Application of NMR Logging for Characterizing Movable and Immovable Fractions of Viscose Oils in Kazakhstan Heavy Oil Field

Size: px
Start display at page:

Download "Application of NMR Logging for Characterizing Movable and Immovable Fractions of Viscose Oils in Kazakhstan Heavy Oil Field"

Transcription

1 SPWLA 47 th Annual Logging Symposium, June 4-7, 006 Application of NMR Logging for Characterizing Movable and Immovable Fractions of Viscose Oils in Kazahstan Heavy Oil Field Chen, S., Munholm, M.S., Shao, W., Jumagaziyev, D., and Begova, N. Baer Atlas and Karazhanbasmunai Copyright 006, held jointly by the Society of Petrophysicists and Well Log Analysts (SPWLA) and the submitting authors. his paper was prepared for presentation at the SPWLA 47 th Annual Logging Symposium held in Veracruz, Mexico, June 4-7, 006. ABSRAC Estimating both the producible and total heavy oil volumes is always a challenging issue with conventional logs and is particularly difficult for shaly sand reservoirs having variable clay content and mineralogy. NMR-based analysis can potentially overcome the difficulty but it also needs to address its own challenges regarding the poor sensitivity of diffusion and the overlapping between heavy oil and bound water. We successfully integrated NMR and conventional logs to interpret heavy oil reservoirs in a pilot study involving nine wells. We demonstrate that the integrated approach overcomes the shortcomings of the individual techniques, and is particularly applicable to the Buzachi heavy oil fields. INRODUCION A significant amount of oil reserves in Buzachi Peninsula in Kazahstan are heavy or viscose oils. In a shallow heavy-oil reservoir, the in-situ viscosity reaches or exceeds 400 cp; yet commercial quantity of oils is produced by spontaneous flow, even at low reservoir temperatures and pressures. he challenge is to discern the flowable heavy oil zones from the immobile zones and quantify the movable oil. Conventional resistivity-based analysis at best provides the quantity (saturation) but not the quality (viscosity and viscosity distribution) of heavy oil. Moreover, the varying clay properties and water salinity increasingly cause the uncertainty of conventional saturation models. hus, NMR is added to the logging program. he multifrequency MREX SM tool is capable of collecting multiple echo trains in a single logging pass (Chen et al, 003). he NMR pilot study in this oil field includes nine heavy oil wells; most of them were logged with Poroperm + Heavy Oil sequence (Sun et al, 006). Quantification of permeability, oil saturation and viscosity are the main objectives for acquiring NMR logs. he shallow reservoir mainly consists of unconsolidated to poorly consolidated sands with significant and variable amounts of clays. he heavy oil distribution overlaps with the CBW and BVI distributions, maing the quantification of irreducible water and heavy oil difficult and subsequently affecting the permeability estimation. hus, the primary issue is to quantify the oil saturation. We used two approaches to interpret the NMR log data. In the first approach, we used the SIME (Sheng et al., 004) processing method, which is a fluids and formation forward-modeling-based inversion method that simultaneously processes all echo trains. o reduce the uncertainty arising from the insensitivity of the diffusion and relaxation time between CBW and heavy oil, we used standard open-hole shale volume estimation such as that based on gamma ray (GR) to quantify the most viscose component of the heavy oil, which is most liely the immobile part, while the movable oil estimated from SIME is not constrained by GR. In the second approach, we applied D NMR inversion to visually separate heavy oil from CBW and BVI. When non-nmr based CBW constraint is needed, the constraint is built into the D inversion process. Consistent results are obtained from the SIME and D NMR interpretations. Furthermore, permeability is estimated based on SIME results, excluding the heavy oil volume from BVI and CBW. We completed our petrophysical analysis by integrating NMR-based saturation analysis with our conventional, resistivitybased method. Moreover, with D NMR, we can truly observe the viscosity variations with depth and the oil constitutional changes from and diffusivity information without the assistance of other logs. he comprehensive study was first conducted on one well. he procedure was then applied to all other wells in the same field without requiring further modification of the interpretation models. NMR LOGGING ECHNIQUE FOR HEAVY OIL DEECION Special Data Acquisition Features for Heavy Oils he mechanism of relaxation decay of fluids in porous roc can be expressed as the collective contributions of the bul, surface, and diffusion-induced relaxation rates,

