Table 1 Summary of conventional productivity equation and analysis method.

Empirical formula

One point method⁸

\({q}_{AOF}=\frac{6q}{\sqrt{1+48\left(\frac{{p}_{R}^{2}-{p}_{wf}^{2}}{{p}_{R}^{2}}\right)}-1}\)

Regression equation coefficient, easy data source, simple application

Stable point productivity binomial⁹

\(p_{R}^{2} - p_{w} f^{2} = A^{\prime}q_{s} c + B^{\prime}q_{s} c^{2}\)

Need to produce a stable point

( quasi-steady state )

Binomial deliverability equation¹⁰

Pressure / pressure square

\({p}_{R}^{2}-{p}_{wf}^{2}=A{q}_{sc}+B{q}_{sc}^{2}\)

According to the regression equation coefficient of test data, the productivity equation is constructed

Quasi-pressure

\({\psi }_{R}-{\psi }_{wf}=A{q}_{sc}+B{q}_{sc}^{2}\)

Exponential productivity equation¹¹

Pressure / pressure square

\({q}_{sc}=C{\left({p}_{R}^{2}-{p}_{wf}^{2}\right)}^{n}\)

Quasi-pressure

\({q}_{sc}=C{\left({\psi }_{R}-{\psi }_{wf}\right)}^{n}\)

Numerical simulation method

Large amount of calculation, complex

Dynamic model method ( well test, numerical well test, material balance coupling 27model, etc. )

Based on the validation dynamic model