For a finite conductivity vertical fracture flow regime (bilinear flow), the pressure change and derivative are offset by a factor of what?

• A. Two
• B. Four
• C. Three
• D. Five

Answer: (B)

In bilinear flow, the fracture and the surrounding formation both influence the flow, creating two parallel diffusion paths. This changes how the pressure response scales with time compared to the rate at which pressure changes. In the standard dimensionless formulation used for finite-conductivity vertical fractures, the relationship between the pressure change Δp and its time derivative dp/dt includes a factor of four. Put simply, the pressure change and its derivative are offset by four. This comes from the diffusion solution for bilinear flow, where the two symmetric diffusion regions around the fracture contribute, producing this characteristic fourfold offset.