The High Field High Density Region (HFSFD) has been experimentally observed in both divertor and limiter tokamak devices. In order to numerically reproduced the HFSHD region in the limiter tokamak device J-TEXT, we first performed SOLPS-ITER simulations on the J-TEXT limiter tokamak with the activation of drifts, which is associated with the HFSHD region. The validated physical models, which is from ASDEX Upgrade (AUG) divertor modelling including full drifts and currents, were implemented. Through a gas puffing rate scan, both attached and detached regimes were obtained in the AUG divertor and J-TEXT limiter. The key plasma parameters in the J-TEXT limiter are evaluated with and without drifts that have a qualitative performance like AUG except the roll-overment of the total ion flux. The drift effects on the target profiles are investigated in which the maximum electron temperature at the outer targets is 15eV and 5eV respectively. When the outer targets are attached in the J-TEXT limiter and AUG divertor, the drifts result in the partial detachment of the inner targets. In the detached regimes, the drifts decrease the electron temperature on AUG divertor targets. However, for the J-TEXT limiter, the electron temperature only decreases at the far SOL region. The effect of drifts on the neutral density is also presented.