2 SPWLA 47 th Annual Logging Symposium, June 4-7, 006 = B = B + S ρs + + V + D ( γ G E) he surface relaxation term, ρ S V, originates from the fluid-roc surface molecular interaction and is significant only for wetting fluids. he combined bul and surface relaxation rates are often called the intrinsic relaxation rate, / int, i.e., int B S D () = +, () because both are the intrinsic properties of fluid and formation, rather than controllable by experiments. hus, for non-wetting phase,, and int nw B S. (3) Equation (3) is also valid for wetting fluid phase when the bul relaxation time is much shorter than the surface relaxation time, B << S. Heavy oils have extremely low relaxation times, and thus Eq. (3) is always valid even though some heavy oil reservoirs may be oil- or mixed-wet. he third term in the right side of Eq. () is the diffusion-induced decay term. It is experimentdependent and can be manipulated to enhance the diffusion effect by monitoring interecho spacing, E, and the magnetic field gradient strength, G. For MREX logging tool, varying operating frequency results in different sensitive volumes, each corresponds to a welldefined magnetic field strength B 0, πf B0 = γ, (4) and a field gradient G = db0 dr. (5) For the MREX tool, the frequency dependence is approximated by.5 G MREX f. (6) Discerning oil and water by NMR logging techniques is based on their apparent relaxation time, intrinsic relaxation time, or diffusivity contrast, or a combination thereof. Both heavy oil and bound water relax quicly, even though the mechanisms of the fast relaxation rate for the two fluids are different. he bul relaxation is dominant for heavy oil and surface relaxation for bound water. Although the diffusivity contrast between the two fluids is profound, it is difficult to detect because any diffusivity-contrast-based technique must first overcome the dominant intrinsic relaxation mechanism. o achieve this, we constructed a PoroPerm + Heavy Oil pulse sequence, which acquires 9 echo trains in one logging pass. Among these echo trains, G varies from about 5 Gauss/cm to nearly 40 Gauss/cm; the E range varies from 0.4ms to 0ms. he practical E upper bound is limited by the intrinsic relaxation time of bound water and heavy oil, thus further increase of E is not desirable. Because of the extremely low diffusivity of heavy oil, the use of a large G E contrast is insufficient to quantify the heavy oil diffusivity but qualitatively trends down the oil signal towards the lower diffusivity range on a D map, thereby departing from the water diffusivity line. In contrast, water has a much larger diffusivity, thus is more sensitive to respond to the G E variation. Although a long E is favored for enhancing the diffusion sensitivity, the rapid decay due to a large G E is detrimental to the overall SNR, because only a few echoes have the signal amplitudes above the noise level. he disadvantage is counteracted in the PoroPerm + Heavy Oil sequence by the following two aspects. First, since the echo train acquired with a larger G E decays much faster, only a small data acquisition window is needed. Consequently, an echo train data acquisition window is designed to be G E dependent with the smallest window for the largest G E echo train. Second, short wait times are used for the large G E echo trains since the rapid relaxing heavy oil and bound water signals do not require a long time to reach full polarization. he time saved by decreasing the echo train window and W is used to increase the number of repetitive measurements of the short echo trains for improving the SNR of the fast decay components. More detailed discussion is described in Sun et al. (006). Introduction to D NMR Processing Method he PoroPerm + Heavy Oil sequence produces multiple echo trains with different wait times (W) and interecho time (E) at up to six frequencies. D NMR maps (Sun et al, 003&006, Hursan et al, 005) were used to view the diffusivity and intrinsic relaxation time simultaneously. he D inversion model,

