Synthetic Fractal Modelling of Heterogeneous and Anisotropic Reservoirs for use in Simulation Studies: Implications on their Hydrocarbon Recovery Prediction

Optimising production from heterogeneous and anisotropic reservoirs challenges the modern hydrocarbon industry because such reservoirs exhibit extreme inter-well variability making them very hard to model. Reasonable reservoir models can be obtained using modern statistical techniques, but all of them rely on significant variability in the reservoir only occurring at a scale at or larger than the inter-well spacing. In this paper we take a different, generic, approach. We have developed a method for constructing realistic synthetic heterogeneous and anisotropic reservoirs which can be made to represent the reservoir under test. The main physical properties of these synthetic reservoirs are distributed fractally. The models are fully controlled and reproducible and can be extended to model multiple facies reservoir types. This paper shows how the models can be constructed and how they have been tested. Varying the fractal dimension and anisotropy factor of each of these physical properties can tell us how sensitive the reservoir is to uncertainties in its heterogeneity and anisotropy as well as how poroperm cross-plot shapes are controlled. Initial reservoir simulation results of the tested models with this approach show that heterogeneity in the reservoir's physical parameters has a little effect on high and moderate porosity and permeability reservoirs. The effect is more pronounced in the models representing tight reservoirs. The production from more heterogeneous reservoirs lasts a little longer, but eventually declines faster. This may be attributed to the fact that water channelling is more significant as heterogeneity increases

Permeability Prediction and Diagenesis in Tight Carbonates Using Machine Learning Techniques

Machine learning techniques have found their way into many problems in geoscience but have not been used significantly in the analysis of tight rocks. We present a case study testing the effectiveness of artificial neural networks and genetic algorithms for the prediction of permeability in tight carbonate rocks. The dataset consists of 130 core plugs from the Portland Formation in southern England, all of which have measurements of Klinkenberg-corrected permeability, helium porosity, characteristic pore throat diameter, and formation resistivity. Permeability has been predicted using genetic algorithms and artificial neural networks, as well as seven conventional ‘benchmark’ models with which the machine learning techniques have been compared. The genetic algorithm technique has provided a new empirical equation that fits the measured permeability better than any of the seven conventional benchmark models. However, the artificial neural network technique provided the best overall prediction method, quantified by the lowest root-mean-square error (RMSE) and highest coefficient of determination value (R2). The lowest RMSE from the conventional permeability equations was from the RGPZ equation, which predicted the test dataset with an RMSE of 0.458, while the highest RMSE came from the Berg equation, with an RMSE of 2.368. By comparison, the RMSE for the genetic algorithm and artificial neural network methods were 0.433 and 0.38, respectively. We attribute the better performance of machine learning techniques over conventional approaches to their enhanced capability to model the connectivity of pore microstructures caused by codependent and competing diagenetic processes. We also provide a qualitative model for the poroperm characteristics of tight carbonate rocks modified by each of eight diagenetic processes. We conclude that, for tight carbonate reservoirs, both machine learning techniques predict permeability more reliably and more accurately than conventional models and may be capable of distinguishing quantitatively between pore microstructures caused by different diagenetic processes

Effects of pore-throat structure on reservoir blockage and wettability alteration during CO2 injection

Injection of CO2 into subsurface reservoirs occurs during Enhanced Oil Recovery (EOR) and also during Carbon Capture and Storage (CCS) operations. During CO2 injection, the efficacy and distribution of fluid flow in sandstone reservoirs is controlled by the pore-throat microstructure of the rock. Furthermore, CO2 injection promotes asphaltene precipitation on the pore surface and can also affect fluid flow in the pore throats, decreasing the permeability and altering reservoir wettability. In this work, miscible and immiscible CO2 flooding experiments under reservoir conditions (up to 70℃, 18 MPa) have been carried out on four samples with very similar permeabilities but different pore-throat structures in order to study the effects of pore-throat microstructure on formation damage. The features of pore-throat structure were evaluated by fractal theory, based on pore size distributions and rate-controlled porosimetry (RCP) mercury intrusion curves. Reservoir rocks with smaller pore throat sizes and more heterogeneous and poorer pore-throat microstructures were found to be more sensitive to asphaltene precipitation, with corresponding 15-20% lower oil recovery and 4-7% greater decreases in permeability than that of rocks with homogeneous and better pore-throat microstructure. However, the water-wettability index of cores with larger and more connected pore-throat microstructures was found to drop by an extra 15-25% than heterogeneous core due to more asphaltene precipitation caused by the larger sweep volume of injected CO2 they consequently experienced, which is a disadvantage for EOR. In addition, immiscible flooding exacerbates the differences from 4-7% to 8-15% in permeability decline of the rocks with different pore-throat structures. Miscible flooding leads to more asphaltenes being precipitated from the crude oil, triggering in average an extra 11% change in wettability in comparison to immiscible flooding

