Ruud Weijermars's research while affiliated with King Fahd University of Petroleum and Minerals and other places

High development cost of shale fields produced with multi-fractured well systems prompts for improved and faster production forecasting tools. This study advances the use of a Gaussian pressure transient-based reservoir model (GRM). In this new simulator, the migration of reservoir fluids is fully controlled by the hydraulic diffusivity; the value of which can be initially estimated for any particular reservoir by history-matching a Gaussian decline curve to early production data. In a next step, the reservoir model based on the Gaussian pressure transient will compute—from the bottomhole pressures in the well system (imposed by the engineering intervention on the initial reservoir pressure)—the spatial and temporal advance of the pressure depletion and fluid flow near the multistage fractured wells. Real-world data from the Hydraulic Fracture Test Site-1, Midland Basin (West Texas), is utilized to validate the Gaussian solutions in comparison with a commercial simulator through history-matching and a comprehensive sensitivity analysis. The validated GPT method allows for fast iteration of well productivity sensitivity to the placement and orientation of the hydraulic fractures, allowing for proper planning to optimize field development plans.

The production rate and cumulative production of hydraulically fractured shale wells can be estimated using the pressure depletion volume (PDV) method. The Gaussian Pressure Transient (GPT) is used to compute the pressure depletion in the drainage region of single or multiple hydraulically fractured wells, and the pressure depletion is then translated to production performance. This new approach does not involve Darcy’s Law, and therefore provides an independent method to evaluate well performance. The pressure depletion in reservoir volume between hydraulic fractures is computed by integrating the normalized GPT for the fractured reservoir region, accounting for each individual fracture. Also included is the pressure drop in the nearby reservoir region from pressure changes initiated via the fracture tips. The total pressure depletion of the drained reservoir, can then be computed for each moment in time as an instantaneous analytical solution. The cumulative production is computed using from the comprehensive compressibility coefficient of the drained reservoir space. The daily production rate can then be computed from the time derivative of the cumulative production at any moment in time. To validate the PVD method, the production rate forecasts were history-matched to (1) real production data from the Eagle Ford shale formation, and separately, to (2) synthetic, noise-free CMG-IMEX production data. Both data sets could be satisfactorily matched. The PVD model can also quantify the relative contribution to production from the fracture tips and fracture box region, as well as determine how their relative importance switches over time. The PDV-method proposed in this paper is based on the GPT model, and can predict both the pressure depletion and production performance over the anticipated field life prior to drilling, which is helpful for optimizing completion designs and maximizing economic benefits.

Fast and rigorous well performance evaluation is made possible by new solutions of the pressure diffusion equation. The derived Gaussian pressure transient (GPT) solutions can be practically formulated as a decline curve analysis (DCA) equation for history matching of historic well rates to then forecast the future well performance and estimate the remaining reserves. Application in rate transient analysis (RTA) mode is also possible to estimate fracture half-lengths. Because GPT solutions are physics-based, these can be used for production forecasting as well as in reservoir simulation mode (by computing the spatial and temporal pressure gradients everywhere in the reservoir section drained by either an existing or a planned well). The present paper focuses on the physics-based production forecasting of so-called “unruly” wells, which at first seem to have production behavior noncompliant with any DCA curve. Four shale wells (one from the Utica, Ohio; one from the Eagle Ford Formation, East Texas; and two from the Wolfcamp Formation, West Texas) are analyzed in detail. Physics-based adjustments are made to the Gaussian DCA history matching process, showing how the production rate of these wells is fully compliant with the rate implied by the hydraulic diffusivity of the reservoir sections where these wells drain from.

Accurate estimation of fracture half-lengths in shale gas and oil reservoirs is critical for optimizing stimulation design, evaluating production potential, monitoring reservoir performance, and making informed economic decisions. Assessing the dimensions of hydraulic fractures and the quality of well completions in shale gas and oil reservoirs typically involves techniques such as chemical tracers, microseismic fiber optics, and production logs, which can be time-consuming and costly. This study demonstrates an alternative approach to estimate fracture half-lengths using the Gaussian pressure transient (GPT) Method, which has recently emerged as a novel technique for quantifying pressure depletion around single wells, multiple wells, and hydraulic fractures. The GPT method is compared to the well-established rate transient analysis (RTA) method to evaluate its effectiveness in estimating fracture parameters. The study used production data from 11 wells at the hydraulic fracture test site 1 in the Midland Basin of West Texas from Upper and Middle Wolfcamp (WC) formations. The data included flow rates and pressure readings, and the fracture half-lengths of the 11 wells were individually estimated by matching the production data to historical records. The GPT method can calculate the fracture half-length from daily production data, given a certain formation permeability. Independently, the traditional RTA method was applied to separately estimate the fracture half-length. The results of the two methods (GPT and RTA) are within an acceptable, small error margin for all 5 of the Middle WC wells studied, and for 5 of the 6 Upper WC wells. The slight deviation in the case of the Upper WC well is due to the different production control and a longer time for the well to reach constant bottomhole pressure. The estimated stimulated surface area for the Middle and Upper WC wells was correlated to the injected proppant volume and the total fluid production. Applying RTA and GPT methods to the historic production data improves the fracture diagnostics accuracy by reducing the uncertainty in the estimation of fracture dimensions, for given formation permeability values of the stimulated rock volume.

Despite significant advancements in geomodelling technologies, Accurately estimating hydraulic fracture half-length remains a challenging task. This paper introduces a detailed estimation approach using the Gaussian Pressure Transient (GPT) method, which is relatively new. The GPT method is iterative, ensuring fast convergence and providing reliable estimations of hydraulic fracture half-length b’ased on a predetermined hydraulic diffusivity value obtained from Gaussian Decline Curve Analysis (DCA). To validate the GPT results, production data from two case study wells in the Wolfcamp Shale Formation, located in the Midland Basin of West Texas, are utilized alongside the traditional Rate-Transient Analysis (RTA) method. Moreover, the GPT method offers the capability to probabilistically estimate hydraulic fracture half-lengths, presenting two innovative approaches to evaluate the robustness of this newly developed method for both deterministic and probabilistic estimations. The simulation results demonstrate a close correlation between the Gaussian method and micro-seismic fracture half-lengths, with separate confirmation from the classic RTA-method. Through the case studies presented in this paper, the GPT-method showcases its utility in estimating hydraulic fracture half-lengths for two Wolfcamp case study wells, effectively demonstrating the validity and practical applicability of this novel method.