1 / 10

Direct Inverse Modeling with Stream Functions Brouwer, G.K., July 16, 2007

,. Direct Inverse Modeling with Stream Functions Brouwer, G.K., July 16, 2007 Poster: Brouwer, G.K., W. Zijl , P. Fokker, TNO, the Netherlands. ,. Contents Intro: well measurements, processes, inversion Revival of stream function Direct inversion with the Double Constraint

dieter
Download Presentation

Direct Inverse Modeling with Stream Functions Brouwer, G.K., July 16, 2007

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. , Direct Inverse Modeling with Stream Functions Brouwer, G.K., July 16, 2007 Poster: Brouwer, G.K., W. Zijl, P. Fokker, TNO, the Netherlands

  2. , Contents Intro: well measurements, processes, inversion Revival of stream function Direct inversion with the Double Constraint Constraints (P,Q), (water cut) Example assimilating water cut measurements Conclusions Future work

  3. , • Well data in an oil reservoir with water injection: • Pressure (t), or flow potential f (t) • Flow oil (t), or Qo (t) (flux), qo(t) (flux density) • Flow water (t) • Two dynamical processes with (very) different time scale: • Pressure propagation • displacement of the phases • Direct inversion model (Darcy): • k=vtot/(flow potential gradient) or:

  4. , (qy=dy/dx=0) q1=-dy1/dy, q2=-dy2/dy df/dx=const k1 w1 w2 k2 l1 l2 (qy=dy/dx=0) qx=-dy/dy=const df/dx=/const k1 k2 w Finding k in flow direction: “k is hidden in f” Solve by requiring S(li/ki)=constant at all times (M=/1) l Finding k perpendicular to flow: An arrival time (y) problem !

  5. , Stream function Mores streamlines Solving y: Implemented in MoReS: “prescribed boundary conditions”

  6. , Double constraint (Wexler, 1985, medical application): pressure BC (wells) > guessed pressure fieldf(x,y) (MoReS pot. run) posterior perm field k (x,y) iterate prior permeability field k (x,y) flux BC (wells) > guessed flow field vx, vy or y(x,y) (MoReS flow run)

  7. , Y=0.67 Y=1.00 prod3 cprod3 injector prod2 c = 0 cprod2 c = inf. cprod1 Y=0.00 Y=0.33 prod1 Constraining on P, Q: For each stream tube: j: porosity DS=Sbf-Swc V=volume

  8. , Correcting on wells first arrival stream tube travel time by changing dy/ds Apply DC iterate

  9. , LINE: “truth” Blue circles: assim. of fluxes and pressures Bluesquares: restored watercut

  10. , • conclusions: • double constraint honours hard data • Water cut (+ saturation fronts from 4-D seismics) can be assimilated • methodology can be applied with any forward simulator • (pressures and velocities have to be available) • recommendations: • reformulation for 3-D • software development for 3D, multi- phase flow • (prototype 3-D available) • integrate with (extended) Kalman filter • explore DC for upscaling

More Related