20-May-1998

Type-Curve Models Available in PIE

The following is a summary of the type-curve models available in the PIE well-test analysis software. The models are grouped by 'type' with each type containing one or more related models. All of these models are computed by using a full analytic solution with the appropriate techniques (e.g. Laplace or Fourier transforms, Bessel functions, etc.). All models include well-bore storage and skin effects.

1) Homogeneous and Double-Porosity Reservoir

• Vertical well
• Homogeneous or double-porosity reservoir (PSS, 1-D, or 3-D inter-porosity flow)
• All reservoir boundary geometry's are supported.
• Available as an Interference-Test model (i.e. it reports a pressure at a location away from the well-bore).

2) Hydraulic-Fracture

• Hydraulic fracture with two 'wings' that extend out from the well-bore.
• Homogeneous or double-porosity reservoir (PSS, 1-D, or 3-D inter-porosity flow)
• Infinite-conductivity with a fracture-skin
• Finite-conductivity
• Finite-conductivity with a fracture-skin (Cinco semi-analytic solution)
• Partial-penetration hydraulic-fracture
• All reservoir boundary geometry's are supported which are added by de-superposition.

3) Layered Reservoir with No Reservoir Cross-flow

• Reservoir layers are separated by impermeable layers. Cross-flow between layers occurs through the well-bore.
• Two to four layers can be specified.
• Includes a rectangular reservoir boundary geometry in each layer. The distance to the boundaries can be specified for each individual layer.
• Vertical well, horizontal-well, or hydraulic-fracture can be specified in the reservoir layers (same type of well must be used in all layers). For example, a horizontal-well is shown in the following figure (the dashed line is the unperforated well-bore):

Multi-Layer, No Cross-Flow, Horizontal-Well

4) Layered Reservoir with Reservoir Cross-Flow

• Vertical well.
• Includes vertical-flow between the reservoir layers together with cross-flow between layers through the well-bore. The vertical flow between layers is computed using pseudo-steady-state flow (an inter-layer "lambda" coefficient).
• All reservoir boundary geometry's are supported.

5) Partial-Penetration Well

• Partial-Penetration (limited entry) well
• homogeneous or double-porosity reservoir (PSS, 1-D, or 3-D inter-porosity flow)
• Rectangular reservoir boundary geometry's are supported.

6) Radial-Composite Reservoir

• Vertical well
• homogeneous or double-porosity reservoir (PSS, 1-D, or 3-D inter-porosity flow)
• All reservoir boundary geometry's are supported which are added by de-superposition.
• Reservoir divided into two radial-zones around the well-bore as shown in the following figure:

Radal-Composite Reservoir

7) Linear-Composite Reservoir

• Vertical well
• Rectangular reservoir boundary geometry's are supported.
• Reservoir is divided into a series of three zones as shown in the following figure:

Linear Composite Reservoir

8) General Radial-Composite Reservoir

• Vertical well
• homogeneous or double-porosity reservoir (PSS, 1-D, or 3-D inter-porosity flow)
• Rectangular reservoir boundary geometry's are supported.
• Available as an Interference-Test model (i.e. it reports a pressure at a location away from the well-bore).
• Up to 10 entries in a "Heterogeneity table" can be specified with each entry defines a "step" change and/or "piece-wise linear" change in the reservoir properties. This set of heterogeneity data can be positioned and 'stretched' in the reservoir (see next figure).

General Radial-Composite Reservoir

9) Horizontal-Well

• Horizontal-well at an arbitrary location in the reservoir (see following figure).
• Homogeneous or double-porosity reservoir (PSS, 1-D, or 3-D inter-porosity flow).
• Rectangular reservoir geometry's are supported.

Cross-section

Plan-view

10) Inclined-Well

• Inclined-well at an arbitrary orientation in the reservoir (see following figure).
• homogeneous or double-porosity reservoir (PSS, 1-D, or 3-D inter-porosity flow).
• Rectangular reservoir geometry's are supported.

Cross-section

Plan-view

11) Horizontal-Well in a Layered Reservoir

• Horizontal-well at an arbitrary vertical location (see next figure).
• Transient 3-D flow between layers.
• Reservoir can have one to four layers with individual properties for each layer.

Multi-Layer Horizontal-Well

12) Inclined-Well in a Layered Reservoir

• Inclined-well at an arbitrary orientation (see next figure)
• Transient 3-D flow between layers.
• Reservoir can have one to four layers with individual properties for each layer.

Multi-Layer Inclined-Well

13) Partial-Penetration Well in a Layered Reservoir

• One to four sets of perforations at an arbitrary location in the reservoir (see next figure)
• Transient 3-D flow between layers.
• Reservoir can have one to four layers with individual properties for each layer.

• Cross-flow through the well-bore between different perforated intervals.

• Option available to off-set the perforations from one-another (see figure)

Cross-section

Plan-view

14) Multi-Lateral Well in a Layered Reservoir

• One to four horizontal "laterals" at an arbitrary location (see next figure).
• Transient 3-D flow between layers.
• Reservoir can have one to four layers with individual properties for each layer.

Multi-Lateral Well in a Multi-Layer Reservoir

• Cross-flow through the well-bore between different perforated intervals.

• Option available to arrange the lateral's in a radial or parallel geometry (see next figure).

Radial Offset

Parallel Offset

15) Layered Reservoir Vertical Interference-Test Model

• One to three sets of producing perforations set at various depths with one observation interval at an arbitrary location in the reservoir (see next figure).
• Transient 3-D flow between layers.
• Cross-flow through the well-bore between different perforated intervals.
• Reservoir can have one to four layers with individual properties for each layer.

Cross-section

Plan-view

16) Layered Reservoir Horizontal-Well Interference-Test Model

• Two horizontal-well segments with one producing segment and the other acting as the observation well (see next figure).
• Transient 3-D flow between layers.
• Reservoir can have one to four layers with individual properties for each layer.

Cross-section

Plan-view

17) Inclined-Well Interference-Test Model

• Two deviated-well segments with one producing fluid and the other acting as the observation well (see next figure).
• Homogeneous or double-porosity reservoir (PSS, 1-D, or 3-D inter-porosity flow)
• Includes all rectangular reservoir boundary geometry's

Cross-section

Plan-view

18) User-Defined Model

• Allows the user to load an arbitrary type-curve model as a look-up table.
• User can supply a set of curves with respect to an arbitrary parameter.

• Can be used just like any other type-curve model. Can even be used for non-linear regression.

19) Fetkovich-Arps Decline-Curve Model

• Vertical well.
• Circular reservoir boundary

• Implements the Arps empirical decline behaviour as a general dimensionless-pressure type-curve model.

20) Two-Layer Radial-Composite Model (ELF version only)

• Vertical well.
• Two reservoir layers with individual properties.
• Individual radial-composite model geometry in each layer.

• Pseudo-steady-state vertical flow between layers (an inter-layer "lambda" coefficient).

21) Linear-Composite Reservoir Interference-Test Model (ELF version only)

• Vertical well
• Rectangular reservoir boundary geometry's are supported.
• Reservoir is divided into a series of three zones.
• Pressure computed at an arbitrary location in the reservoir.