3 SPWLA 47 th Annual Logging Symposium, June 4-7, 006 M( t, W) R n, j 3 t exp =, N L = M 0, jl, n, j n l n j = = = intn intn 3,3 and t = W exp R ( G E) Dl γ t (7) (,,..., K) E, requires no prior nowledge of fluid types and properties prior to inversion process. he interpretation of fluids is based on the location of signal intensities on the D map. Since different W data are included in the data processing, the inversion model taes into account the longitudinal relaxation time,, transverse relaxation time, int, and diffusivity, D. In order to reduce the size of the inversion matrix, we replaced the parameter with the ratio parameter R = int. Since is the same or slightly greater than int for any type of fluids, R is generally a number greater than and approximately unity. hus, we can discretize R to no more than three bins instead of discretizing the whole range that would involve 0-30 bins. he three D maps corresponding to different R values are summed up to construct a single D map: = [ map( D,, ] map ). (8) ( D, int ) int R j j A D map can be further reconstructed to a D spectrum by summing over different D components: P ( int ) int ). (9) = [ map( D, ] Interpretation with NMR and Conventional Log Although the data acquisition and processing methods described in the previous sections improve the sensitivity of discerning heavy oil and bound water from NMR data alone, there are circumstances where quantitative separation of heavy oil from extremely fast decaying bound water components is difficult. Examples of such situations include () highly conductive boreholes which reduce NMR SNR significantly, and () formation roc minerals which cause high internal gradient and consequently, the smeared intensity distribution on and diffusivity map. When the heavy oil and bound water can not be separated well, integrating NMR log with another log or logs can significantly improve interpretation quantitatively. In such cases, an NMR independent clay bound water estimate can be very useful. he non-nmr CBW estimate should be based on a shale indicator appropriate for the formation. Examples of logs used for shale volume determination include gamma-ray 3 (GR), spontaneous potential (SP), a combination of neutron and density porosity, resistivity, or a combination of the above. he choice is often based on their sensitivity to the particular formation; in this section we use a generic symbol, CBW, to represent the non-nmr-based CBW estimate. In the following, we consider two methods for integration of a non-nmr-based CBW with an NMR log. Heavy oil usually has a broad spectrum. SIME and/or D NMR may have the sensitivity to estimate the longer components of the heavy oil spectrum but may not have the sensitivity for the shortest components in the heavy oil spectrum. herefore, our strategy in the first approach consists of the following steps: () Perform SIME processing with the heavy oil range set to be above the CBW cutoff. hus, all the shortest heavy oil components are lumped to the pseudo-cbw, denoted CBW ': CBW ' =, CBWcoutoff i=, P( ) int, i. (0) he heavy oil volume obtained from SIME inversion contains the lighter components in the crude heavy oil. his light component is denoted as V,. HO L () Compute the difference between CBW and the non-nmr log derived CBW. he over-estimation of NMR-based clay-bound water is part of the heavy oil that overlaps with CBW on the spectrum. V HO, H = CBW ' CBW. () (3) he NMR-based porosity estimate is compared to another porosity estimate, such as a density-based porosity. If φ MREX underestimates porosity compared to density porosity, by more than φ ZDEN the random error margin, the difference represents the extra-viscose components that are not observable by the MREX tool when using E = 0.4ms: VHO, M = φ ZDEN φ MREX () and, thus, should be included in the total heavy oil volume:

4 SPWLA 47 th Annual Logging Symposium, June 4-7, 006 V HO VHO, L + VHO, H + VHO, M =. (3) Obviously, the validity of Eqns. () and () relies on the robustness of the non-nmr log information. Practically, a non-negative constraint is always applied on V HO, H and V HO, M. In the subsequent sections, the above approach is referred to as SIME-based integrated petrophysical analysis. For a reservoir that exhibits significant lithology variations, the second approach, described below, may be more preferable. he second approach uses the non-nmr-based CBW estimate as a constraint built into the inversion process. he detail of the second approach is given in Appendix A. Here, only an outline is described. For notation simplification purposes, a matrix form is used for describing the inversion problem: d = Am, (4) where d is the experimental data, m is the unnown vector, and A is the inversion model matrix. he inversion process is the least squares solution of Eq. (4) with the inclusion of a regularization term that stabilizes the solution Am d + α m = min, (5) Wm subject to () the non-negative constraint, m 0, (6) and the CBW constraint, 0 CBW tor tor mi, j CBW + int < CBW cutoff D> water diffusivity cutoff where the two tolerances, tor and tor, are set by the user and can be field specific and depend on the robustness of CBW. FIELD EXAMPLES In the pilot study in a heavy oil field in the Buzachi Peninsula of Kazahstan, MREX logs data have been acquired in nine wells. he ey objectives for acquiring NMR data in this field are to obtain permeability estimates and to quantify the heavy oil saturations. Knowing that NMR relaxation time or diffusivity estimates correlate with the oil viscosity, we also want to determine whether NMR has the sensitivity to distinguish different grade oils. Since heavy oil overlaps with bound water (capillary bound water 4 (BVI) and clay bound water (CBW)), correctly estimating bound water and permeability requires separating the oil and water volumes first. hus, the essential NMR data analysis is to discern the heavy oil. hese objectives are successfully met by applying the D NMR and the SIME-based integrated petrophysical analysis methods as described in the previous sections. Geology he field was discovered in the 970 s. Production drilling began in 980; since then, thousands of wells have been drilled in the field. he reservoir formations contain unconsolidated sands, poorly-cemented sandstones, and aleurolites interlayered with shale. Overall clay content and mineralogy show large variation over the field with significant amount of chlorite, smectite, hydromica and aolinite. From the many wells drilled in the field, the reservoir rocs are nown for their high variability vertically and laterally, which compromises the reliability of density and neutron-based porosity estimation. For this reason, the mineralogy- and lithology-independent NMR porosity is useful in this field. he crude oil in the field is a low-gor, heavy oil with fluid densities in the range of g/m 3 and viscosities in the range of cp under reservoir conditions. he oil often contains highly resinous components (up to 0 %) but relatively lower amounts of paraffin. Resins in general have short and times, rendering the resins signal particularly challenging to separate from bound water in the NMR data. Furthermore, the non-newtonian fluid nature of resins may cause the resin-rich crude oil not to obey the nown relaxation time-viscosity correlations (Vinegar, 995, Morris, 997, Zhang et al., 998, Chen et al., 004) in which case these nown correlations may not be applicable for characterization or quantification of the oil volume and quality. SIME-Based Integrated Data Analysis In addition to the MREX log, wireline gamma ray, density, neutron, acoustic and resistivity logs were also included in the logging program for these wells. In the initial analysis, a volumetric shaly sand analysis was carried out based on the conventional open hole log data alone, plotted in the first trac of Fig., and the resultant V sh is subsequently integrated with the MREX data. For BVI and CBW estimates, the simple approach of applying cutoff values to the NMR spectrum for separation of the fractional porosities does not wor for