Seismo-electric Conversion in Sandstones and Shales using 2 Different Experimental Approaches, Modelling and Theory

The development of seismo-electric (SE) exploration techniques relies significantly upon being able to understand and quantify the strength of frequency-dependent SE conversion. However, there have been very few SE measurements or modelling carried out. In this paper we present two experimental methods for making such measurements, and examine how the strength of SE conversion depends on frequency, porosity, permeability, and why it is unusual in shales. The first is based on an electromagnetic shaker and can be used in the 1 Hz to 2 kHz frequency range. The second is a piezo-electric water-bath apparatus which can be used in the 1kHz to 500 kHz frequency range. The first apparatus has been tested on samples of Berea sandstone. Both the in-phase and in-quadrature components of the streaming potential coefficient have been measured with an uncertainty of better than ±4%. The experimental measurements show the critical frequency at which the quadrature component is maximal, and the frequency of this component is shown to agree very well with both permeability and grain size. The experimental measurements have been modelled using several different methods. The second apparatus was used to measure SE coupling as a function of porosity and permeability, interpreting the results using a micro-capillary model and current theory. We found a general agreement between the theoretical curves and the test data, indicating that SE conversion is enhanced by increases in porosity over a range of different frequencies. However, SE conversion has a complex relationship with rock permeability, which changes with frequency, and which is more sensitive to changes in the petrophysical properties of low-permeability samples. This observation suggests that seismic conversion may have advantages in characterizing low permeability reservoirs such as tight gas and tight oil reservoirs as well as shale gas reservoirs. We have also carried out SE measurements on Sichuan Basin shales (permeability 1.47 – 107 nD), together with some comparative measurements on sandstones (0.2 – 60 mD). Experimental results show that SE conversion in shales is comparable to that exhibited by sandstones, and is approximately independent of frequency in the seismic frequency range (<1 kHz). Anisotropy which arises from bedding in the shales results in anisotropy in the streaming potential coefficient. Numerical modelling has been used to examine the effects of varying zeta potential, porosity, tortuosity, dimensionless number and permeability. It was found that SE conversion is highly sensitive to changes in porosity, tortuosity and zeta potential in shales. Numerical modelling suggests that the cause of the SE conversion in shales is enhanced zeta potentials caused by clay minerals, which are highly frequency dependent. This is supported by a comparison of our experimental data with numerical modelling as a function of clay mineral composition from XRD measurements. Consequently, the sensitivity of SE coupling to the clay minerals suggests that SE exploration may have potential for the characterization of clay minerals in shale gas and shale oil reservoirs

Seismo-electric conversion in shale: experiment and analytical modelling

The development of seismo-electric exploration techniques relies critically upon the strength of the seismo-electric conversion. However, there have been very few seismo-electric measurements or modelling on shales, despite shales accounting for the majority of unconventional reservoirs. We have carried out seismo-electric measurements on Sichuan Basin shales (permeability 0.00147–0.107 mD), together with some comparative measurements on sandstones (permeability 0.2–60 mD). Experimental results show that the amplitudes of the seismo-electric coupling coefficient in shales are comparable to that exhibited by sandstones, and are approximately independent of frequency in the seismic frequency range (<1 kHz). Numerical modelling has also been used to examine the effects of varying (i) dimensionless number, (ii) porosity, (iii) permeability, (iv) tortuosity and (v) zeta potential on seismo-electric conversion in porous media. It was found that while changes in dimensionless number and permeability seem to have little effect, seismo-electric coupling coefficient is highly sensitive to changes in porosity, tortuosity and zeta potential. Numerical modelling suggests that the origin of the seismo-electric conversion in shales is enhanced zeta potentials caused by clay minerals, which are highly frequency dependent. This is supported by a comparison of our numerical modelling with our experimental data, together with an analysis of seismo-electric conversion as a function of clay mineral composition from XRD measurements. The sensitivity of seismo-electric coupling to the clay minerals suggests that seismo-electric exploration may have potential for the characterization of clay minerals in shale gas and shale oil reservoirs

