Low boost pressure is the no. 1 cause of excess black smoke out the tailpipe when accelerating.
As 03Black said, check all the boost hoses for any cracks or leaks. Check all the vacuum hoses, especially the one that runs from the vacuum modulator valve over to the turbo vane actuator diaphragm on top of the turbo. Check turbo vanes for ease of operation by manually stroking the vanes by hand. The vanes can get sticky at times.
Is your EGR still in operation? If so the EGR valve can fail and allow boost to leak backwards through it and dump into the exhaust manifold. Or the FCV can stick partly shut due to its little metal gears in its operator failing. Very common problem.
Installing a mechanical boost gauge will help greatly in diagnosing the problem.
Report back what you find to help others.

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Supporting Vendor and Moderator of LOST05 Jeep Liberty CRD Limited 
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