5 SPWLA 47 th Annual Logging Symposium, June 4-7, 006 the heavy-oil reservoir intervals. Shown in rac of Fig. are the standard wellsite MREX deliverables for Well # based on the use of default CBW and capillary bound water cutoff values. Because these standard wellsite deliverables are based on the partition of apparent spectrum which does not separate oil from water, the BVI and CBW volumes are potentially contaminated with heavy oil signals. Consequently, the Coates permeability computed from these BVI and BVM values is not reliable. rac 3 compares the wellsite permeability estimate with two different postprocessing permeability estimates. he wellsite permeability corresponds to the effective permeability for the case that none of the heavy oil can be produced. However, it is much too small for the poorly consolidated, high-porosity sands in the reservoir. Furthermore, the permeability curve derived from the wellsite shows only a wea correlation with the sand volume computed from the conventional shaly sand analysis, suggesting that those are heavy oil-bearing sands. he permeability curve, mared as Perm without V HO,H in rac 3 and derived from the SIME analysis (rac 4), shows much higher permeability in the reservoir sand zone. Since SIME first separates heavy oil from water and then includes the heavy oil volume into BVM such that BVM = MBVMW + V HO, L (7) the SIME-based permeability analysis represents the effective permeability of the reservoir for the case that the lighter components of the heavy oil is movable. In the permeability trac, the third permeability curve corresponds to the situation where both V, and HO H HO L V, should be movable, which is unrealistic for the reservoir situation but would be compatible to the cleaned formation roc absolute permeability. In fact, this permeability estimate is in the same range as the core permeability reported from historical core data and well tests. he details of the SIME analysis and the determination of heavy vs. extra heavy oil volumes are discussed in the subsequent paragraphs. In the post-processing analysis, the V sh is determined based on conventional log analysis (rac ). he reservoir shale properties have been studied extensively in the field in the past. herefore, the variation of the shale properties are well understood and incorporated in the analysis to obtain reliable V sh estimates. However, as all the reservoir sands contain dispersed shale with high variability in clay mineralogy, the electrical effects from clay are challenging to a resistivity-based saturation analysis. Furthermore, uncertainty in saturation exponent and reservoir water salinity also add to the complexity of the saturation analysis for the 5 field as a whole. In that aspect, an independent saturation analysis from NMR is desired for crossvalidation. We applied the SIME-based integrated petrophysical analysis, described in the previous section, to MREX and V sh data. Because there is no porosity underestimation occuring, namely all heavy oil signals are detectable by MREX with E = 0.4ms, only the first two steps of the analysis methods are used. he SIME-based integrated analysis result is shown in rac 4. Except for the vertical resolution difference, the shale intervals of the conventional and NMR data are in general agreement. In the reservoir shaly sand intervals, the field bound water volume (MVBW+MBVI) is much too high. Specifically for clay bound water, which reaches an unrealistic pu for an interval with 5-0% total shale volume at approximately xx6-xx8 m. SIME-based integrated analysis yielded much improvement in the interpretation of the reservoir fluids and has identified much of the apparent MCBW as heavy oil. In rac 4, the oil volumes directly obtained from the SIME without integrating V sh is shown in light green color, representing V,. Extra heavy oil components, HO L shown in dar green color and represented by V HO,H, are obtained from the integrated analysis. he V HO, L oil has a longer relaxation time than that of VHO,H, thus is liely to produce. Note that the relaxation time range of V, oil is consistent with the typical resinous HO L hydrocarbon component. Adding resin to heavy oil helps to produce; therefore, this oil volume is considered to be ultimately producible. he oil associated with V, is not expected to be producible HO H but is part of the total oil-in-place and quantification of this oil volume is important for the construction of an accurate water saturation model. Comparison of SIME and D NMR-Based Analysis In this section we illustrate the results of using the two integrated approaches to obtain the heavy oil and extra heavy oil volumes. Figure shows the result also for Well#. he resistivity logs and SIME-based permeability are shown in the 3 rd trac. he NMR and neutron-density porosities are shown in the 4 th trac. We see MREX porosity is in good agreement with the density porosity in the sand zone. In the shale-rich zones, however, density porosity is incorrect when the sand matrix density value is used. On the other hand, MREX porosity is not affected by the clay densities. Shown in the 5 th and 6 th tracs are the int distributions of water and heavy oil, respectively, derived from

