Jincai Zhang

Dual-porosity poroelastic analyses of wellbore stability

This paper presents a numerical solution of dual-porosity poroelastic formulations that couple solid deformations with fluid flow in both matrix and fracture systems of naturally fractured reservoirs. The finite element numerical method was applied to solve the inclined wellbore problem in which mud weight was considered for both permeable and impermeable boundary conditions. Failure criteria relevant to tensile, collapse, and shear failure modes were introduced into the numerical model and resulting failure areas around boreholes were subsequently defined. Several related applications, including the stability of inclined and horizontal wellbores under various in situ stress regimes, were evaluated. Upper and lower mud weight bounds and the most stable borehole orientations were determined. The best trajectory selections for horizontal boreholes were also investigated.

Wellbore Stability Modeling and Real-Time Surveillance for Deepwater Drilling to Weak Bedding Planes and Depleted Reservoirs

Wellbore instability is the primary cause of losses in boreholes and represents a serious challenge in the drilling industry. Drilling along bedding planes and in depleted reservoirs is risky, and when a well is drilled at shallow angles to thinly bedded shales, it is often highly unstable. Rock failure can occur as a result of large anisotropy in rock strength caused by bedding- parallel weak planes. In these cases, an increased mud weight while drilling is required. However, when the reservoir immediately beneath the bedded shales is depleted, the increased mud weight can lead to lost circulation. This paper presents some of the cases we encountered in surveying offset wells in depleted reservoirs located in deepwater Gulf of Mexico for a new predrill study, where borehole instabilities resulted in a loss of a hole section and a casing shoe became massively fractured. The key solutions are to not only improve wellbore stability modeling associated with bedding planes, rock anisotropy, and pressure depletion, but also to account for their impact on horizontal stresses. These factors are considered in the proposed model, thereby enabling calculations of wellbore failures along borehole trajectories with various drilling orientations versus bedding directions. The model has been verified by case studies. The minimum stress and fracture gradient calculations are also implemented to consider rock anisotropy and the depletion. Lab test data of rock strengths with different loading directions are analyzed. A new correlation is developed to allow for predicting anisotropic rock strength from sonic velocities.

Dual-porosity elastoplastic analyses of non-isothermal one-dimensional consolidation

A numerical solution, using the finite difference method, and based on a porothermo-elasto-plastic formulation for dual-porosity one-dimensional consolidation has been presented. The model is fully coupled to ensure the interactive behavior of fluid flow, heat flow and solid deformations in the conservation of momentum, mass and energy equations. A bi-linear stress-strain relationship is used to accommodate elastoplastic deformation behavior. A double effective stress law, proposed by Elsworth and Bai (1992), is applied to describe constitutive relationships among the stresses, pressures and temperatures. In order to examine the dual-porosity and thermal effects on the soil consolidation individually, isothermal and non-isothermal consolidations for a dual-porosity column are analyzed. In comparison to the single porosity approach, the present study shows that the pore pressure dissipation is faster and Mandels effect (Mandel, 1953) is more pronounced at early times of the source disturbance for dual-porosity consolidation. One of the significant parameters affecting the dual-porosity consolidation is the fracture spacing (fracture density); the smaller the fracture spacing, the faster the column drainage.

Fracture gradient prediction: an overview and an improved method

The fracture gradient is a critical parameter for drilling mud weight design in the energy industry. A new method in fracture gradient prediction is proposed based on analyzing worldwide leak-off test (LOT) data in offshore drilling. Current fracture gradient prediction methods are also reviewed and compared to the proposed method. We analyze more than 200 LOT data in several offshore petroleum basins and find that the fracture gradient depends not only on the overburden stress and pore pressure, but also on the depth. The data indicate that the effective stress coefficient is higher at a shallower depth than that at a deeper depth in the shale formations. Based on this finding, a depth-dependent effective stress coefficient is proposed and applied for fracture gradient prediction. In some petroleum basins, many wells need to be drilled through long sections of salt formations to reach hydrocarbon reservoirs. The fracture gradient in salt formations is very different from that in other sedimentary rocks. Leak-off test data in the salt formations are investigated, and a fracture gradient prediction method is proposed. Case applications are examined to compare different fracture gradient methods and validate the proposed methods. The reasons why the LOT value is higher than its overburden gradient are also explained.

