#### The Failure of Decline Curve Analysis for Real 3D Multiphase Systems1

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Graphical extrapolation of production data is entirely empirical.  It has no basis or any possible guidance in flow theory or behavior of real heterogeneous multiphase systems.  No analytical solutions apply to such systems, thus numerical models (reservoir simulators) are required to optimize or predict their behavior as a function of their description and applied process (boundary conditions).  There is no such thing as a "flow regime" in heterogeneous reservoirs with arbitrary boundaries.  Heterogeneity in geology and/or in initial fluid distributions along with multiphase flow and arbitrary boundaries and applied boundary conditions can cause production curves to take any shape.

The first simple example is homogeneous in geology and regular in geometry.  The 20-year production history is (gas is red, oil is green, water is blue):

This simple homogeneous and isotropic 20-layer reservoir contains an initial gas cap, an oil zone, and an aquifer at the bottom.

Before 600 days (gascap breakthrough), most estimators would say that the reservoir is in "transient" and would not attempt to make any production projections based on decline.  But if they did, they would probably be in huge error in any predictions.

No decline curve analysis (DCA) can make a useful production projection for this reservoir at any time during its entire 20 year producing life, since gas production does not reach final decline until the end of it.

Even if the gas rate were in decline at later times in this example, no DCA can reliably project oil production  because it can not predict the water rate behavior and its strong effect following breakthrough.  The Sensor data is spe1_dcatest.dat.  The full set of output production data is given in spe1_dcatest.xlsx.  The problem is SPE12 with the following changes:

homogeneous and isotropic, k=.1 md
20 layers each 10 ft thick
layers 11-20 are aquifer
layers 1-2 are gas cap
single well depletion, bhp=500
x-direction horizontal well in center of layer 8, 5000 ft long, completed in i=3:7,j=5
top of reservoir depth = 8300 ft, GOC=8320, HWC=8400
Initial pressure and Psat are 7000 psia at the GOC

The next example will demonstrate an extreme failure of DCA.  A sealed fault near the well will break when the stress differential across it reaches 2000 psia.  This occurs after several years of production.  Any decline curve analysis made before that time can not possibly predict the massive increase in production caused by the breaking fault seal.

An infinite number of similar cases of the failure of DCA due to heterogeneity in geology and/or fluid distributions can be easily imagined and demonstrated.

1. Taken from an SPE Reservoir group technical discussion "Exponential Decline of Waterflood Production Forecast - Myth or Reality", October, 2016 (SPE login is required).

2.  Odeh, A.S., "Comparison of Solutions to a Three-Dimensional Black-Oil Reservoir Simulation Problem", JPT (Jan. 1981) Vol. 33 p 13025

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