20-May-1998

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.

- 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).

- 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.

- 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

- 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.

- 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.

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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.

- Vertical well.
- Circular reservoir boundary

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

- 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).

- 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.