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You may copy this document (including all “© 2000, Laine & Associates, Inc.” copyright marks) as is, but only for non-profit, personal use. See license agreement for details.

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Laine & Associates, Inc.www.EricLaine.com

© 2000Pseudo-Kr and Pseudo-Pc Calculations

Pseudo-Kr and Pseudo-PcSpreadsheets

for

predicting pseudo-relative permeability curves

to be used in any

Reservoir Simulation Software *

* for commercial & academic simulation software

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© 2000Preface and Introduction

Preface

Thank you for visiting www.EricLaine.com.

The primary purpose of this document is to serve as a memory aid for theauthor. Thus, the author is also the target audience. (In other words, thequality of the composition is 100% sufficient for me to understand what I wrote.)

The secondary purpose is to share this tutorial with the public. I appreciate thepossibility that the general public may have some difficulty understanding themy personal abbreviations and my intuitive logic.

Introduction This user guide highlights several spreadsheets the author uses to calculatepseudo-relative permeability curves. These include:

Gravity Segregation,Thomas,Hearn low rate, andHearn high rate

Endpoint modifications are applied to:Straight-line (Thomas) curves, and

Curved (Corey) curvesDirect input of modified endpointsPseudo-capillary pressure curves are included as well.

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© 2000

Laine & Associates, Inc. LICENSE AND WARRANTY NOTICELaine & Associates, Inc. LICENSE AND WARRANTY NOTICE

LAINE & ASSOCIATES, INC. (Laine) LICENSES THIS SOFTWARE TO YOU ONLY UPON THE CONDITION THAT YOU ACCEPTLAINE & ASSOCIATES, INC. (Laine) LICENSES THIS SOFTWARE TO YOU ONLY UPON THE CONDITION THAT YOU ACCEPTALL OF THE TERMS AND CONDITIONS CONTAINED IN THIS LICENSE AGREEMENT. PLEASE READ THESE TERMSALL OF THE TERMS AND CONDITIONS CONTAINED IN THIS LICENSE AGREEMENT. PLEASE READ THESE TERMSCAREFULLY. IF YOU DO NOT AGREE TO THESE TERMS, PLEASE DESTROY THE DOCUMENT(S) YOU HAVE DOWNLOADEDCAREFULLY. IF YOU DO NOT AGREE TO THESE TERMS, PLEASE DESTROY THE DOCUMENT(S) YOU HAVE DOWNLOADEDIMMEDIATELY.IMMEDIATELY.

The software and documents which accompany this license (Software) are the property of Laine or its licensors and is protected byThe software and documents which accompany this license (Software) are the property of Laine or its licensors and is protected bycopyright law. While Laine continues to own the Software, you will have certain rights to use the Software after your acceptance of thiscopyright law. While Laine continues to own the Software, you will have certain rights to use the Software after your acceptance of thislicense.license.

Except as may be modified by a license addendum which accompanies this license, your rights and obligations with respect to the useExcept as may be modified by a license addendum which accompanies this license, your rights and obligations with respect to the useof this Software are as follows:of this Software are as follows:

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(i) have limited permission to copy and distribute this Software, but only for non-profit, personal use, provided there is no charge, fee,(i) have limited permission to copy and distribute this Software, but only for non-profit, personal use, provided there is no charge, fee,etc. for said distribution, and further provided that all copyright marks and all references to Laine & Associates, Inc. and toetc. for said distribution, and further provided that all copyright marks and all references to Laine & Associates, Inc. and towww.www.EricLaineEricLaine.com and to Eric Laine are included in the distribution;.com and to Eric Laine are included in the distribution;

