## Permeability Estimation Using Pulsed Neutron Logging

### Introduction

Traditional methods of well logging allow to assess the main reservoir properties: porosity factor and permeability factor.

Porosity factor describes total volume of pores and as a rule is defined by methods of gamma-gamma density logging, neutron logging and acoustic logging– so-called porosity methods. One of the above-mentioned methods or their combination are widely used in various geological and technical conditions within limits of solving a system of equations. Method of self-spontaneous polarization has been historically widely used in conditions of terrigenous reservoirs of West Siberia for porosity assessment. However currently technical and methodological provision of gamma-gamma density log tools has assured the leading position for gamma-gamma density log method.

Permeability describes capability of the rock to pass fluid through it in case of pressure differential. It is not possible to directly measure permeability with routine methods of well logging, because it is controlled not only by porosity, but also by structure of pore spaces, which includes level of cementing and size of grains, level of tortuosity and communication of filtration channels, etc. Therefore commonly used practice of permeability assessment with use of porosity has high level of uncertainty. Currently empiric correlations are often applied to improve forecast and actual permeability data.

The only widely applied special method of well logging allowing to assess permeability is nuclear magnetic resonanse log in strong field (NMR). Such feature of the method made it indispensable and so required, particularly in exploration drilling. The model of Timur-Coates with use of measured free fluid porosity is successfully applied for permeability assessment. Obviously, for better correlation it is required to perform calibration by core, but the result is significantly better than with use of traditional approach.

Similar approach is suggested for application of pulsed neutron capture log technology: assess permeability through free fluid porosity.

At the first stages of field development in West Siberia some attempts were made to use pulsed neutron capture log for assessment of current oil saturation. However in conditions of formation water low salinity, oil and water are not contrasting by measured parameter of pulsed neutron capture log. Salinity of formation waters in Salym group of fields comprises 12-17 g/l, which restricts applicability of pulsed neutron capture log for assessment of oil saturation. In this relation the most commonly used is method of spectrometric pulsed neutron capture log, more known as C/О logging. On the other hand, low salinity of formation water is a favorable factor for exclusion of saturation nature effect when solving the task of assessment of reservoir permeability in oil fields.

This work describes the main methodological pre-requisitions for application of pulsed neutron capture log for permeability assessment. It contains examples of comparison with traditional methods of well logging, nuclear magnetic log, and also core data in wells of Cherkashinskaya suite in Salym group of fields in West Siberia.

### Goal setting

Permeability is an important filtration parameter of geological rock. Correctly determined permeability of formations allows to directly define well productivity index. For this purpose, vertically integrated products of fluid permeability multiplied by efficient thickness of reservoirs, also known Kh fluid parameters are determined in intervals of perforations. After that well productivity factors are determined by Darcy equation. Then the received forecast values are used by process engineers in order to select a pump and perforating strategy. Moreover, reliable information on permeability is used as a reliable basis for building hydrodynamic model.

As mentioned above, commonly used approach of permeability (К) estimation through porosity (φ) gives significant inaccuracies. Correlation factor К = f (φ) has low values, so up to two-three permeability decades may correspond to one porocity value (Fig.1).

*Fig.1. General dependency of permeability (K) upon porosity (φ)*

Due to this reason SPD needed other more reliable approach to calculation of permeability factor. From all diversity of empiric models of K preference was given to Timur model.

Thus, the following equation was received as a result of re-setting of Timur model to actual data:

(1)where φe = φ(1-SWirr), φe is free fluid porosity, SWirr is irreducible water saturation received in centrifuge.

Analysis of sensitivity of various methods and their combinations was performed in order to determine SW_{irr}. On the basis of built correlations with core material the most preferable parameter was water content of solid phase. This parameter was determined as difference of total water content (neutron porosity) by neutron log and porosity factor by gamma-gamma.

Built model allowed to significantly improve reliability of permeability factor forecast compared to dependency Permeability factor = f (porosity factor) and improve correlation factor from 0.62 to 0.78 [1].

