1 introduction 2 forms of superposition principle 3.application 4, conclusion

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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