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Laine does not warrant that the Software will meet your requirements or that operation of the Software will be uninterrupted or that theLaine does not warrant that the Software will meet your requirements or that operation of the Software will be uninterrupted or that theSoftware will be error free. THIS SOFTWARE IS PROVIDED AS IS, WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESS ORSoftware will be error free. THIS SOFTWARE IS PROVIDED AS IS, WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESS ORIMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF PERFORMANCE, MERCHANTABILITY, FITNESSIMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF PERFORMANCE, MERCHANTABILITY, FITNESSFOR A PARTICULAR PURPOSE, ACCURACY, OMISSIONS, COMPLETENESS, CURRENTNESS, AND NON-INFRINGEMENT.FOR A PARTICULAR PURPOSE, ACCURACY, OMISSIONS, COMPLETENESS, CURRENTNESS, AND NON-INFRINGEMENT.THE AUTHOR EXPRESSLY DISCLAIMS ANY REPRESENTATION OR WARRANTY, WHETHER WRITTEN OR ORAL, THAT THISTHE AUTHOR EXPRESSLY DISCLAIMS ANY REPRESENTATION OR WARRANTY, WHETHER WRITTEN OR ORAL, THAT THISSOFTWARE WILL BE ERROR FREE OR UNAMBIGUOUS. YOU ACKNOWLEDGE THAT USE OF THIS SOFTWARE IS AT YOURSOFTWARE WILL BE ERROR FREE OR UNAMBIGUOUS. YOU ACKNOWLEDGE THAT USE OF THIS SOFTWARE IS AT YOURSOLE RISK, AND YOU AGREE THAT ANY INFORMATION, SERVICE OR PRODUCT, WHETHER BASED IN PART OR IN WHOLESOLE RISK, AND YOU AGREE THAT ANY INFORMATION, SERVICE OR PRODUCT, WHETHER BASED IN PART OR IN WHOLEON THIS SOFTWARE, IS WITHOUT WARRANTY, EITHER EXPRESSED OR IMPLIED.ON THIS SOFTWARE, IS WITHOUT WARRANTY, EITHER EXPRESSED OR IMPLIED.

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© 2000Agreement (2 of 2)

Laine & Associates, Inc. LICENSE AND WARRANTY NOTICE, continuedLaine & Associates, Inc. LICENSE AND WARRANTY NOTICE, continued

DISCLAIMER OF DAMAGES:DISCLAIMER OF DAMAGES:

IN NO EVENT WILL LAINE BE LIABLE TO YOU FOR ANY SPECIAL, CONSEQUENTIAL, INDIRECT OR SIMILAR DAMAGES,IN NO EVENT WILL LAINE BE LIABLE TO YOU FOR ANY SPECIAL, CONSEQUENTIAL, INDIRECT OR SIMILAR DAMAGES,INCLUDING ANY LOST PROFITS OR LOST DATA ARISING OUT OF THE USE OR INABILITY TO USE THE SOFTWARE, EVEN IFINCLUDING ANY LOST PROFITS OR LOST DATA ARISING OUT OF THE USE OR INABILITY TO USE THE SOFTWARE, EVEN IFLAINE HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. SOME STATES DO NOT ALLOW THE LIMITATION ORLAINE HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. SOME STATES DO NOT ALLOW THE LIMITATION OREXCLUSION OF LIABILITY FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES SO THE ABOVE LIMITATION OR EXCLUSIONEXCLUSION OF LIABILITY FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES SO THE ABOVE LIMITATION OR EXCLUSIONMAY NOT APPLY TO YOU. IN NO CASE SHALL LAINE'S LIABILITY EXCEED THE PURCHASE PRICE FOR THE SOFTWARE.MAY NOT APPLY TO YOU. IN NO CASE SHALL LAINE'S LIABILITY EXCEED THE PURCHASE PRICE FOR THE SOFTWARE.THE DISCLAIMERS AND LIMITATIONS SET FORTH ABOVE WILL APPLY REGARDLESS OF WHETHER YOU ACCEPT THETHE DISCLAIMERS AND LIMITATIONS SET FORTH ABOVE WILL APPLY REGARDLESS OF WHETHER YOU ACCEPT THESOFTWARE.SOFTWARE.

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The author has made a good faith effort to advise all vendors of the software used to develop this Software of his intention to share thisThe author has made a good faith effort to advise all vendors of the software used to develop this Software of his intention to share thisSoftware with others. Those vendors have neither endorsed nor declined to endorse the contents of this Software.Software with others. Those vendors have neither endorsed nor declined to endorse the contents of this Software.

Nothing in this Software will give you any right, title or interest in or to any ofNothing in this Software will give you any right, title or interest in or to any of Laine’s Laine’s trademarks, trade names, service marks, insignia, trademarks, trade names, service marks, insignia,labels or designs, or any of the same, except a mere privilege and license during its term, to display and use the same according to thelabels or designs, or any of the same, except a mere privilege and license during its term, to display and use the same according to theforegoing limitations.foregoing limitations.

