This paper presents a backpressure equation (BPE) for wells producing from layered gas reservoirs with or without communication. The proposed BPE handles backflow between the layers through the wellbore for non-communicating layered systems, and accurately describes performance of wells experiencing differential depletion.The proposed multi-layer BPE has the same form as the familiar backpressure equation for single-layer gas reservoirs, where the correct averages are defined for reservoir pressure and backpressure constants.The BPE is validated against numerical simulation models, as well as field data which include decades of historical production performance and annual shut-in pressures. All numerical models and field data used to validate the BPE are publicly available. This paper gives guidelines on welltest design to quantify reservoir parameters in layered systems, based on systematic studies with numerical simulation models.
BackgroundLayered reservoirs without communication, also referred to as layered no-crossflow reservoirs, consist of separate layers without communication within the reservoir; layers only communicate through the wellbore.One of the first attempts to study the transient performance of layered reservoirs was Lefkovits et al. (1961). They show individual layer gas rates as a function of each layer kh product, but do not consider production performance solutions for boundary-dominated (pseudosteady state, PSS) conditions. Fetkovich et al. (1990) studied and identified all key performance characteristics of layered no-crossflow systems producing under boundary-dominated conditions. One of their many important observations is Curve 6 in their Fig. 12, showing that the backpressure relation for a differentially depleting system is, in fact, a straight line with exponent n~1. We show, in this paper, that this is an expected and general observation for any layered system, and that the layered no-crossflow backpressure equation is the same as for a single-layer system with equal total kh, but using the layer PI-averaged shut-in pressure.El-Banbi and Wattenbarger (1996) developed a model to match production data from a layered no-crossflow system during boundary-dominated conditions, using individual-layer coupling of material balance and PSS rate equations. This model is used to estimate individual layer properties, for the assumption of constant bottomhole flowing pressure. Another attempt to estimate layer properties and gas in place for layered no-crossflow reservoirs was Kuppe et al. (2000). This work allows changes in bottomhole flowing pressure, but does not handle extended shut-ins resulting in backflow through the wellbore. This paper will primarily consider layered no-crossflow reservoirs, but some results are shown to be applicable to reservoirs with partially-or fully-communicating layers. The backpressure equation presented is valid for all layered reservoirs, but the coupled material balance approach is only valid for non-communicating layer systems.