We have found a considerable volume of free gas in the annular space (between tubing and casing), I believe is becasue the horizontal section (more than 4,000 ft) works as a separator and the solution would be to run packers. But, why the yield trend is still decreasing?
A decrease in yield with time is to be expected in any completion. There are a large number of factors that figure into how quickly the production rates decline and these include reservoir issues, past production rates, phase behavior of the production under well conditions, completion design and current flow velocities for all of the phases in the horizontal section.
And yes, the horizontal section can act as a three phase separator if the flow rate of the fluids is not very high. Flow modeling using some best guess assumptions about flow rates into the horizontal section vs distance from TD should help to clarify this. But do not forget about phase behavior of the HC fluids.
Another issue to think about is whether you are starting to get scale formation in the perforations or at the rock face if you have an open hole. The local pressure drop at the skin surface of the reservoir can result in CO2 flashing into the gas phase. This can change the pH of the produced water and result in rapid formation of mineral scales on the reservoir face. These scales can result in reduced flow from the areas that were previously producing higher liquid volumes, but usually leave the higher GOR areas flowing more freely.
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