Numerical simulation results are the basis of numerous oil and gas field developments. We based the numerical simulation models (or dynamic models) on 3D geological models. We constructed a geological model using core and log data obtained from wells as inputs to create a reservoir prototype. This paper describes the applications of artificial intelligence (AI) algorithms for parameterization of static and dynamic modeling processes. Accordingly, a hypothetical 3D geological model was created, and porosity and permeability were distributed using sequential Gaussian simulation. Then, Petro-physical rock types (PRT) were defined in the 3D space as a function of porosity and permeability using a hypothetical Winland's R35 equation. Finally, hypothetical saturation-height functions (SHFs) were defined for different PRTs to populate water saturation in the 3D geological model. Subsequently, some wells were randomly defined in the 3D model to obtain the logs of porosity, permeability, SHF, PRT, repeat formation tester pressure (RFT), and datum pressures that are used in this study. A multivariate Gaussian regression was applied for anomaly detection, while core porosity and permeability were filtered. Subsequently, a fixed window average was used to detect the boundaries of core data stationarity and propose the optimum reservoir zone required to describe the internal heterogeneities of the reservoir. Then, we deployed the k-means clustering algorithm to determine the PRT and saturation height function (SHF) based on the core and log data derived from the hypothetical geological model. Finally, we used the clustering-based pattern recognition to cluster well datum pressures into homogeneous groups and create a connected reservoir region CRR map to be used as an input in the 3D permeability distribution. Our results demonstrate the value of additional diagnostics that can be used in conjunction with the traditional semi-log plot of porosity and permeability. This additional diagnostic approach is a semi-log plot of permeability versus depth, which can help check whether intra-reservoir heterogeneities observable in core data have been preserved in the 3D model. In our case, a 3D model created using the core and log data from the hypothetical model and honoring the internal reservoir architecture resulted in a better history match regarding the hypothetical geo-model's RFT pressure signature. Our results further demonstrate that PRT and SHF derived from k-means clustering are sufficiently similar to those of the hypothetical model. Time series anomaly filtering of pressures helped detect incorrect well data that may otherwise have gone unnoticed. Using the nearest-neighbor property distribution resulted in a geological model whose diagnostic plots indicated an excellent match with core data and allowed a better assessment of modeling uncertainties. The ML approaches presented in this study could help obtain data-derived PRT and SHF to complement Winland's interpretation when Mercury Injection Capillary Pressure (MICP) experiments are limited or unavailable, saving both time and cost. Using the fixed window averaging helps optimize the geological model zone assessment, resulting in a better intra-reservoir architecture. Finally, we derive insights into a more efficient core acquisition plan.
The purpose of this paper is to highlight the similarity between Connected Reservoir Regions (CRR)map created using time-lapse pressure groups (Kayode et.al 2018)and other reservoir quality maps like Seismic Acoustic Impedance (SAI) map and petro-physical rock quality map. Time-lapse average reservoir pressure from producers and injectors spanning several years of field production were sorted into groups of similar pressure trends. Wells that show similar pressure trend were classified into same CRR, while wells that show different pressure trends were classified into different CRRs. Only wells operating within the same reservoir zone have been used in the pressure grouping in order to ensure that the observed pressure trend differences are only due to lateral variations of reservoir quality and not due to vertical zonation. A geo-modelling software was used to create connected reservoir regions map in which all wells within the same pressure group are identified with a unique colour code and polygons are drawn to delineate the spatial limits of wells within each pressure group. The CRR map thus obtained, was then compared with SAI map and permeability quality map. Similarity was observed between the CRR map, SAI map and petro-physical rock quality map. Areas indicated as poor quality (high impedance) on the SAI map and indicated as low permeability on petro-physical map were consistent with CRR regions that are characterized by high injection pressure and poor pressure support. Areas indicated as good quality (low impedance) on SAI map and high permeability on petro-physical rock quality map were consistent with CRR regions that are characterized by low injection pressure and excellent producer-injector communication. In addition, a particular well was sidetracked in order to improve reservoir sweep, this producer whose pressure had been historically fairly steady, experienced a sudden increase of time-lapse average reservoir pressure. When the pre and post sidetrack locations of this well were plotted on CRR map, the reason for the sudden pressure increase became obvious; well was sidetracked across CRR boundary, from a poor reservoir quality to a good reservoir quality CRR. In certain cases, oil and gas fields may not have seismic data, in other cases the resolution of the returned seismic signal may be weak. In such cases, CRR maps created using time-lapse average reservoir pressure groups could be used during geo-modelling,for controlling the distribution of 3-D properties away from well control points, instead of seismic acoustic impedance reservoir quality map.