Real-Time Pore Pressure Detection: Indicators and Improved Methods

High uncertainties may exist in the predrill pore pressure prediction in new prospects and deepwater subsalt wells; therefore, real-time pore pressure detection is highly needed to reduce drilling risks. The methods for pore pressure detection (the resistivity, sonic, and corrected -exponent methods) are improved using the depth-dependent normal compaction equations to adapt to the requirements of the real-time monitoring. A new method is proposed to calculate pore pressure from the connection gas or elevated background gas, which can be used for real-time pore pressure detection. The pore pressure detection using the logging-while-drilling, measurement-while-drilling, and mud logging data is also implemented and evaluated. Abnormal pore pressure indicators from the well logs, mud logs, and wellbore instability events are identified and analyzed to interpret abnormal pore pressures for guiding real-time drilling decisions. The principles for identifying abnormal pressure indicators are proposed to improve real-time pore pressure monitoring.

Pore Pressure Prediction in Unconventional Resources

Understanding pore pressure prediction in unconventional plays is important for executing a safe drilling strategy and for accurate production modeling. Experience from several unconventional plays highlights key aspects of pore pressure prediction work that are different from conventional exploration settings. In conventional exploration, the most common source of overpressure is disequilibrium compaction, where porosity is preserved in mudrocks as pore fluids take on additional overburden load. Traditional petrophysical methods use resistivity, sonic and density data to measure porosity and associate it with vertical effective stress (VES), which is overburden minus pore pressure. In unconventional plays, secondary pressure mechanisms and uplift require other methods because of two influences on pore pressure: (1) hydrocarbon generation and (2) variations in burial and uplift history. Both of these situations mean that the relationships between vertical effective stress (VES), velocity, density and resistivity will follow unloading paths, not compaction trends. The unloading paths vary depending on the amount of hydrocarbon generated and the amount of uplift. In organic-rich sections, an additional complication arises because pore pressure cannot be de-convolved from total organic carbon (TOC) and gas effects on shale compressional velocity and resistivity. In conventional settings, fluid gradients and contacts are used to translate measured pressure data from one location to another. In unconventional tight reservoirs, the fluids are not connected and this method will not work. Pressure data must be inferred from drilling event and diagnostic fracture injection test interpretations, and a different way to translate data between locations is required. The majority of pressure data in unconventional reservoirs shows that often, the way to translate pressure information from one location to another in the same tight rocks is to use a constant VES. This method combined with understanding variations in uplift history and hydrocarbon generation has been used to successfully predict pressure ranges in multiple unconventional plays.

PKN Solution Revisit: 3-D Hydraulic Fracture Size and Stress Anisotropy Effects

Hydraulic fracturing is a very important stimulation technology which enables the operators to produce from those tight and extremely low-permeable reservoirs (e.g., shale oil and shale gas plays). For hydraulic fracturing design, the hydraulic fracture volume needs to be calculated. The PKN solution (Perkins and Kern 1961; Nordgren 1972) has widely been applied in calculating the induced fracture width by hydraulic fracturing. The PKN solution is a 2-D analytical solution with assumption of plane strain deformation in the vertical plane. Perkins and Kern assumed that each vertical cross section acts independently; i.e., the fracture height is fixed and independent to the fracture length (or length ≫ height). In practice, this is true if the fracture length is much greater than the height. This assumption may create uncertainties for applying the PKN solution in 3-D conditions, particularly when the fracture length is relatively small. Geertsma and de Klerk (1969) presented another 2-D analytical solution (KGD model) for a linearly propagating fracture by assuming that the fracture height is much greater than its length (height ≫ length). Geertsma and de Klerk assumed the plane strain to be in the horizontal direction; i.e., all horizontal cross sections act independently or equivalently (Mack and Warpinski 2000). In recent years, the numerical modeling technique (e.g., the finite element and finite difference methods) enables one to model the hydraulic fractures in pseudo-3-D and 3-D conditions and simulate the interactions of multiple hydraulic fractures and natural fractures in unconventional reservoirs (e.g., Adachi et al. 2007; Weng et al. 2011; Roussel and Sharma 2011; Bunger et al. 2012; Kress et al. 2013; Castonguay et al. 2013; Dohmen et al. 2014a, b; Detournay 2016; Li et al. 2017). However, different numerical methods give very different