6 SPWLA 47 th Annual Logging Symposium, June 4-7, 006 SIME with the oil range restricted to be above 3 ms. Any heavy oil signals below 3ms are included in the clay bound water and subsequently determined by integration with V sh. Consequently, the SIME-based total oil saturation estimate is shown in the 7 th trac and the volumetrics, including the breadown of V HO,L and V HO,H, are plotted in rac 8. In order to verify the SIME result, D NMR analysis is also performed on Well# and the V sh constraint is applied during the inversion. he D NMR-based volumetrics are plotted in rac 9 and the corresponding D NMR maps are shown in rac 0. With the application of V sh constraints, the D maps show clean distinction between CBW (e.g., xx30) and heavy oil (xx0-8). Moreover, among the heavy oil depths, D NMR is able to distinguish oil that has more of the heaviest components (e.g., xx6-xx7) from oil that contains only small amounts of the heaviest components (e.g., xx3-xx35) and these estimations are in good agreement with SIME-based integrated interpretation (rac 8). he heaviest components are observed at the lowest int end of the heavy oil signal. Note that because D maps occupy more plotting space than D curves, the exact depth that each D map corresponds to should be considered a close approximation. he analysis shows some movable water over the oilfilled sands. Considering that MREX has a depth of investigation of.4-4 inches, that may be due to invasion of the water-based mud in the MREX investigative volume. he resistivity-based saturation analysis of the open hole analysis is based on the deeper reading induction log, which should see less, if any, invasion. Overall, we find that for relatively thic oil sands, the resistivity based Sw is in good agreement with MREX-based BVI, supporting the argument that the movable water seen by MREX is in fact due to invasion. he SIME estimate of movable water and oil corrected through integration with the conventional analysis is considered the best estimate provider of hydrocarbon storage capacity for the reservoir. Qualification of Clay ypes Figure 3 shows a section from Well# of a shaly sand formation with heavy oil intervals separated by shale barriers. If we compare the depth intervals that are dominated by shale, we find some shale intervals over which the density and NMR porosities match very well (depths mared by I) and other intervals over which NMR porosity is significantly higher than density 6 porosity. In the absence of a tool problem, the difference must originate from the variations in clay types with different densities. When the sand matrix density is used to plot the density porosity, clays with higher matrix densities appear to have lower shale porosities. he difference between MREX and density porosities is useful information that may qualitatively reveal the dominant clay types. For shale intervals over which NMR and density porosities agree well (Mared I in Fig. 3), the clay density is close to.65, thus the dominant clay type may be illite. On the other hand, for intervals with NMR and density porosity mismatch, we can estimate the shale matrix density using ρ φ w NMR + ρ sh ( φ NMR ) = ρ w φden + ρ sand ( φden ) where NMR porosity in the shale is considered to be the true porosity and φ den is the apparent density porosity computed by assuming shale matrix density to be the same as the sand matrix density. hus, ρ sand ( φden ) ρ w ( φ NMR φden ) ρ sh = (8) φ NMR For example, the zone mared C has φ 0.8 and φ 0.4, den NMR using ρ.65 and ρ = we obtain sand = w ρ sh =.78, which may indicate that the dominant clay type is chlorite. We intend to further investigate the possibility of using this approach for qualification of clay types in other wells. CONCLUSIONS We developed methodology of integrating conventional logs with NMR logs to improve the heavy oil reservoir quantification. he conventional log-based shale estimate can be integrated in either domain or during the echo train inversion process with SIME or D NMR approaches. We applied the new approaches to heavy oil fields in Buzachi Peninsula in Kazahstan. he integrated analysis and standard open hole volumetric analysis provides reliable irreducible water, movable water, movable hydrocarbon and effective porosity from MREX PoroPerm + Heavy Oil acquisition. Furthermore, we have attempted utilizing the difference between the apparent density porosity and NMR porosity in shale intervals to qualify dominant clay types. ACKNOWLEDGEMENS We than Arpad Mayer, Darcy Dorscher and Ed Kueber of Karazhanbasmunai and Geoff Page, Gabor

