Deep carbonate gas reservoirs exhibit diverse reservoir types and complex seepage patterns. To study the gas production capabilities of different composite reservoir types, we classified the reservoirs of the fourth member of the Dengying Formation in the Anyue Gas Field into high-quality reservoirs (HRs) and poor-quality reservoirs (PRs) based on high-pressure mercury injection (HPMI) experiment results. By varying the differential pressure of the depletion experiment and the connection method, as well as the permeability and water saturation of the composite core, the effects of well location deployment, permeability ratio of the high-quality reservoir and poor-quality reservoir (PRHPR), gas well production pressure difference (GWPPD), and water saturation on the depletion gas production characteristics of the composite reservoir were studied. The research results show that (1) deploying wells on HR enables high gas production rates and ultimate recovery rates; (2) only when the PRHPR falls within a reasonable range (21.88–43.19) can the “dynamic recharge” capability of PR and the high permeability of HR be coordinated to achieve high gas recovery rates; (3) a GWPPD of 3 MPa is optimal, resulting in fast gas production rates and high ultimate recovery rates for PR; (4) high water saturation (≥50%) leads to premature water breakthrough at the well bottom, decreased gas production rate, and sealing of HR and PR reserves by formation water. Combining experimental results with field production data is our next research focus. Our future research focus will be on integrating experimental results with field production data to provide solid theoretical support for the efficient development of this type of gas reservoir.