Miscible Flood Simulation in Sensor
Primary Miscible / Near-Miscible Flooding
and CO2 Sequestration and
Generalized Automatic Global Predictive Optimization,
Example 1. The optimal producing bhp for gas flooding
in the optimal producing strategy for SPE5 (3755.3 psia) is just below the
first-contact miscible pressure (3874.8), and demonstrates that the given
lab MMP (3000) is meaningless in the reservoir, and that "miscible flood"
models assuming a fixed miscibility pressure do not apply in general. That
example also demonstrates the non-existence of any competent AI/ML method in
engineering for design, optimization, or forecasting.
Sensor simulates miscible floods very
efficiently. When the first-contact miscibility (FCM) assumption is
warranted, more than two orders of magnitude performance improvement can be
obtained over the competition. Even without that assumption, well over an
order of magnitude speedup can be obtained. A published paper1 gives a 1000-block, quarter
5-spot example miscible flood problem, and reports a run time of 520 cpu
seconds. Sensor runs that problem (without the FCM assumption) in 13.8 cpu
seconds on a 2.8 GHz desktop. Details are discussed below.
The Sensor FCM option applies to first-contact
miscible flood simulation2. It uses state-of-the-art technology
to internally (automatically)
pseudoize the entered n-component
equation-of-state fluid description to two components. This
pseudoization is exact in that the density and
viscosity of the reservoir fluid as functions of composition and pressure
are exactly the same whether computed in n-component mode or pseudo
two-component mode. The Sensor FCM option applies with or without water
injection – say, WAG. Input data include bypassed oil fraction and a parameter to
control numerical dispersion or extend it to represent viscous fingering.
This FCM "first-contact miscible" assumption requires that reservoir
pressures lie above the p-z phase envelope. If local violations of
that assumption occur near producing wells, then the effects of 3-phase
conditions near those wells are assumed to be second order effects. The
model itself can be used to check the validity of that assumption. We
illustrate with a published example for which we find the FCM assumption to
not be valid.
The example problem discussed here1
is a 7305-day, quarter 5-spot, two-well solvent flood with no water
gridblock in the 10x10x10 3D grid is 120’ x 120’
x 2’. A 7-component
equation-of-state fluid description is given. The maximum pressure of
the p-z phase diagram is about 4300 psia (see Reference 2).
The producer operates on pressure constraint at a bottomhole pressure limit
of 2547 psia. Therefore, significant near-producer reservoir volumes will
experience 3-phase conditions.
The Sensor dataset for this problem is
Printed results are in the file
(FCM Implicit case). The figures
below compare results with and without the FCM assumption:
All Sensor Impes runs mentioned here were made with stable-step control using
CFL=2. Impes without stable-step control was highly unstable for this
problem. All Sensor run times are on a 2004-vintage 2.8 GHz desktop
(Machine 1 of
Sensor FCM runs: Cpu times
are 3.3 seconds (Impes) and 2 seconds (Implicit).
Sensor non-FCM runs: Cpu
times are 13.8 seconds (Impes) and 18.3 seconds (Implicit).
Reference 1 reports non-FCM run cpu of about
520 seconds (AIM), 720 seconds (Impes), and 1360 seconds (Implicit).
Their machine information was not
reported. We assume the model is
Eclipse 300, since the Schlumberger authors reference the Eclipse manual.
The authors describe a complex remedy to a problem in their modeling of
phase behavior, which does not exist in Sensor.
The plots comparing FCM with non-FCM results
show similar oil rate and cumulative oil vs time, but significantly
different gor and gas injection vs time. In this problem, formation of
the 3-phase region in the non-FCM case significantly reduces solvent
throughput, compared to the FCM case.
The Sensor FCM option logic is simple and
fast. Its accuracy is (a) high when the reservoir flood pressures lie
above the p-z diagram, and (b) problem-dependent when near-producer
pressures are in the 3-phase region of the diagram. Phase diagram
analysis and model test runs should always be performed to determine if the
FCM option is applicable.
1. Bowen, G. and
P., "A New Formulation for the Implicit Compositional Simulation of
Miscible Gas Injection Processes", SPE 79762-MS presented at the SPE
Reservoir Simulation Symposium held in Houston, Texas, February 3-5, 2003.
2. Coats, K.H., Thomas, L.K., and Pierson, R.G., "Simulation
of Miscible Flow Including Bypassed Oil and Dispersion Control", SPE
Reservoir Evaluation and Engineering, Vol. 10, No. 5, October 2007.