Effect of a Pore Throat Microstructure on Miscible CO2 Soaking Alternating Gas Flooding of Tight Sandstone Reservoirs

Miscible CO2 soaking alternating gas (CO2-SAG) flooding is an improved version of CO2 flooding, which compensates for the insufficient interaction of CO2 and crude oil in the reservoir by adding a CO2 soaking process after the CO2 breakthrough (BT). The transmission of CO2 in the reservoir during the soaking process is controlled by the pore throat structure of the formation, which in turn affects the displacement efficiency of the subsequent secondary CO2 flooding. In this work, CO2-SAG flooding experiments at reservoir conditions (up to 70 °C, 18 MPa) have been carried out on four samples with very similar permeabilities but significantly different pore size distributions and pore throat structures. The results have been compared with the results of CO2 flooding on the same samples. It was found that the oil recovery factors (RFs) when using CO2-SAG flooding are higher than those when using CO2 flooding by 8–14%. In addition, we find greater improvements in the RF for rocks with greater heterogeneity of their pore throat microstructure compared with CO2 flooding. The CO2 soaking process compensates effectively for the insufficient interaction between CO2 and crude oil because of premature CO2 BT in heterogeneous cores. Moreover, rocks with a more homogeneous pore throat microstructure exhibit a higher pressure decay rate in the CO2 soaking process. The initial rapid pressure decay stage lasts for 80–135 min (in our experimental cores), accounting for over 80% of the total decay pressure. Rocks with the larger and more homogeneous pore throat microstructure exhibit smaller permeability decreases because of asphaltene precipitation after CO2-SAG flooding, possibly because the permeability of rocks with a more heterogeneous and smaller pore throat microstructure is more susceptible to damage from asphaltene precipitation. However, the overall permeability decline is 0.6–3.6% higher than that of normal CO2 flooding because of the increased time for asphaltene precipitation. Nevertheless, the corresponding permeability average decline per 1% oil RF is 0.11–0.34%, which is lower than that for CO2 flooding, making the process worthwhile. We have shown that CO2-SAG flooding has the potential to improve oil RFs with relatively less damage to cores, especially for cores with small and heterogeneous pore throat microstructures, but for which severe wettability changes due to the CO2 soaking process can become significant

Microstructural controls on reservoir quality in tight oil carbonate reservoir rocks

In carbonate reservoir rocks the complex interaction between the petrophysical properties corresponds to the various depositional microstructures which are modified by various diagenetic processes that ultimately define the reservoir quality, and pose challenges to the prediction of permeability. The permeability heterogeneity in the carbonate oil reservoirs of northern Iraq varies widely and is thought to be controlled by a number of different factors. In this work, controls of matrix permeability for the Cretaceous Kometan formation selected from five oil fields in Kirkuk embayment zone have been investigated. Helium porosity, helium pulse decay permeability , brine permeability, Nuclear Magnetic Resonance (NMR), Mercury Injection Capillary pressure (MICP) , Scanning Electronic Microscopy (SEM), X-Ray diffraction (XRD), and photomicrography of thin section have been used to investigate the effect of microstructure on the variation of permeability in the Kometan Formation. The formation has porosities and permeabilities which range from 0.5±0.5% to 29±0.5% and from 0.65±0.08 μD to 700±0.08 μD respectively. Three types of pore systems have been investigated using pore type, pore size and pore-throat size as characterizing parameters. We have recognized three microstructural types: (i) matrix composed of nano-intercrystalline pores (pore diameter dp smaller than 1 μm and a nanoporous pore-throat size), (ii) matrix composed of micro-intercrystalline pores (110 μm) also with microporous pore-throat radii. The nano-intercrystalline pore system is common across northern Iraq and represents the effective pore system type in the reservoirs of the Kirkuk embayment zone. For these tight carbonate reservoirs, the mineralogy, especially of quartz and clay minerals (illite and smectite), has little relationship with the measured Klinkenberg-corrected permeability. Consequently, mineralogy is not a useful controlling factor for permeability. Diagenetic processes have altered the depositional texture significantly, resulting in changes to the pore size and pore-throat size distribution and affecting the permeability. In addition the matrix permeability is sensitive to stress, with permeability decreases between -4×10‾⁴mD/psi and -4 ×10‾⁵mD/psi in the effective stress range from 0 psi to 4000 psi. It has been found that of the three microstructure pore types the nano-intercrystalline pore system is more sensitive to increasing effective stress compared to the micro-intercrystalline and meso-intragranular pore systems. Laboratory experiments have shown that stylolisation resulting from regional fluid movements has also affected matrix permeability, with the stylolites acting as barriers to fluid flow and considered to be an important source of tightness of the Kometan formation in the Kirkuk embayment fields

