During injection testing, the pressures in geothermal wells used for reinjection sometimes initially increase but then decline as injection continues. Injection tests carried out at the Yutsubo geothermal field in Kyushu, Japan, exhibit this peculiar behavior. During injection testing of Yutsubo well YT-2, the observed downhole pressures eventually began to decline despite sustained injection rates. We have carried out numerical simulation studies using a radial flow model to examine this behavior. Double porosity (MINC) models are adopted, in which the fracture porosity increases as a result of both cooling and pressure build-up, and the permeability is very sensitive to porosity changes. This extreme sensitivity of fracture permeability to porosity appears to be necessary to reproduce the late-time pressure decline, and suggests that fractures were opened by injection-induced cooling near the well.