I think you may have the answer to your question, in the text of your question. If the water comes to the surface at 4000psi as you say,it will be injected back down the well/bore at the same pressure! No pumps needed. All a pump does is pressurise the water. Deep well pumps [lineshaft turbines usually,sometimes electric submersibles],have to be placed way down the well under the water level and "push" the water up to the surface where it may arrive at little or great pressure, depending on the head that the pump produces. That is from my irrigation knowledge perspective. QED
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