • From principle of superposition theorm , we can calculate
pwf of the well(pwf=Pi-Pn) after derivate
• From the principe of superposition theorm , we control
the affects on trasient test analysis test
Conclusion
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