Rate Transient Analysis in Shale Gas Reservoirs with Transient Linear Behavior

Many hydraulically fractured shale gas horizontal wells in the Barnett shale have been observed to exhibit transient linear behavior. This transient linear behavior is characterized by a one-half slope on a log-log plot of rate against time. This transient linear flow regime is believed to be caused by transient drainage of low permeability matrix blocks into adjoining fractures. This transient flow regime is the only flow regime available for analysis in many wells. The hydraulically fractured shale gas reservoir system was described in this work by a linear dual porosity model. This consisted of a bounded rectangular reservoir with slab matrix blocks draining into adjoining fractures and subsequently to a horizontal well in the centre. The horizontal well fully penetrates the rectangular reservoir. Convergence skin is incorporated into the linear model to account for the presence of the horizontal wellbore. Five flow regions were identified with this model. Region 1 is due to transient flow only in the fractures. Region 2 is bilinear flow and occurs when the matrix drainage begins simultaneously with the transient flow in the fractures. Region 3 is the response for a homogeneous reservoir. Region 4 is dominated by transient matrix drainage and is the transient flow regime of interest. Region 5 is the boundary dominated transient response. New working equations were developed and presented for analysis of Regions 1 to 4. No equation was presented for Region 5 as it requires a combination of material balance and productivity index equations beyond the scope of this work. It is concluded that the transient linear region observed in field data occurs in Region 4 – drainage of the matrix. A procedure is presented for analysis. The only parameter that can be determined with available data is the matrix drainage area, Acm. It was also demonstrated in this work that the effect of skin under constant rate and constant bottomhole pressure conditions is not similar for a linear reservoir. The constant rate case is the usual parallel lines with an offset but the constant bottomhole pressure shows a gradual diminishing effect of skin. A new analytical equation was presented to describe the constant bottomhole pressure effect of skin in a linear reservoir. It was also demonstrated that different shape factor formulations (Warren and Root, Zimmerman and Kazemi) result in similar Region 4 transient linear response provided that the appropriate f(s) modifications consistent with lAc calculations are conducted. It was also demonstrated that different matrix geometry exhibit the same Region 4 transient linear response when the area-volume ratios are similar