Chicheng Xu

Pore System Characterization and Petrophysical Rock Classification Using a Bimodal Gaussian Density Function

This paper introduces a bimodal Gaussian density function to characterize pore-size distributions in terms of incremental pore volume versus logarithmic pore-throat radius. An inverse problem is formulated and solved to reconstruct mercury injection capillary pressure curves by enforcing a bimodal Gaussian pore-size distribution. The bimodal Gaussian model generates six petrophysically interpretable attributes which provide a quantitative basis for petrophysical modeling and rock typing. Correlations between these attributes and their associated petrophysical properties are investigated to verify interpretations. In the field case, the correlation coefficient (R2) between absolute permeability, end-point gas relative permeability and the mean value of large pore-throat size mode are 0.93 and 0.715, respectively. Correlation (R2=0.613) is also observed between critical water saturation and pore volume connected by small pore-throat sizes. Petrophysical modeling based on the bimodal Gaussian pore-size distribution with sufficient core data calibration predicts static and dynamic petrophysical properties that are in agreement with laboratory core measurements. The quantitative pore-system description underlies a new petrophysical rock typing method that combines all relevant pore-system attributes. Verification of the method was performed with field data from two key wells in the Hugoton carbonate gas field, Kansas.

Rock Classification in Carbonate Reservoirs based on Static and Dynamic Petrophysical Properties Estimated from Conventional Well Logs

Rock typing in carbonate reservoirs is challenging due to high spatial heterogeneity and complex pore structure. In extreme cases, conventional rock typing methods such as Lev erett’s J-function, Winland’s R35, and flow zone indicator are inadequate to capture the heterogeneity and complexity of carb onate petrofacies. Furthermore, these methods are b s d on core measurements, hence are not applicable to uncored r es rvoir zones. This paper introduces a new method for petrophysica l rock classification in carbonate reservoirs that onors multiple well logs and emphasizes the signature of mud-filtrate i nvasion. The method classifies rocks based on both static and dynamic petrophysical properties. An inversion-based algori thm is implemented to simultaneously estimate miner alogy, porosity, and water saturation from well logs. We numerically sim ulate the process of mud-filtrate invasion in each rock type and quantify the corresponding effects on nuclear and resistivit y measurements to derive invasion-induced well-log attributes, which are subsequently integrated into the rock classificatio n. Under favorable conditions, the interpretation m ethod advanced in this paper can distinguish bimodal from uni-modal behavi or in saturation-dependent capillary pressure other wis only possible with special core analysis. We successfully apply the new method to a mixed cla sti -carbonate sequence in the Hugoton gas field, K ansas. Rock types derived with the new method are in good agreement w ith lithofacies described from core samples. The di stribution of permeability and saturation estimated from well-log derived rock types agrees with routine core measur ements, with the corresponding uncertainty significantly reduced whe n compared to results obtained with conventional po rosity-permeability correlations.

Petrophysical rock classification in the Cotton Valley tight-gas sandstone reservoir with a clustering pore-system orthogonality matrix

Petrophysical rock classification is an important component of the interpretation of core data and well logs acquired in complex reservoirs. Tight-gas sandstones exhibit large variability in all petrophysical properties due to complex pore topology resulting from diagenesis. Conventional methods that rely dominantly on hydraulic radius to classify and rank reservoir rocks are prone to rock misclassification at the low-porosity and lowpermeability end of the spectrum. We introduce a bimodal Gaussian density function to quantify complex pore systems in terms of pore volume, major pore-throat radii, and pore-throat radius uniformity. We define petrophysical dissimilarity (referred to as orthogonality) between two different pore systems by invoking the classic “bundle of capillary tubes” model and subsequently classify rocks by clustering an orthogonality matrix constructed with all available mercury injection capillary pressure data. The new method combines several rock textural attributes including porosity, pore-throat radius, and tortuosity for ranking reservoir rock quality in terms of flow capacity. We verify the new rock classification method with field data acquired in the Cotton Valley tight-gas sandstone reservoir located in the East Texas basin. The field case shows that the new method consistently identifies and ranks rock classes in various petrophysical data domains, including porositypermeability trends, pore-size distribution, mercury injection capillary pressure, and NMR transverse relaxation time (T2) spectra. Relative permeability curves, which are difficult to measure in the laboratory for tight rocks, are quantified with Corey-Burdine’s model using the bimodal Gaussian pore-size distribution and are validated with core data.

Interpretation of hydraulic rock types with resistivity logs in Tertiary deepwater turbidite reservoirs: Pore-scale modeling verified with field observations in the Gulf of Mexico, USA