7 SPWLA 47 th Annual Logging Symposium, June 4-7, 006 Hursan, Weidong Li, and Jason Chen of Baer Atlas for support, discussions and assistance. We would also lie to than Karazhanbasmunai and Baer Atlas for permission to publish this paper. ABOU HE AUHORS Songhua Chen is a senior staff scientist and project manager for NMR interpretation development at Baer Atlas Houston echnology Center. Prior to joining Baer Atlas in 996, he was a research scientist for 5 years with exas Engineering Experiment Station in College Station, exas, where he wored in the area of NMR and MRI applications to flow in porous media. Songhua earned a BS from Nanjing Institute of echnology in China and a PhD from University of Utah, both in Physics. Mette Munholm is a staff petrophysicist with Baer Atlas in Copenhagen, Denmar, presently with a special focus on NMR geoscience applications. Prior to the Copenhagen assignment, she wored as petrophysicist for Z&S Geology, Stavanger and Baer Atlas, Milan. She holds a BS degree in physics and chemistry and MS and PhD degrees in geophysics from the University of Aarhus, Denmar. Wei Shao is a scientific software engineer for NMR interpretation development at Baer Atlas Houston echnology Center. Wei Shao earned a PhD from the University of South Carolina in applied mathematics. Dossan Jumagaziyev is a senior petrophysical engineer with Baer Atlas in Atau, Kazahstan. Prior to joining Baer Atlas in 00, he wored as GIS analyst for engizchevroil and as senior geologist for Karazhanbasmunai, Kazahstan. He holds a BS degree in oil and gas geology from the Kazah National echnical University of Almaty, Kazahstan. Nina Alesandrovna Begova is the Principal Geologist of Geology & Engineering Department of Karazhanabsmunai JSC, experienced in classic technologies of oil well designing, up-to-date techniques of oil reservoirs development and simulation of HC deposits. She graduated from Gubin Petroleum Institute, Faculty of Geology, Moscow in 979. Her major scientific interests include the integration and application of geological and geophysical data for digital simulation of geological objects and the analysis of subsurface geology and evaluation of current state of deposits using various software pacages. 7 NOMENCLAURES A inversion model matrix B vector for CBW constraint B 0 static field strength B RF field strength CBW Clay bound water CBW Clay bound water estimate from non-nmr log CBW pseudo clay bound water signal which includes rue CBW and overlapping heavy oil Components CBW GR CBW estimate derived from GR D diffusivity e,e Echo amplitude with and without noise included f frequency G RF field gradient strength GR Gamma ray GR sh Gamma ray reading from shale zone GR sd Gamma ray reading from sand zone L echo length, N E E M Echo magnetization amplitude N E number of echoes in an echo train P distribution function R ratio of / int S E Sum of echoes longitudinal relaxation time transverse relaxation time B bul fluid transverse relaxation time cutoff dividing time between BVI and BVM diff extra decay time factor due to diffusion int intrinsic relaxation time surf surface relaxation time E interecho time W wait time W Regularization (stabilizing) matrix V HO Volume of heavy oil V HO,L Volume of lighter components of heavy oil V HO,H Volume of heavier components in heavy oil V HO,M Volume of extra-heavy components of heavy oil that can not be sensed by NMR logging tool α Regularization parameter φ porosity APPENDIX A. Description of the Inversion Problem NMR echo signal amplitudes for fluids in porous media can be expressed by a multi-exponential decay model. he general multi-exponential model can be divided into two categories. he first category assumes no prior nowledge of fluid properties in the subject porous roc, thus the broadest possible ranges of the ey NMR properties, intrinsic relaxation time int, i and diffusivity D, are used in the inversion model. hat is, j

