Pressure transient survey in producer during the pressure rise period caused by shutting well down or reducing its production rate.
Shut-in survey after production period with a constant rate (see Fig. 1):
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| Fig 1. Horner test procedure |
Interpretation
Interpretation of BUS is based on:
- visual analysis of PTA diagnostic plot
- selecting diffusion model from PTA Type Library
- fitting selected diffusion model to pressure gauge data records
both production T and shut-in \Delta t period reach radial flow regime: T > t_{IARF}, \Delta t > t_{IARF}
total duration of production and shut-in do not reach the boundary
T+\Delta t < t_e
one can uses Horner model which is a simplified version of BUS interpretation procedure and based on the following pressure diffusion model:
| (1) | p_{wf}(\Delta t) = p_e - \frac{q_t}{4 \pi \sigma} \, \ln \left( 1 + \frac{T}{\Delta t} \right) |
The main features of Horner model are:
it provides reliable estimation of formation pressure p_e and formation transmissibility \sigma
it does not require the knowledge of pressure diffusivity \chi (unlike the case of a drawdown test)
it does not depend on diffusion model specifics as soon as IARF is developed during the test
it does not provide skin-factor estimation
The formula (1) shows that pressure during the shut-in segment of Honer test is not dependant on skin-factor and pressure diffusivity.
The formation pressure p_e and transmissibility \sigma are estimated with LSQ regression:
| \left \{ p_{wf} \right \} = p_e - b \, \left \{ \ln \left( 1 + \frac{T}{\Delta t} \right) \right \} |
| \sigma = \frac{q_t}{4 \pi b} |
Horner model is a good example of how a complicated problem of non-linear regression on three parameters \{ p_e, \, S, \, \sigma \} with upfront knowledge of pressure diffusivity may sometimes be simplified to a fast-track linear regression on two parameters without any additional assumptions on reservoir properties.