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Dynamic Data Analysis – v5.12.01 - © KAPPA 1988-2017
Chapte
r 4 – R ate Transient Analysis (RTA)- p156/743
J(θ) =
1
2
∑(θ
T
x
(i)
− q
(i)
)
2
n
i=1
+ λ∑θ
j
2
p
j=1
Where λ ≥ 0 is called the tuning parameter and controls the relative weight on a better fit and
smaller parameters. A ten-fold cross-validation is used to select an appropriate value of λ [2].
Once λ is determined, θ can be evaluated as:
θ = (X
T
X + λI)
−1
X
T
q
where I is the identity matrix.
Once the relationship between the pressure drop and the rate has been learned, one can
predict the rates given the selected features, proposed pressure drops and constants θ:
q
pred
= X
pred
θ
References
[1] Tian, T. and Horne, R. N., ‘Applying Machine Learning Techniques to Interpret Flow Rate,
Pressure and Temperature Data from Permanent Downhole Gauges’, SPE 174034.
[2] Hastie, T., Tibshirani, R. and Friedman, J., ‘The Elements of Statistical Learning, 2
nd
Edition’, 2009.
4.E.6.d
Implementation in Topaze
The user can select whether the target data to be used should be rates or cumulative
production.
A Features panel allows the user to select which features to include in the regression process:
Fig. 4.E.4 – Topaze RTA deconvolution dialog