**An Analytical Solution for Transient Productivity Prediction of Multi-Fractured Horizontal Wells in Tight Gas Reservoirs Considering Nonlinear Porous Flow Mechanisms**

#### **Qiang Wang 1,2, Jifang Wan 1,3,\*, Langfeng Mu 4,5, Ruichen Shen 3, Maria Jose Jurado 6,\* and Yufeng Ye 7**


Received: 16 January 2020; Accepted: 25 February 2020; Published: 1 March 2020

**Abstract:** Multi-fractured horizontal wells (MFHW) is one of the most effective technologies to develop tight gas reservoirs. The gas seepage from tight formations in MFHW can be divided into three stages: early stage with high productivity, transitional stage with declined productivity, and final stage with stable productivity. Considering the characteristics and mechanisms of porous flows in different regions and at different stages, we derive three coupled equations, namely the equations of porous flow from matrix to fracture, from fracture to near wellbore region, and from new wellbore region to wellbore then an unstable productivity prediction model for a MFHW in a tight gas reservoir is well established. Then, the reliability of this new model, which considers the multi-fracture interference, is verified using a commercial simulator (CMG). Finally, using this transient productivity prediction model, the sensitivity of horizontal well's productivity to several relevant factors is analyzed. The results illustrate that threshold pressure gradient has the most significant influence on well productivity, followed by stress sensitivity, turbulence flow, and slippage flow. To summarize, the proposed model has demonstrated a potential practical usage to predict the productivity of multi-stage fractured horizontal wells and to analyze the effects of certain factors on gas production in tight gas reservoirs.

**Keywords:** tight gas reservoir; multi-fractured horizontal well (MFHW); unstable productivity model; productivity forecast; influencing factor analysis
