Production data analysis (PDA) is a very useful methodology to conduct transient rate and pressure analysis for shale gas wells. However, frequent shut-ins as well as nozzle size changing and well interference often occur for shale gas wells in China. This leads to abrupt changes, fluctuation, or even loss of production data. The existing PDA methods are incapable of addressing this issue.

A new PDA method is proposed to solve the above problem. First, the model for shale gas wells is established and solved by Duhamel's principle and Laplace transform. The log-log curve curve for PDA is obtained. Second, the formation pressure distributions and the average formation pressures within the SRV area are calculated. Then, a virtual equivalent time is proposed by use of the average formation pressure. Thus, the production data with abrupt changes can be converted into several interconnected segments with known initial formation pressures. Numerical validations and field cases are conducted to verify the proposed method.

For the field shale gas wells with several abrupt rate and pressure changes, the history matching provided by the commercial software with a skin factor agrees with the field data before the first shut-in. However, the estimated pressure and gas rate start to deviate from the field data continuously since the first shut-in, and the deviation becomes greater over time. Particularly after the third shut-in, the deviation is too large to history matching. The offset is mainly caused by significant discontinuities and subsequent cumulative errors. On the contrary, the history matching of pressure and gas rate with correction by virtual equivalent time are both in good agreement with the field data. This implies that the issues caused by abrupt changes or significant discontinuities of production data are satisfactorily addressed. Therefore, the results interpreted from the PDA such as fracture half-length and SRV are more accurate and confident.

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