Well-log-based hydraulic rock typing is critical in deepwater reservoir description and modeling. Resistivity logs are often used for hydraulic rock typing due to their high sensitivity to rock textural attributes such as porosity and tortuosity. However, resistivity logs measured at different water saturation conditions need to be cautiously used for hydraulic rock typing because, by definition, the properties of hydraulic rock types (HRT) are independent of fluid saturation. We compare theoretical models of electrical and hydraulic conductivity of clastic rocks exhibiting different pore-size distributions and originating from different sedimentary grain sizes. When rocks exhibiting similar porosity ranges are fully saturated with high-salinity water, hydraulic conductivity is dominantly controlled by characteristic pore size while electrical conductivity is only marginally affected by the characteristic pore size. As a result, rock types with similar porosity but different characteristic pore sizes cannot be effectively differentiated with resistivity logs in a water-bearing zone. In a hydrocarbon-bearing zone at irreducible water saturation, capillary pressure gives rise to specific desaturation behaviors in different rock types during hydrocarbon migration, thereby causing differentiable resistivity log attributes that are suitable for classifying HRT. Core data and well logs acquired from a deep-drilling exploration well penetrating Tertiary turbidite oil reservoirs in the Gulf of Mexico, verify that inclusion of resistivity logs in the rock classification workflow can significantly improve the accuracy of hydraulic rock typing in zones at irreducible water saturation. Classification results exhibit a good agreement with those obtained from nuclear magnetic resonance logs, but have relatively lower vertical resolution. The detected and ranked HRT exhibit different grain-size distributions, which provide useful information for sedimentary facies analysis.

Quantifying fluid distribution and phase connectivity with a simple 3D cubic pore network model constrained by NMR and MICP data

A computer algorithm is implemented to construct 3D cubic pore networks that simultaneously honor nuclear magnetic resonance (NMR) and mercury injection capillary pressure (MICP) measurements on core samples. The algorithm uses discretized pore-body size distributions from NMR and pore-throat size versus incremental pore-volume fraction information from MICP as initial inputs. Both pore-throat radius distribution and body-throat correlation are iteratively refined to match percolation-simulated primary drainage capillary pressure with MICP data. It outputs a pore-throat radius distribution which is not directly measurable with either NMR or MICP. In addition, quasi-static fluid distribution and single-phase connectivity are quantified at each capillary pressure stage. NMR measurements on desaturating core samples are simulated from the quantitative fluid distribution in a gas-displacing-water drainage process and are verified with laboratory measurements. We invoke effective medium theory to quantify the single-phase connectivity in two-phase flow by simulating percolation in equivalent sub-pore-networks that consider the remaining fluid phase as solid cementation. Primary drainage relative permeability curves quantified from fluid distribution and phase connectivity show petrophysical consistency after applying a hydrated-water saturation correction. Core measurements of tight-gas sandstone samples from the Cotton Valley formation, East Texas, are used to verify the new algorithm. Inverse estimation of pore-network attributes from NMR and MICP data.Quantification of fluid distribution and phase connectivity in a cubic pore-network.Relative permeability modeling for tight-gas sandstone samples.

Connate Water Saturation - Irreducible or Not: The Key to Reliable Hydraulic Rock Typing in Reservoirs Straddling Multiple Capillary Windows

Irreducible water saturation is an important attribute to quantify reservoir petrophysical quality in terms of flow capacity. High in-situ capillary pressure causes connate water saturation in reservoir rocks to approach the irreducible stage, thereby providing a direct link between electrical and hydraulic conductivities. A new hydraulic rock typing method is developed by relating resistivity-saturation equations with core-calibrated Timur-Tixier’s permeability model, both of which are expressions of porosity and irreducible water saturation in this special reservoir context. Petrophysical quantities equivalent to Leverett’s reservoir quality index (RQI) and Amaefule’s flow zone indicator (FZI) are derived from petrophysical analysis based solely on conventional logs, including gamma ray, neutron porosity, bulk density, and resistivity. We test the new method on a deltaic gas reservoir from offshore Trinidad (Columbus Basin). In the field case, rock typing accuracy based on the new rock typing method is improved by 12% in terms of their contingency coefficients with corebased hydraulic rock types. We also discuss the limitations of the new method in detecting and ranking reservoir rock types in complex contexts of reservoir saturation-height. A new concept, referred to as capillary window, is developed to categorize the applicability of the new rock typing method. At extremely high capillary pressure, irreducible water saturation of different rock types is shown to have significant overlapping, thereby introducing large uncertainty in rock typing. Across capillary transition zones, methods to correct for the presence of free water are necessary to extend the new rock typing method to multiple wells penetrating multiple capillary windows. In the aquifer window, the new method for rock classification is not practical because of the absence of capillary pressure. One important conclusion is that rock typing based on water saturation needs to be exercised with caution in different capillary windows to honor the reservoir’s saturation-height behavior.

Bayesian rock classification and petrophysical uncertainty characterization with fast well-log forward modeling in thin-bed reservoirs

ABSTRACTRock typing is critical in deepwater reservoir characterization to construct stratigraphic models populated with static and dynamic petrophysical properties. Rock typing based on multiple well logs is subject to large uncertainty in thinly bedded reservoirs because true physical properties cannot be resolved by low-resolution logging tools due to shoulder-bed effects. We have introduced a new Bayesian approach that inherently adopts the scientific method of iterative hypothesis testing to perform rock typing by simultaneously honoring different logging-tool physics in a multilayered earth model. In addition to estimating the vertical distribution of rock types with maximum likelihood, the Bayesian method quantifies the uncertainty of rock types and the associated petrophysical properties layer by layer. Bayesian rock classification is performed with a fast sampling technique based on the Markov-chain Monte Carlo method, thereby enabling an efficient search of rock types to obtain the final results...