# PIE Type-curve Analysis Methods

PIE uses type-curves to analyse rate and pressure data from an oil or gas well. A type-curve is an analytic solution to flow in a porous medium for a particular well geometry and type of reservoir. PIE has four ways to use type-curves:

### 1) Draw-down Type-Curve Analysis

This type of analysis is the most primitive use of type-curves. The type-curve is drawn as a curve on a log-log plot assuming the well is producing at a constant rate (i.e. the well is being "drawn down" from the initial reservoir pressure). The scales for this plot are normalised into a dimensionless pressure and dimensionless time so an overlay of the data on the type-curve will define the dimensionless coefficients. The type-curve parameters are then derived from these coefficients. A virtually useless analysis method that is available only because it is widely known.

### 2) Type-Curve Simulation

This type of analysis is the main "engine" for doing a well-test analysis in PIE. Given measured production rates for a well, a type-curve model can be 'convolved' with the rate-history to calculate an expected pressure response for that model. The calculated response can then be compared to the measured pressure data and the model parameters adjusted in order to obtain the best fit to the data. Non-linear regression can be used to adjust the model parameters to automatically find the best fit to the data.

### 3) History-Match Simulation

A type-curve simulation is controlled by specifying a rate-history from which the pressure response is calculated for a given model. A history-match simulation is controlled by a set of arbitrary rate and pressure constraints from which the pressure or rate response is calculated. The production constraints allows an arbitrary production history to be matched using the most logical control for the analysis. Non-linear regression can be used to adjust the model parameters automatically to find the best fit of the history-match simulation to the measured rate or pressure data.

For example, a pressure data was measured for a well which was flowed on a wide-open choke for 12 hours, then put through a separator to measure the rates for 3 hours, and finally shut-in for 6 hours for a pressure build-up. For a selected type-curve model, the history-match simulation would use a fixed pressure constraint to compute the rates for the period the well was on an open choke, then switch to a fixed rate constraint to compute the flowing pressures while the well was flowed through the separator, and then switch to a fixed rate of zero to compute the pressure build-up.

### 4) Multi-Well Simulation

A multi-well simulation calculates the behavior at an "observation" well subjected to the influence of up to nine surrounding wells for a given type-curve model. At its simplest, using two wells in a multi-well simulation is like an interference-test with an observation well and an active well located some distance away. However, the multi-well simulation in PIE goes far beyond this simple system and allows the observer and the surrounding wells to produce under arbitrary production constraints (just like the "history-match" simulation above). In effect, the multi-well simulation is like a numerical simulator except analytic type-curve models are used instead of a numerical solution.

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