A comprehensive model of pressure behavior in a minifrac test with a compressible fluid (a fluid for which the density is a function of temperature and pressure) has been developed to simulate the pressure behavior more accurately and realistically. Since for minifrac tests, the fracture will more likely be radially expanding, Geertsma's penny-shaped fracture geometry model has been introduced to modify an existing linear fracture model. The new model handles a wide range of frac fluids using the proper equations of state to simulate slightly compressible fluids or highly compressible fluids such as high quality foams. In the case of surface shut-in, the effect of wellbore fluid warming due to the geothermal heating along the wellbore on the pressure decline is also examined.

Numerical solution of the model shows that the pressure decline after shut-in will be affected by the frac-fluid warming if the fluid is compressible. The higher the gas quality of a foam is, the more pronounced this effect will be. The leakoff coefficient evaluated frompressure decline using the Nolte model will be in error at early shut-in time. The wellbore fluid warming adds more inaccuracy to the leakoff estimation. The estimate error caused by the fluid warming in the fracture will decrease to zero as the fracture closure time fracture approaches.

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