Proper Kv/Kh for reservoir simulation: use of core images

Burdakov D.A.¹, Merkulov V.P.¹, Shotsky R.S.²

¹Tomsk Polytechnic University, Tomsk, Russia; ²Freelancer, Novosibirsk, Russia

[e-mail]

Engineers in Russian field development project teams often pay little attention or just do not know how to estimate vertical permeability, and commonly use it as a parameter to change in history matching or take ‘reasonable’ value of 0.1 for permz multiplier. Certainly core perms are of great value here, but unfortunately they cannot measure heterogeneity in the scale of well influence radius. Core vertical permeability measurements are only useful for a clean sand without mud drapes, since it will show zero values [1]. RFT and MDT data, partial penetration well testing can be used to directly measure or to derive analytically the desired vertical permeability value, but unfortunately rarely are these data present when you have an input for a new project. The paper will show how one can estimate k_v/k_h ratio with the use of standard field data: well logs and core. An actual practical technique was applied to an oil field with shallow marine tidal reservoir with varying amount of thin mud drapes. Data on 62 wells 9 of which has core was used.

Using numerically acquired relations [2] and general knowledge about fluid flow in porous media it is relatively easy to produce a full field 3d grid that will give performance prediction of increased accuracy. The relations give equations that were derived in a series of numerical experiments using special software simulating various sedimentary structures that appear in tidal environment. In essence, it is a series of equations that show relation between amount of thin shale beds and vertical permeability. For horizontal permeability it is a simple linear function: K_h=K_sand – A*V_m, where A=(k_sand-k_mud)/V_{mud max} and a power law for vertical permeability K_v = k_sand 10^(-b*V_m), where b = (log k_sand – log k_mud) / V_intercept. Deviding this two values yields kv/kh ratio. It is important to notice, that mud content here is actually a number of shale beds or small scale net to gross ratio, and that is the trickiest thing that was done by author.

Workflow for creating grid of kv/kh

1) Get the core in one line and convert it into black and white pixels only

2) Using special software count the amount of ‘blacks’ and ‘whites’ across the section with the chosen averaging window à mud content

3) Calculate kv/kh and make sure that actual anisotropy measurements are replicated (they usually do)

4) Find a correlation between mud content and log shaliness for wells without core (author used Larionov’s model)

5) Calculate kv/kh in wells without core using acquired relations

6)

Interpolate and make 3d grid àrun the simulation, analyze field performance.

Fig. The result of kv/kh calculation and its comparison to core data

As seen in example on Fig. calculated values from core images, processed in the way described above give really nice match with actual core measured data while filling the gaps in the parts of the section where data points are not present.

Correlation between number of thin shale beds and shaliness calculated from gamma ray is obviously present and cross plot of GR shaliness vs core image k_v/k_h shows R² of 0.69 for studied case. Using the relation obtained from the cross plot log derived shaliness is converted to the one that can be used it analytical equations for k_v/k_h Then, the interpolated grid of shaliness was transformed do permz grid. Usage of permz grid instead of simply using multiplier for permx of 0.1 gave sufficiently better match of simulated bottom hole pressures of horizontal wells and made full field simulation options with drilling of horizontal wells more justified.

References:

1.Auzerais F.M., Ellis D.V., Luthi E.B., Dussan V. and Pinoteau B.J. (1990) Laboratory characterization of anisotropic rocks, SPE 20602;

2. Ringrose P. S., Skjetne E. and Alfenbein C. (2003) Permeability Estimation Functions Based on Forward Modeling of Sesimentary Heterogeneity, SPE 84275.

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