At the same time in SPD practice there is experience of using nuclear magnetic log for assessment of permeability. This method also solves a number of tasks: assessment of porosity, residual water, determination of structure and size of pores, nature, level of saturation of reservoirs, viscosity of hydrocarbons, etc. The advantage of this method is insensitivity to mineral composition of rocks, at the same time due to small depth of the study, poor state of the wellbore may introduce significant distortions.

Various empiric models of permeability are applied for forecast purposes. All of them are not universal and require adjustment on core [7]. After adjustment of dependency K=f(φ(NMR))) on reservoirs of Salym group of fields and comparison with core material, correlation factor of permeability factor - porosity factor comprised 0.86, which obviously makes this method number one for solving tasks associated with determination of permeability and porosity.

At the same time, taking into account cost of implementation of nuclear magnetic logging and sufficiently robust correlation of Timur model, method of nuclear magnetic logging did not achieve common application in SPD for solving the task of determination of permeability and porosity.

At the same time there arose a necessity to assess permeability without application of chemical sources and highly expensive nuclear magnetic logging. It is associated with start of project for drilling infill pattern using sidetracks with horizontal ends in Salym group of fields.

### Theoretical pre-requisitions of pulsed neutron capture log application for permeability forecast

For the main tool of pulsed neutron capture log we used PILK^{TM} tool with cable and independent design options [5]. These instruments are designed for surveys in open and cased wells by method of pulsed neutron capture log by heat neutrons. The tool contains gas-filled generator tube capable to irradiate neutrons at frequency up to 20 kHz. At two distances from pulsed neutron source, detectors of neutrons register speed of accounting heat neutrons during neutron pulse and temporary specters of decrease in the flow of heat neutrons after completion of neutron pulse. As a result of primary treatment and introduction of corrections for technical specifications of survey implementation it is possible to calculate macro cross-section of neutron trapping and water content (neutron porosity). Gamma-log channel is used for the purpose of reference to geological cross-section.

Pre-requisition for application of pulsed neutron capture method for lithological tasks is high differentiation between absorption macro cross-section value and neutron porosity depending upon reservoir properties of cross-section [8,9]. Thus, in conditions of terrigenous reservoirs in West Siberia (low salinity of formation water and similarity of rock skeletons in shales and sandstones), the method indicators are mainly defined by clayiness and porosity.

Under condition that hydrogen is only in composition of connate water and mobile fluid, by measuring total water content in the rock and macro cross-section of absorption of heat neutrons in it is possible to calculate free fluid porosity of the reservoir [2].

The essence of methodological provision is decomposition of rock model into components and solving a system of equations. Thus, for conditions of terrigenous reservoir, rock model can be presented in the following form:

##### **1 = Vma + Vsh + φe, (2)**

where Vma – volume of rock skeleton taking into account its connate water; Vsh – volume of shales taking into account their connate water; φ_{e} – free fluid porosity.

The following parameters for rock skeleton: TNPHma – porosity by pulsed neutron capture log, Σma – capture cross-section. For shales respectively we know porosity TNPHsh and cross-section Σsh, for fluid – Σw. An assumption is made that in the reservoir correlation between volumes of shales and connate (physically and chemically) water remains constant and is equal to such correlation in formation of shales. Similar assumption is made in relation to parameters of rock skeleton. Then it is possible to compile the following formulas:

##### **Σa = Σma ×Vma + Σsh ×Vsh + Σw × φ**_{e}**, (3) **

** TNPH = TNPHma ×Vma + Vsh ×TNPHsh + φ**_{e}** (4)**

where: Σa – measured value of rock capture cross-section by pulsed neutron capture log; TNPH – measured value of porosity by pulsed neutron capture log (water content).

