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The ADBV essentially is a check valve that prohibits the oil from flowing out of the filter when the system is shut down. This is most generally achieved by using a nitrile or silicone formed gasket near the holes. Depending upon location of filter, and orientation of filter, on the engine, the effectiveness of the ADBV can be substantial or moderate.
The BP valve in the filter is a pressure relief valve. It's there first and foremost to protect the media of the filter from a rupture if the pressure differential (dP) across the media becomes very significant. This most often happens when the filter is first installed dry, or when the ADBV does not hold the filter full upon shut down. Additionally, the BP valve can have a secondary benefit, but one that we'd hope does not come into use. If the media were to become so loaded with particulate that it were to "blind off" (fully or partially) to a point where the flow requirement of the engine exceeded the flow ability of the filter, the BP would start to crack open and aleviate the dP, thereby saving the filter from a rupture (avoiding media bits going into the stream) as well as giving vital flow to the engine. This BP function does not happen nearly as often as many infer. Jim Allen did some data logging testing on a live engine in normal use, and found that the only time the BP opened up was at really cold starts, with an oil thicker than was spec'd for his truck, and only for a second or two until the dP balanced out. With warmed oils, or the right fluid, it didn't happen at all. How does it work? It's essentially a spring loaded relief valve. There are a few different variations in the designs used by various makers, but they all seem to work just fine. Some are on the dome end; others the base end. Different spring sizes, shapes and locations don't seem to matter in function nearly as much as they matter for fodder in a BITOG debate ... Some vehicle even have this BP feature in the engine block and it's not part of the filter, but most applications have this in the filter itself. So some filters may not list a BP value in the product data, because they don't have one.
You didn't ask, but I'll round out the last tidbit here. The oil system has a BP relief valve to protect the pump and filter. It's function is to keep the oil pressure from spiking to a point of rupturing the filter canister, and/or harming the pump as they are of positive displacement design. It will bleed off pressure to keep it at a safe level for system supply and yet still provide oil flow and pressure to the engine lube circuit. They are spec'd to the right dP and flow requirements to balance the need for relief with the need for supply.