Modelling and Simulation of Heterogeneous and Anisotropic Formations using Advanced Fractal Reservoir Models

Energy and carbon-efficient exploitation, management, and remediation of subsurface aquifers, gas and oil resources, CO2-disposal sites, and energy storage reservoirs all require high quality modelling and simulation. The heterogeneity and anisotropy of such subsurface formations has always been a challenge to modellers, with the best current technology not being able to deal with variations at scales of less than about 30-50 m. Most formations exhibit heterogeneities and anisotropy which result in variations of the petrophysical properties controlling fluid flow down to millimetre scale and below. These variations are apparent in well-logs and core material, but cannot be characterised in the inter-well volume which makes up the great majority of the formation. This paper describes a new fractal approach to the modelling and simulation of heterogeneous and anisotropic aquifers and reservoirs. This approach includes data at all scales such that it can represent the heterogeneity of the reservoir correctly at each scale. Advanced Fractal Reservoir Models (AFRMs) in 3D can be produced using our code. These AFRMs can be used to model fluid flow in formations generically to understand the effects of an imposed degree of heterogeneity and anisotropy, or can be conditioned to match the characteristics of real aquifers and reservoirs. This paper will show how 3D AFRMs can be created such that they represent critical petrophysical parameters, as well as how fractal 3D porosity and permeability maps, synthetic poro-perm cross-plots, water saturation maps and relative permeability curves can all be calculated. It will also show how quantitative controlled variation of heterogeneity and anisotropy of generic models affects fluid flow. We also show how AFRMs can be conditioned to represent real reservoirs, and how they provide a much better simulated fluid flow than the current best technology. Results of generic modelling and simulation with AFRMs show how total hydrocarbon production, hydrocarbon production rate, water cut and the time to water breakthrough all depend strongly on heterogeneity, and also depend upon anisotropy. Modelling with different degrees and directions of anisotropy shows how critical hydrocarbon production data depends on the direction of the anisotropy, and how that changes over the lifetime of the reservoir. Advanced fractal reservoir models are of greatest utility if they can be conditioned to represent individual reservoirs. We have developed a method for matching AFRMs to aquifer and reservoir data across a wide range of scales that exceeds the range of scales currently used in such modelling. We show a hydrocarbon production case study which compares the hydrocarbon production characteristics of such an approach to a conventional krigging approach. The comparison shows that modelling of hydrocarbon production is appreciably improved when AFRMs are used, especially if heterogeneity and anisotropy are high. In this study AFRMs in moderate to high heterogeneity reservoirs always provided results within 5% of the reference case, while the conventional approach resulted in massive systematic underestimations of production rate by over 70%

Permeability of fault rocks in siliciclastic reservoirs: Recent advances

It is common practice to create geologically realistic production simulation models of fault compartmentalized reservoirs. Data on fault rock properties are required, to calculate transmissibility multipliers that are incorporated into these models, to take into account the impact of fault rocks on fluid flow. Industry has generated large databases of fault rock permeability, which are commonly used for this purpose. Much of the permeability data were collected using two inappropriate laboratory practices with measurements being made at low confining pressure with distilled water as the permeant. New fault rock permeability measurements have been made at high confining pressures using formation compatible brines as the permeant. Fault permeability decreases by an average of five fold as net confining pressure is increased from that used in previous measurements (i.e. ∼70 psi) to that approaching in situ conditions (i.e. 5000 psi). On the other hand, permeability increases by around the same amount if reservoir brine is used as the permeant instead of distilled water. So overall, these two inappropriate laboratory practices used in previous studies cancel each other out meaning that legacy fault rock property data may still have value for modelling cross-fault flow in petroleum reservoirs. A poor correlation exists between clay content and fault rock permeability, which is easily explained by the application of a simple clay-sand mixing model. This emphasises the need to gather fault permeability data directly from the reservoir of interest. The cost of such studies could be significantly reduced by screening core samples using a CT scanner so that only samples that are likely to impact fluid flow are analyzed in detail. The stress dependence of fault permeability identified in this study is likely to be primarily caused by damage generated during or following coring. So it is probably not necessary to take into account the impact of stress on fault permeability in simulation models unless the faults of interest are likely to reach failure and reactivate