In the traditional sequential workflow approach, the geomodeler builds static models based solely on log and core data interpretations, sometimes supplemented with geological understanding, without any dynamic data considerations. In the consequent step in the traditional workflow, the simulation engineer modifies the static model, as required, to achieve a match to the dynamic data, sometimes ending up with a modified geomodel that is significantly different from the original static geomodel. In the modern integrated reservoir modeling practice, the established workflows have become a cyclical process where learnings from the history match are taken back to refine the geomodel. For example, if a well does not produce its historical rate during history match, the permeability-thickness product (KH) around the well is caliberated to well-testing KH using pressure transient derivative matching and the discrepancy is taken back to the geomodel to be resolved. With the intent to reduce history match cycle time, different approaches have been developed to use underlying data input, e.g., seismic impedance, object-based geological features, pressure transient derivative signature or pressure stream lines, to constrain the geomodel 3-D property population to more realistic outcomes based on the geological understanding and available dynamic data. This publication proposes a new such approach: Pressure Conditioned Modeling (PCM). The PCM concept is based on grouping wells with similar time-lapse static reservoir pressure trends into the same Connected Reservoir Region (CRR). PCM is based on the assumption that similarity of time-lapse shut-in reservoir pressure trends between wells in a reservoir is an indication that the producers are draining from same connected reservoir region (same CRR), and no large scale geomodel permeability barrier is allowed to exist between these wells. Time-lapse shut-in pressure data of all wells in the reservoir are grouped on the basis of similar trends. A CRR map is created to reflect the spatial distribution of the hydraulically connected wells. The geomodeler then uses this CRR map as input in the 3-D permeability variogram definition. The core permeability data existing within each CRR is distributed only inside the subject CRR in such a way that no undesirable intra-CRR permeability barrier occurs. The PCM methodology imposes a connectivity range on 3-D permeability distribution thereby ensuring that the connected areas within a globally heterogeneous reservoir are properly designated. A synthetic model example discussed in this paper resulted in a better pre-modification history match of wells and hence would require less time for history matching. More realistic field development predictions would also be achieved due to the improved connectivity between injectors and producers within each CRR in a fashion consistent with the observed field data. For reservoirs with different multiple distinct multi-well pressure trends in the existing production history, the PCM concept should be used as it will produce a higher quality initial geomodel and significantly reduce the time required to obtain a history matched model without the need for significant modifications.
Due to reservoir description uncertainties, the building of multiple geologic realizations has become an acceptable industry standard for geo-modelling. This paper discusses an approach to rank these multiple realizations, and to determine the geological realization(s) which is/are the closest to reality. It then describes how to further calibrate this best ranked geo-realization(s), especially in situations where there are no production and static pressure data to be used for history matching. The proposed approach allows us to screen multiple geologic realizations using pressure transient data, and to improve the distribution of permeability away from well control points. The objective is to Rank the several geo-realizations on the basis of global best fit between the simulated pressure transient derivative and the observed pressure transient derivative, then perform a history Match of the pressure derivative for the best geo-model using permeability multipliers, and finally, create a permeability multiplier map, and Spread this permeability multiplier map over the entire best fit geo-model. Sometimes, the observed pressure transient data may indicate a boundary away from the well, which the original static geo-model may not capture. More so, information from 3D-siesmic may not also indicate any barrier near this well. Using this proposed approach, we can reproduce the well's pressure transient by introducing stratigraphic features in the static model. In the conventional approach, static modeling is solely based on core data measured at well control points, but in this new approach, a dynamic correction factor based on average drainage area permeability is also applied, resulting in a better characterization of the permeability and boundary features. This approach adds an additional layer of reservoir characterization to geo-modeling by ensuring that the geo-model contains as much dynamic features as possible. In the case of non-producing fields, where there is no further history matching to be done, this new approach guarantees a more reliable static geomodel.
In this paper, we investigate the cause of the time-shift that occurs between the derivatives of the observed and simulated pressure transient data and present a methodology to perform full-field transient modeling without the need for single well fine grid sector models. Pressure transient modeling is the process of simulating an observed well test sequence with the goal of comparing the derivative of field measured pressure transient to the derivative of numerically simulated pressure transient. Beginning from first principles, we investigated and showed in the current paper that simulation grid-block size introduces an undesireable shift in the derivative of simulated data which disappears as we approach fine grid simulation. We have termed this shift as grid-block storage phenomenon. As a result of this undesireable shift that occurs when coarse gid blocks are used, transient modeling is currently done using local grid refinement on sector models. The limitations of the current practice include; (i) large simulation run times due to use of fine grid simulation (ii) error related to boundary conditions when using sector models. In this paper, we develop the equations governing pressure buildup behavior during grid-block storage dominated period as a function of simulation grid-size and simulation grid permeability. The insight from the derived equations reveals that the infinite acting radial flow stabilization (IARF) of the derivative of simulated pressure transient is always the same regardless of simulation grid-size. However, the onset of this stabilization is delayed as simulation grid-size increases and as simulation grid permeability decreases. Based on this insight, we then present the basis for an approach to history match the derivative of observed pressure transient without using local grid refinement on sector models. This approach is based on the use of derivative time-shift. Instead of using a fine grid sector model, we simply use the coarse full-field model to simulate pressure transient until the onset of IARF stabilization. We then shift the derivative of observed pressure transient right-wards to overlay corresponding features of the derivative of simulated data in a manner similar to type-curve matching. This new approach called Time-Shift Methodology (TSM), presents a practical and efficient way of performing transient modeling on a full-field multi-well model without resorting to the time consuming conventional approach of using several single-well fine grid sector models.
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