Some Improvements of the "Ideal" Theory for Real Reservoirs

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Some Improvements of the "Ideal" Theory for Real
Reservoirs
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The general diffusivity equation Shape Factor

• Inner boundary(well)
• No flow (shut-in)
• Constant rate
• Constant flowing pressure

• Outer boundary
• Infinite acting
• No flow
• Constant pressure (or given influx)

Wellbore storage or not

• Time behavior
• Transient
• Stabilized (time invariant in some respect)
• Steady-state
• Pseudo-steady state
• Boundary dominated flow regime

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Dietz Shape Factor CA

• Well centered in a circular reservoir
• General

A area in ft2 rw wellbore radius in ft expg
1.781 CA shape factor (31.62 for a centered
circular reservoir) 1/cr 141.2 for field units
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Dietz Shape FactorsShape of drainage area AND
location of well
CA 30.88
CA 31.62
CA 21.86
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Sometimes the effect of shape is also expressed
in the form of a skin factor.
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CA 2.07
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Some Forms of PSS Gas Deliverability for "Real"
Gases

• Original "slightly compressible" AND Gas
  pressure form
• Gas pressure-square form
• Gas Pseudo-pressure form

where Bg is in RB/MSCF
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Some modifications for multiphase flow

• Perrine and Martin What to consider "total"
  compressibility for a multiphase system?

oil expands
water expands
gas expands
Pore space gets smaller
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Some modifications for non-Darcy flow

• Can be incorporated into any form, here we show
  how to incorporate it into the Pseudo-pressure
  form

Non-Darcy "skin effect" (rate dependent)
Origin Forcheimer Correlations for D are
available
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• Basic concepts of PVT
• Well testing basics
• Material balance
• Steady-state solution, skin, equivalent wellbore
  radius
• Pseudo-steady state and Boundary dominated flow
  regime
• Productivity Index
• Transient solution log approximation
• Gas diffusivity eq forms, "deviations from
  ideality"
• CALCULATE