Any and all opinions found in this Software are of the author. The author reserves the right to modify any and all opinions as, if, andAny and all opinions found in this Software are of the author. The author reserves the right to modify any and all opinions as, if, andwhen new information is made available. Factual input, whether supportive and dissenting, is welcome. Your input will receive duewhen new information is made available. Factual input, whether supportive and dissenting, is welcome. Your input will receive dueconsideration and will surely affect the author's future efforts. The author expresses advance appreciation for the time and effort youconsideration and will surely affect the author's future efforts. The author expresses advance appreciation for the time and effort youdevote to your communications.devote to your communications.

This is an agreement between you and the author regarding your use of this Software. You agree by your use or possession of any orThis is an agreement between you and the author regarding your use of this Software. You agree by your use or possession of any orall of this Software to the conditions and limitations of this agreement.all of this Software to the conditions and limitations of this agreement.

This agreement is an integral part of this Software. Failure to include this entire agreement in any and all distributions of this SoftwareThis agreement is an integral part of this Software. Failure to include this entire agreement in any and all distributions of this Softwareshall be a breach of this license agreement, and shall not sever, void, or nullify the meaning or the intention of this agreement.shall be a breach of this license agreement, and shall not sever, void, or nullify the meaning or the intention of this agreement.

This Agreement will be governed by the laws of the State of Texas. This Agreement may only by modified by a license addendumThis Agreement will be governed by the laws of the State of Texas. This Agreement may only by modified by a license addendumwhich accompanies this license or by a written document which has been signed by both you and Laine.which accompanies this license or by a written document which has been signed by both you and Laine.

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© 2000Gravity Segregated (Input )

The gravity-segregated methodology and the Thomas pseudo-Kr methodology share mostof the same input data. See both input-data slides in order to see all the input data.

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© 2000Gravity Segregated (Output )

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© 2000Thomas (Input)

The gravity-segregated methodology and the Thomas pseudo-Kr methodology share mostof the same input data. See both input-data slides in order to see all the input data.

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© 2000Thomas (Output)

Thomas recommends starting with straight-line pseudo-relative permeability curves.

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© 2000Hearn High-Rate, Low-API (General )

High fluid velocity and low oAPI discourage gravity-segregation.

Hearn concluded the layer with the highest K /φ /(1-Swc -Sor) dominates horizontal flow.

Layer sorting is the only difference between Hearn’s low-rate and high-rate methods.

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© 2000Hearn High-Rate, Low-API (Porosity)

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© 2000Hearn High-Rate, Low-API (Thickness )

Layer 1st column 12th column

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© 2000Hearn High-Rate, Low-API (K )


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© 2000Hearn High-Rate, Low-API (Sor, Swc, Krow, Krw, & Sat Adjust)

1st column 12th column

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© 2000Hearn High-Rate, Low-API (Verify Layer Sort )


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© 2000Hearn High-Rate, Low-API (11th Layer Krow and Krw )

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© 2000Hearn High-Rate, Low-API (12th Layer Krog and Krg)

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© 2000Hearn Low-Rate, High-API (UN-Sorted Layers )

Low fluid velocity and high oAPI both favor gravity-segregation.

Hearn concluded there is no need to sort the layers because the dominant fluid flow is up.

Layer sorting is the only difference between Hearn’s low-rate and high-rate methods.

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© 2000Original Endpoints - Krow and Krw

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© 2000Summary and Conclusions

Spreadsheets greatly improve personal productivity when calculation staticpseudo-relative permeability curves.

The author’s experience indicates that ease of adjusting Corey curvaturescombined with the ease of changing endpoints is an important productivity issuewhen upscaling (to coarse grids from fine grids.)

These same spreadsheets are great productivity tools during the fine-tuningprocess that seems to be required for all fine-grid-to-coarse-grid upscalingsimulations.

The author’s experience also suggests that none of the available predictionmethods consistently provides an automatic, high-quality 1st-run match with fine-grid simulation results using laboratory Kr curves. This applies to both static anddynamic pseudo-relative permeability curves.

Pseudo-capillary pressure curves can be calculated (Corey).

It is technically possible to use spreadsheets to predict dynamic pseudo curves;however, this effectively requires customizing spreadsheets to accept intermediateflow and saturation data from specific reservoir simulators. It appears to be farmore productive to use commercial software (e.g., Schlumberger’s PSEUDO) tocalculate dynamic pseudo curves.

to be used in any predicting pseudo-relative permeability ... · pseudo-relative permeability...

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