An apparatus for pumping fluid, the apparatus including a pump housing including a plunger connected to a terminal end of a coiled tubing and a first port. The apparatus further including the plunger configured to move longitudinally upward and downward, wherein the plunger includes a second port and a surface pumping unit configured to modulate between two modes, a first mode configured to limit a stroke length of the plunger so that the first and second ports do not engage, and a second mode wherein the first and second ports engage. Also, a method for pumping fluid into a wellbore using an apparatus, the method comprising inserting a housing including a coiled tubing and a plunger into the wellbore, wherein the plunger is located at a terminal end of the coiled tubing, and wherein the housing includes a first port and a plunger includes a second port. The method further including moving the plunger longitudinally upward and downward within the housing wherein a stroke length of the plunger is limited during the moving the plunger and extracting fluid from the wellbore. The method further including extracting fluid from the wellbore, pulling the plunger longitudinally upward until the first and second ports are aligned, and circulating fluid into the wellbore through the coiled rubbing and first and second ports discharging into an annulus of the wellbore.