Miscible Flood Simulation in Sensor

Also see:  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 injection.  Each 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 spe79692.dat.  Printed results are in the file spe79692.out (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 Benchmarks page).

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 Crumpton, 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.