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The decomposition algorithm is based on the minimisation of correlation functional between functional
between generating well pressure variation
and pressure trend
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| body | \delta p_{R,{\rm tr}}(t) |
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at receiving well after deducting the simulated pressure pulse-code response:
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| anchor | TPTM2puGG |
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| alignment | left |
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X[p_{uGG}] = \left < | p_{G,{\rm tr}}(t) | , \, |\delta p_G(t)| \right > \rightarrow \min |
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X[p_{uGR}] = \left < | \delta p_{R,{\rm tr}}(t) | , \, |\delta p_GR(t)| \right > \rightarrow \min |
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p_G(t) = p_{G,{\rm tr}}(t) - \delta p_G(t), \quad \delta p_G(t) = \int_0^t p_{uGG}(t-\tau) \, dq_G(\tau) |
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p_R(t) = p_{R,{\rm tr}}(t) - \delta p_R(t), \quad \delta p_R(t) = \int_0^t p_{uGR}(t-\tau) \, dq_G(\tau) |
The generator's flowrate history
, generator's wellbore pressure history and receiver's wellbore pressure history are assumed to be known for the whole period of the test.
The result of decomposition is the set of the unit-rate transient responses, DTRs
and
CTRs
), which characterise reservoir properties round generator and between generator and receiver.
The pressure trends at generator
and receiver
may have unknown origin but in order for
decomposition to work they should have minimum correlation with generating well
pressure flowrate variation
. In terms of spectral analysis this means that
pressure trend
's spectrum contains minimum overlap with spectrum of
pressure flowrate variation
at generator.
The contamination components of the trends should either have This particularly means that pressure trends at generating and receiving wells may contain:
- low frequencies (created by monotonous
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- activities of distant wells), which are lower than frequency range of the generating well flow variation
or
- high frequencies (created by lift instability at generating/receiving well), which are higher than frequency range of the generating well flow variation
If pressure ).If for some reasons the trends contain components correlated with
(for example receiving well or distant wells have been synchronously varying the rates with generating well) then
decomposition is not unique and should not be considered.
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