System of equations (3) and (4) supplemented with balance equation (2) provides for calculation of free fluid porosity

##### **φ**_{e}** = {Σa – Σsh – (Σma – Σsh) ×(TNPH – TNPHsh)/( TNPHma – TNPHsh)}/ {Σw – Σsh – (Σma – Σsh) ×(1 – TNPHsh)/( TNPHma –**

##### **-TNPHsh} (5)**

### Practical results of studies

In order to solve the task of assessment of permeability and porosity without chemical sources in Salym group of oil fields we reviewed practical results of pulsed neutron capture log on example of three wells: core directional cased well, production directional perforated well and sidetrack with horizontal end.

### Core well (well 1)

At the first stage it was required to perform verification of suggested methodology. For that purpose we performed surveys in cased wellbore with previously performed standard and special complexes of geophysical surveys and core-taking. The main target of surveys is represented with non-perforated intervals of oil-saturated and water-saturated sandstones. Core covers the entire interval of survey target with high density per unit of cross-section length (on average 8 samples per meter).

The first three tracks present data of standard well logging, then tracks 4 and 5 present registered data of pulsed neutron capture log, other tracks present results of comparison of permeability and porosity assessments by core, routine and special methods of well logging (Fig.2).

*Fig. 2. Comparison of data of well logging, core and special methods of well logging.*

Permeability by routine method is calculated in two ways: standard approach with use of link К = f (φ) (Fig.1) and on the basis of Timur model described above. Poor correlation of permeability is noted in case of standard approach application, error of one order is tracked in top part of the formation. At the same time SPD basic methodology for assessment of permeability shows reliable convergence (Track 7).

Track 8 reflects permeability curves received by data of nuclear magnetic log. Two permeability models are used: Timur and SDR (Shlumberger-Doll Research). Both of them show satisfactory convergence with core data, however there is significant flatness of curves associated with different vertical resolution of the tool and core data.

Free fluid porosity φ_{e} by pulsed neutron capture log is calculated in compliance with the above methodology with use of two key beds: sandstone and shales. Formation water cross-section is accepted as 27 c.u. based on salinity of formation water [6] and recommendations [4]. Good convergence with core data and nuclear magnetic log (track 6) is noted. Free fluid porosity by core was defined by the expression φ_{e} = φ(1-SW_{irr}).

Then we performed calculation of permeability with use of modified formula of Timur-Coats on the basis of generalization of core materials of Jurassic and Cretaceous depositions in West Siberia. This approach is the basic and applicable in cases when core information is not available. Good correlation of data with permeability by core is noted (track 9).

However the best correlation (R=0.96) is achieved with use of the link К = f (φ_{e}) for this field (Fig. 3),

*Fig.3. Generalized dependency of permeability K upon efficient porosity φ _{e} *

Further, with use of the link SW_{irr}= f(φ_{e}) (Fig. 4), SW_{irr}=100EXP(-0.08) we calculated water retaining capacity factor (track 10), which also allowed to calculate total porosity (track 11).

*Fig.4. Generalized dependency of irreducible water saturation SWirr upon efficient porosity*

In general, comparing permeability curves received by different methods it is worth noting the best vertical resolution of data received by data of gamma-gamma density log, less preferable is pulsed neutron capture log, neutron magnetic log has the worst resolution.

Thus, received prospective results of permeability and porosity assessment by data of pulsed neutron capture log allowed to continue further studies of this method application.

### Directional well (well 2)

The second well is represented with similar depositions, however it is perforated in the interval of the studied target. The well has been in operation for a long time, after which a decision was made to perform repeated frac job. Pulsed neutron capture log and cross-dipole log was performed in order to assess height of fracture lifting before and after the frac job by resources of OJSC KogalymNefteGeofizika. Marked proppant containing elements with abnormal capture cross-section was used to improve contrast of impact on pulsed neutron capture log indicators.

