Multilayer Cylindrical with Unequal Pi Model

This model simulates the transient flow in any number of independent layers commingled at the wellbore as shown below.

Each layer is considered to have a cylindrical geometry with an unequal initial pressure (pi) to other layers, as well as its own skin factor, reservoir properties, and outer boundary condition. No crossflow between the layers can occur except at the wellbore. The dual porosity flow within each layer can be modeled either as pseudo-steady state or transient interporosity flow.

When the layers have unequal initial pressures, crossflow in the wellbore can occur from one layer to another upon perforating the layers, or after shut-in as the pressures equalize. The following figure illustrates the crossflow in the wellbore when the well is shut-in (pre-production period).

This shows that fluid is entering Layer 2 and Layer 3 from Layer 1 (the top layer) during crossflow through the wellbore. The model calculates the sandface rate from each layer with time, where a positive rate means fluid is leaving the layer, and a negative rate means fluid is entering the layer. The amount of crossflow at a given time is a function of many factors including the initial pressure (pi), skin damage (sd), flow capacity (kh), storativity, boundary condition, and pore volume (Vp) of the individual layers, as well as wellbore storage.

Hydrostatic pressure differences between layers can also be accounted for in this model by entering a datum depth (Ddatum) and individual layer depths (Dlayer). All depths are referenced from the surface.

References

1. "The New Analytical Solution to Pressure Transient Problems in Commingled, Layered Zones with Unequal Initial Pressures Subject to Stepped Changes in Production Rates", N.M. Anisur Rahman and L. Mattar, Paper SPE 90087 for Presentation in SPE Annual Technical Meeting and Exhibition, Houston, TX, September 2004.

2. "A Study of the Behaviour of Bounded Reservoir Composed of Stratified Layers", H.C. Lefkovits, P. Hazebroek, E.E. Allen and C.S. Matthews, SPEJ (March 1961) 43 - 58.

3. "Wells Producing Commingled Zones with Unequal Initial Pressures and Reservoir Properties", L. Larsen, Paper SPE 10325 for Presentation in AFTCE, San Antonio, TX, October 5 - 7, 1981.

4. "An Efficient Algorithm for Computation of Well Responses in Commingled Reservoirs", J.B. Spath, E. Ozkan and R. Raghavan, SPEFE (June 1994) 115 - 121.