8 SPWLA 47 th Annual Logging Symposium, June 4-7, 006 the model does not tag fluid types, water, oil, or gas, to the protons that contribute to the measured NMR signal. he tas of finding the fluid types and quantities is done in the parameter domain after the parameters are obtained from inversion. An example is D NMR inversion. he second category assumes the fluid types and properties are nown or predictable; therefore, the inversion models included the prior information to reduce the parameter space. SIME is an example of the second category. In this appendix, we limit our discussion to the first category approach. he echo amplitude is d( t, W, E ) = L N M p l= j= i= m q i, j W exp Rl exp ( int, i D + j p int, i ( γ G E ) q ( t ) ) (A) where t = (,,..., K ) E is the time associated with the th echo. MREX PoroPerm + Heavy Oil sequence acquires data with an assortment of wait times W and interecho times E, which may also have different echo train lengths K. Inverting the echo trains described by Eq. (A) yields the signal intensity. For simplicity, m i, j Eq. (A) is often expressed in a linear matrix equation format d = Am, (A) where d is the experimental data and m is the unnown and W p A ijl = exp Rl int, i (A3) ( ) D j γ G Eq exp ( + )( t ) int, i is the matrix element. he direct inversion of this equation is ill-conditioned, thus a regularization term is often used, Am d + α m = min subject to m 0. (A4) Wm In the above expression, the condition m 0 is nown as the non-negative constraint. It means that all molecules must either positively contribute or do not contribute to the total echo signal, but cannot contribute it as a negative amplitude. B. Non-NMR-Based CBW Constraint A non-nmr CBW estimate can be derived from gamma-ray (GR), resistivity, spontaneous potentials (SP) log, neutron and density porosity log, a resistivity log, or a combination of them. For example, we can use GR as the non-nmr CBW estimate. Practically, one can use the GR measured at 00% shale and 00% sand depths, and a porosity log to construct a clay-boundwater curve, CBW : CBW GR sh GR GR GRsd = φ sh. (A5) GR GR sd In this appendix, we use a generic symbol, CBW, to represent the non-nmr-based CBW estimate. Most of the non-nmr-based CBW estimates are based on the mineralogy effects distinctive or weighted more to clays. NMR-derived CBW is based on the strong surface relaxivity, a significant amount of surface water, and the extra-fine particle sizes associated with clay. herefore, directly equating the NMR and non- NMR-based clay estimates sometimes may not be practical. Instead of forcing CBW = CBW, we allow user-defined tolerances in the constraint, 0 CBW tor m tor i, j CBW + int < cbw cutoff D> water diffusivity cutoff (A6) where the two tolerances, tor and tor are set by the user and can be field specific. C. Inversion By combining Eqns. (A4) and (A6), the inversion problem is equivalent to the following minimization problem: Am d subject to m 0 and + α Wm m = min 0 CBW tor m CBW tor. i, j + int < CBW cutoff D> water diffusivity cutoff 8

