session2_flow_to_well_idealized_reservoir - Session 2 Flow...

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Session 2 Flow to a well in an idealized reservoir
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Line source solution Assumptions - constant production rate - infinite reservoir - vanishingly small wellbore radius
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Line source solution constant rate, infinite reservoir, vanishingly small wellbore radius Infinite acting when
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Line source solution constant rate, infinite reservoir, vanishingly small wellbore radius
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Line source solution constant rate, infinite reservoir, vanishingly small wellbore radius Boltzman transform PDE in two variable r and t
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Line source solution constant rate, infinite reservoir, vanishingly small wellbore radius Boltzman transform ODE in one variable s PDE in two variable r and t dimensionless
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Simple integration by separation of variables Let Equation becomes Separating variables
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Simple integration by separation of variables Integrating
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Apply wellbore BC to evaluate constant of integration
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Line-source or Exponential Integral solution Dimensionless form
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1 10 100 1 10 3 1 10 4 0.1 1 10 Line-source or Exponential Integral solution
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Line-source or Exponential Integral solution
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Line-source or Exponential Integral solution Logarithmic approximation
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Constant rate, infinite reservoir with finite wellbore
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