Background pulsed neutron capture log before frac job was considered in order to evaluate opportunities of permeability assessment in perforated intervals. For that purpose permeability and porosity were calculated similarly and comparison with data of routing logging and SPD basic methodology for calculation of permeability was performed (Fig. 5). Good correlation of permeability factor by pulsed neutron capture log and SPD methodology is noted, however there are differences in top two intervals of perforations (red curve in track 7). Obviously well kill fluid - KCl brine with density of 1.02 g/cm3 resulted in change of free fluid capture cross-section in the zone of surveys by the method. Such effect of pulsed neutron capture log is applied during surveys by the technology “logging – injection – logging” in order to identify producing intervals, leaks, cross flows, and also for analysis of depletion of reserves and assessment of displacement factor [3].

*Fig. 5. Comparison of these routine methods and pulsed neutron capture log in perforated intervals.*

In order to check kill fluid injection directly into intervals of permeability factor difference by pulsed neutron capture log and basic model we analyzed production logging tool (PLT) by Y-tool technology with flow initiation using a pump (Fig.5 track 9, 10).

By well logging data the main fluid flow comes from top interval of perforations, and also top of middle interval of perforations, work of lower interval of perforations is not observed. Intervals of cross-flows are not identified. Thus, PLT confirms suggestion on presence of kill fluid in top two intervals of perforations.

In order to exclude impact of kill fluid, we introduced correction into pulsed neutron capture log data based on density and type of solution. In the assumption that all free fluid porosity is filled with water different from formation water by salinity, correction in Σa was calculated as free fluid porosity factor multiplied by difference of kill fluid and formation water capture cross-section. After introduction of correction into pulsed neutron capture log, results of permeability and porosity assessment became closer to results of routine methods (Fig. 5, pink curve in track 7).

### Horizontal sidetrack well (well 3)

Eventually, having confirmed reliability of pulsed neutron capture log for assessment of porosity and permeability of terrigenous reservoirs in Salym group of fields, we performed logging in sidetrack with horizontal track. In this case the tool was conveyed on drill pipe with record in independent memory. Gamma-gamma logging tools and neutron logging tools were not used (Fig. 6).

By results of surveys in well 3 using gamma log, induction log and pulsed neutron capture log complex, SPD subsurface petrophysical service made a decision to run a liner and completion system, and also obtained valuable information on permeability and porosity in penetrated reservoirs.

*Fig. 6. Assessment of permeability and porosity by pulsed neutron capture log in sidetrack with horizontal end.*

### Conclusions

The following key conclusions were formulated as a result of performed surveys, on the basis of available data and in relation to the target of surveys:

- Low level of information of standard approach to permeability assessment by the link К = f (φ) was demonstrated again;
- Application of pulsed neutron capture log allows to assess key permeability and porosity parameters in reservoirs of terrigenous depositions in oil fields. Benchmarking with data by core, nuclear magnetic log and adapted Timur model shows high level of information of pulsed neutron capture log method;
- The link K = f (φ
_{e}) is sufficiently strong, which allows to directly calculate permeability. In case of lack of statistically sufficient core material it is acceptable to use empiric modified model of Timur-Coats by pulsed neutron capture log data; - During implementation of pulsed neutron capture logging in intervals of perforations there are distortions of indicators associated with impact of kill fluid (its different salinity compared to formation water). Knowledge of producing or accepting intervals and kill fluid salinity allows to reduce this factor;
- Opposite to pulsed neutron capture logging tools with vacuum generator tube, the applied tools are capable to simultaneously operate in two modes and irradiate neutrons at high frequency. This allows to perform simultaneous quality measurements of not only macro cross-section of neutron capture, but also water content. The use of neutron generators reduces risks of accidents caused by sticking and loss of tools in the well.

Thus, suggested methodology for qualitative assessment of permeability and porosity without application of chemical source can be successfully applied in terrigenous reservoirs.

### Acknowledgement

The authors would like to thank management of Salym Petroleum Development N.V. Company for permission and support of this article publication.

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Авторы: Rinat Isyangulov, OJSC “Kogalymneftgeofizika”, Maxim Podberezhny, Salym Petroleum Development N.V.

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