9 SPWLA 47 th Annual Logging Symposium, June 4-7, 006 o implement the CBW constraint, two new variables, u and v, are introduced so that we can convert the CBW inequality constraint to the following constraints: mi, j + u = CBW + int < CBW cutoff D> water diffusivity cutoff tor, (A7) LIERAURE CIED Chen, S., Beard, D.R., Gillen, M., Fang, S., and Zhang, G., MR Explorer Log Acquisition Methods: Petrophysical Objective-Oriented Approach., paper presented at the 003 SPWLA Annual Symposium and Exhibitions, Galveston, exas. m i, j int < cbw ccbw D> water diffusivity cutoff subject to u 0, v 0. v = CBW tor, (A8) Chen, S., Kwa, H., Zhang, G., Edwards, C., Ren, J., and Chen, J.: Laboratory Investigation of NMR Crude Oils and Mud Filtrates Properties in Ambient and Reservoir Conditions, paper SPE 90533, presented at 004 SPE ACE, Houston, exas, Sept 6-8. he details of the algorithm are documented in Chen et al. (006). Eqns. (A7-A8) can be combined with Eq. (A) to form a new equation A = (A9) m d where d d = cbw, GR + tor (A0) cbwgr tor m m = u, (A) v and A 0 0 A = B 0. (A) B 0 In Eq. (A), B is a vector corresponding to the CBW constraint. Using these notations, Eqns. (A4) and (A6) can be expressed in the following matrix form: d m = A m + α W m min, (A3) with the positive constraints of m, u, v 0. (A4) Chen, S., Shao, W., Fang, S., Munholm, M., and Gillen, M., Method and Apparatus for Characterizing Heavy Oil Components in Petroleum Reservoirs, U.S. patent pending, 006. Fang, S., Chen, S., au, R., Philippe, F., and Georgi, D., Quantification of Hydrocarbon Saturation in Carbonate Formations Using Simultaneous Inversion of Multiple NMR Echo rains, SPE paper 90569, presented at 004 ACE, Houston, X. where Hursan, G., Chen, S., and Murphy, E., New NMR wo-dimensional Inversion of / app vs. app Method for Gas Well Petrophysical Interpretation, Paper GGG presented at 46 th SPWLA Annual Symposium, New Orleans, June 6-9, 005. Morriss, C.E., Freedman, R., Straley, C., Vinegar, H., and utunjian, P.N.: "Hydrocarbon Saturation and Viscosity Estimation from NMR Logging in the Belridge Diatomite," he Log Analyst (997) March- April, Sun, B. and Dunn, K-J., Characterization of Porous Medium Properties Using D NMR, presented at Am. Phys. Soc. 003 Annual March Meeting. Sun, B.Q., Olson, M, Baranowsi, J., Chen, S., Li, W., and Georgi, D., Direct Fluid yping and Quantification of Orinoco Belt Heavy Oil Reservoirs Using D NMR Logs, to be presented in 006 SPWLA Annual Symposium and Exhibition, Veracruz, Mexico, June 4-7, 006. Vinegar, H.: "NMR Fluid Properties," SPWLA Short Course on Nuclear Magnetic Resonance Logging, D.. Georgi (ed.), SPWLA, Paris (995), Section 3. Zhang, Q., Lo, S-W., Hirasai, G.: "Some Exceptions to Default NMR Roc and Fluid Properties," SPWLA 39th Annual Logging Symposium, Keystone, June, (998). 9

10 SPWLA 47 th Annual Logging Symposium, June 4-7, 006 Figure. Comparison of BVI, CBW, and permeability estimates derived from the overall apparent distribution and from SIME based analysis. he latter separates the heavy oil from bound water first, then includes the heavy oil in the movable fluid volume for permeability estimation. he movable water shown in the log is most liely from invaded water-based mud filtrate. 0

11 SPWLA 47 th Annual Logging Symposium, June 4-7, 006 Figure. D NMR and SIME-based integrated interpretation for Well#. rac : GR, SP, Caliper and Bit size. rac : Measured depth in meter. rac 3: Resistivities. Coates permeability. rac 4: Density- Neutron on sandstone matrix. otal and effective MREX porosity. rac 5: fluid distribution for CBW, BVI and BVMW with CBW cutoff at 3.3 ms and cutoff at 33 ms. rac 6: fluid distribution for heavy oil. rac 7: otal water saturation from SIME-based integrated interpretation. rac 8: Fractional porosity for CBW, BVI, moveable water and oil from SIME. Pore volume filled by CBW in brown, BVI in pale blue, moveable water in blue, V HO,L in light green, and V HO,H, in dar green. rac 9: Fractional porosity for CBW, BVI, moveable water and oil from D NMR. Pore volume filled by CBW in brown, BVI in pale blue, moveable water in blue, V HO,L in light green, and V HO,H, in dar green. rac 0: D NMR diffusivity versus maps.

12 SPWLA 47 th Annual Logging Symposium, June 4-7, 006 C C I Figure 3. SIME-based integrated interpretation for Well#. Zones I show good agreement between density and MREX porosity. Zones C and C show higher MREX porosity than apparent density porosity. rac : GR, SP, Caliper and Bit size. rac : Measured depth in meter. rac 3: Resistivities. Coates permeability. rac 4: Density- Neutron on sandstone matrix. otal and effective MREX porosity. rac 5: fluid distribution for CBW, BVI and BVMW with CBW cutoff at 3.3 ms and cutoff at 33 ms. rac 6: fluid distribution for heavy oil. rac 7: otal water saturation from SIME-based integrated interpretation. rac 8: Fractional porosity for CBW, BVI, movable water and oil. Pore volume filled by CBW in brown, BVI in pale blue, movable water in blue, V HO,L in light green, and V HO,H, in dar green. I