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| LaTeX Math Block |
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p_R(t) = p_{R,{\rm tr}}(t) - \delta p_R(t), \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 variation
. In terms of spectral analysis this means that trend's spectrum contains minimum overlap with spectrum of pressure variation
at generator.
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