Imbibition Assisted Recovery

Imbibition Assisted Recovery Orkhan H Pashayev Petroleum Engineering Department Texas A&M University February 2004 Masters Division

Presentation Outline • Introduction • Problem Statement • Background and Literature Review • Objectives • Numerical Modeling • Grid Sensitivity • Matching Experimental Results • Numerical Analyses of Spontaneous Imbibition • Imbibition Upscaling • Conclusions February 2004 Imbibition Assisted Recovery

Problem Statement • An understanding the role of imbibition in Naturally Fractured Reservoirs in order to achieve maximum recovery • Lack of knowledge in upscaling laboratory imbibition experiments to field dimensions February 2004 Imbibition Assisted Recovery

Background and Literature Review • Two methods of modeling Naturally Fractured Reservoirs • Numerical model with sufficiently refined grid to adequately represent matrix/fracture geometry • Dual Porosity Model (Warren and Root, 1963) February 2004 Imbibition Assisted Recovery

Background and Literature Review • Expulsion of oil from matrix block to the surrounding fractures by capillary imbibition of water is the most important oil recovery in Naturally Fractured Reservoirs February 2004 Imbibition Assisted Recovery

Background and Literature Review • Transfer Functions: • Transfer functions that use Darcy’s Law • Diffusivity transfer functions • Empirical transfer functions • Scaling transfer functions February 2004 Imbibition Assisted Recovery

Background and Literature Review • Scaling transfer functions: • Rapoport (1952) • Graham and Richardson (1959), Mattax and Kyte (1962) • Hamon and Vidal (1986), Bourblaux and Kalaidjian (1995), Akin and Kovsek (1998), etc • Du Prey (1978), Kazemi (1992), Ma et.al (1996), etc February 2004 Imbibition Assisted Recovery

Objectives • Conduct numerical studies with matrix block surrounded by fractures to better understand the characteristic of spontaneous imbibition • Evaluate dimensionless time tD and investigate the limitations of the upscaling laboratory imbibition experiments to field dimensions February 2004 Imbibition Assisted Recovery

Simulation Parameters • Two phase black-oil commercial simulator, CMG™ • Core = 3.2cm x 3.2cm x 4.9cm • K = 74.7 • SWi= 41.61% • Φ = 15.91% • μOIL= 3.52 cp • μWATER= 0.68 cp • APIOIL= 31° February 2004 Imbibition Assisted Recovery

Grid Sensitivity Analyses • Cartesian grid system February 2004 Imbibition Assisted Recovery

Grid Sensitivity Analyses February 2004 Imbibition Assisted Recovery

Grid Sensitivity Analyses 10000 8000 4096 1728 February 2004 Imbibition Assisted Recovery

Reservoir Grid • I = 20, J = 20, K = 20 • No. of gridblocks = 8000 • Grid dimensions • I: 1x0.01cm 18x0.178cm 1x0.01cm • J:1x0.01cm 18x0.178cm 1x0.01cm • K:1x0.01cm 19x0.259cm February 2004 Imbibition Assisted Recovery

Matching Experimental Results February 2004 Imbibition Assisted Recovery

Matching Experimental Results • The following logarithmic capillary pressure relationship was used • PC°- threshold capillary pressure • SW – water saturation February 2004 Imbibition Assisted Recovery

Matching Experimental Results February 2004 Imbibition Assisted Recovery

Gravity Effect • Bond number • ρWATER= 1 g/cc • ρOIL= 0.8635 g/cc • ρWATER=ρOIL= 0.8635 g/cc February 2004 Imbibition Assisted Recovery

Different Boundary Conditions • All Faces Open • Two Ends Closed • Two Ends Open • One End Open No Flow Surfaces February 2004 Imbibition Assisted Recovery

Different Boundary Conditions February 2004 Imbibition Assisted Recovery

K4 K3 K2 K1 Heterogeneities • One End Open • Case 1: K1 > K2 > K3 > K4 • Case 2: K1 < K2 < K3 < K4 water February 2004 Imbibition Assisted Recovery

Heterogeneities February 2004 Imbibition Assisted Recovery

Spontaneous Imbibition Upscaling Theory • Recovery behavior for a large reservoir matrix block could be predicted from lab experiments • Mattax and Kyte • Ma et.al February 2004 Imbibition Assisted Recovery

Spontaneous Imbibition Upscaling • All Faces Open, Two Ends Closed, Two Ends Open and One End Open • Semi-log plot: • Normalized Recovery vs. Dimensionless Time February 2004 Imbibition Assisted Recovery

Spontaneous Imbibition Upscaling Comparison February 2004 Imbibition Assisted Recovery

Spontaneous Imbibition Upscaling Varying Mobility Ratio February 2004 Imbibition Assisted Recovery

Spontaneous Imbibition Upscaling Varying Mobility Ratio • Mobility Ratio - not included • Need to include mobility ratio into the formulation of dimensionless time February 2004 Imbibition Assisted Recovery

Spontaneous Imbibition Upscaling Varying Mobility Ratio February 2004 Imbibition Assisted Recovery

Spontaneous Imbibition Upscaling TEO February 2004 Imbibition Assisted Recovery

Spontaneous Imbibition Upscaling TEC February 2004 Imbibition Assisted Recovery

K4 K3 K2 K1 Spontaneous Imbibition Upscaling Heterogeneous Core • One End Open • Case 1: K1 > K2 > K3 > K4 • Case 2: K1 < K2 < K3 < K4 water February 2004 Imbibition Assisted Recovery

Spontaneous Imbibition Upscaling Heterogeneous Core February 2004 Imbibition Assisted Recovery

Conclusions • It was observed that time required to saturate core to Sw=60% increases exponentially as the number of faces available for imbibition decrease • Results proved that using characteristic length in the equation of dimensionless time, instead of length of the core improves upscaling of spontaneous imbibition February 2004 Imbibition Assisted Recovery

Conclusions • Further investigation revealed that upscaling correlations could be significantly improved by taking into account end-point mobilities and mobility ratio • Spontaneous imbibition recovery is higher for a flow in the direction of decreasing permeability than in the case of a flow in the direction of increasing permeability February 2004 Imbibition Assisted Recovery

Conclusions • Some discrepancy observed in correlations, while upscaling heterogeneous core, indicated that existing transfer functions can not precisely account for heterogeneities in the core February 2004 Imbibition Assisted Recovery

Acknowledgement • Finally I would like to express my sincere gratitude and appreciation to my advisor Dr. David Schechter and Dr. Erwin Putra. Thank You! February 2004 Imbibition Assisted Recovery

Imbibition Assisted Recovery Orkhan H Pashayev Petroleum Engineering Department Texas A&M University February 2004 Masters Division

Imbibition Assisted Recovery