Lost circulation is one of the major issues that lead to unwanted non-productive time (NPT) while drilling with a narrow mud weight window and it requires engineered solutions to address the problem. In several instances in the past, wellbore strengthening was achieved by treating the drilling fluid with lost circulation material (LCM), utilizing Stress Caging or Wellbore Strengthening theory. Small fractures were propped and sealed with a proper size distribution of particles that isolates the fracture tip from fluid pressure and controls the fracture propagation, effectively increasing the near wellbore hoop stress.Laboratory data and field experience indicate limited success may occur if a single material such as sized calcium carbonate is used alone for wellbore strengthening. This is possibly due to size reduction that may occur while drilling or due to fracture closure stresses (FCS) acting on the particles. However, using calcium carbonate in conjunction with resilient graphitic carbon (RGC) material has shown to be effective in increasing the formation integrity.The effect of mechanical properties of LCMs on wellbore strengthening has been investigated using compression/crush tests at different confining pressures simulating a wide range of FCS. Crush test demonstrated compaction and significant crushing of the ground marble and ground nut shells at high confining pressure (~ 5000 Psi). Considerable improvement in the crushing resistance and resiliency of these materials was observed with small additions of RGC. Knowledge of deformation and failure behavior of different LCM materials may result in better design. In this paper recommendations are made on different combinations of LCM that may be used more effectively to provide wellbore strengthening.
Significant operating costs are incurred from treatments designed to remove waxy deposits from production tubing or squeeze treatments designed to inhibit wax deposition. The costs are further increased by formation damage and loss of production that may result from these treatments. Our studies show that paraffin deposition can be prevented or greatly retarded by using chemical surfactants known as dispersants. Two specific surfactants were selected that proved to be very effective paraffin dispersants. One is oil soluble and the other is water soluble. These dispersants can be continuously injected into the well or they can be added in larger quantities in a "batch treatment" at specific time intervals. The choice of whether to use batch or continuous treatment is governed by the type and number of wells requiring treatment. Introduction PARAFFIN DEPOSITION PARAFFIN DEPOSITION The mechanism of paraffin deposition and the fact that paraffin wax does come out of solution at the cloud point of the paraffin wax does come out of solution at the cloud point of the wax when present in paraffin base crude oil is well documented. It is also known that the precipitate may or may not adhere to an exposed surface and result in a deposit. Deposits can range from almost pure white paraffin wax to a totally asphaltic material. Most deposits, however, fall somewhere between these two extremes and are composed of a mixture of asphaltic material; solid hydrocarbon waxes; and varying amounts of retained oil, water, sand, silt, metal oxides, sulfates, and carbonates. PROBLEMS CAUSED BY PARAFFIN DEPOSITION PROBLEMS CAUSED BY PARAFFIN DEPOSITION Paraffin deposits collect in well bores, production tubing, Paraffin deposits collect in well bores, production tubing, and flow lines. Under certain conditions paraffin deposition may also occur in the producing formation. The problem caused by these deposits are all related to restricted flow which leads to increased flow line pressure, decreased production, and mechanical problems. These and other problems are also well documented in problems. These and other problems are also well documented in the literature as described by Shock et al., EnDean, Newberry, and Sifferman. METHODS USED TO TREAT PARAFFIN PROBLEMS There are numerous methods used to handle paraffin deposition. These can be divided into the following four categories: a. Mechanical b. Thermal c. Chemical d. Combinations of the above. Mechanical The method of running a scraper which mechanically cuts the deposit from the tubing has been widely utilized. Wire lining tubing and "pigging" flow lines are two examples. Thermal This treatment method normally consists of minimizing radiation heat losses and the addition of external heat to the system. Insulation of flow lines and maintaining a higher pressure in the flow lines which minimize cooling through dissolved gas expansion are two examples of minimizing radiation heat losses. Such procedures as steaming the flow lines, installing bottom-hole heaters, and circulation of hot oil or hot water are examples of the application of heat in an effort to melt or increase the solubility of the deposit. Chemical Control Chemical control, which this paper is based on, falls into the following classes: those in which a solvent is used to dissolve the deposit once it has formed, and those which inhibit wax crystal growth or inhibits its adherence to the tubing wall. 1. Solvents Solvents used for dissolving paraffin deposits generally have a high aromatic content. A variety of solvents, including crude oils, are heated when used. 2. Wax Crystal Modifiers These are polymers which inhibit or alterwax crystal growth.
Summary This paper provides an analysis of perforation-tunnel stability through a set of three-dimensional (3D) transient fluid-flow and geomechanical finite-element codes. The results are quantitatively accurate and can be applied to field design completion problems. The paper clarifies the causes of sand problems occurring in a field and suggests techniques to minimize the problems. Introduction A dimensional analysis with a set of equations governing perforation stability showed that the main factors affecting sand production areEquation 1 where ?pw=well pressure, gpn=normalized pressure gradient at cavity surface, ?sH,?sV=in-situ stresses, HL=loading history, D, F=deformation and failure characters of rock, sp,?p=perforation geometry and density, a=borehole inclination, Pc=capillarypressure, and Rch=rock-weakening effect by chemical reaction. Analytical models can handle some of these parameters but require simplification before data are entered, particularly the problems concerning the directional in-situ stresses, rock deformation character, and perforation geometry and spacing. These problems are studied intensively in this work by use of a set of 3D numerical models. Because of computer cost limitations, the results from analytical models are also used when the quantitative accuracy is not critical. Although many finite-element codes are commercially available, two obstacles prevented us from using them:commercially available finite-element fluid-flow codes are not flexible enough to handle oil flow through porous media where oil properties are complex and non-Darcy flow is included, andcommercially available geostructural codes use simple plastic or nonlinear materials suitable for metals but cannot properly simulate geological materials, which volumetrically behave in a complex manner where the hardening effect is highly dependent on the hydrostatic-stress component. Because of these obstacles, a set of finite-element and rock-processing codes was developed. Field problems involve many parameters simultaneously, as shown in Eq. 1, making it very difficult for field engineers to diagnose the parameters and seriously affecting the sand problems for specific reservoirs.1 This paper attempts to clarify the complex nature of sand-production problems and to give guidelines for solving field problems. Instead of discussing the effect of each parameter on sand-production problems, we present the analysis from a field-applications viewpoint. The topics are selected from typical field problems encountered in several North sea reservoirs.2 Calculation Procedure for Perforatlon Stability The effect of each parameter in Eq. 1 on sand production is studied by two finite-element models: a transient fluid-flow model and a geostructural model coupled with fluid force. The transient fluid-flow model calculates pore-pressure distribution around perforation holes for a given set of boundary conditions. The geostructural model, with the pore-pressure input evaluated by the fluid model, calculates stress state, deformation, and plastic deformation. The stability of perforations is judged by use of a postprocessor from the stress state or the plastic strain, with appropriate failure criteria suitable for the rock. Fig. 1 shows an example element configuration used for this work. The number of elements was minimized by taking advantage of the geometrical symmetry. The geometry consists of a borehole cemented to a rigid casing with ellipsoidal perforation tunnels. The sizes and shapes of the perforation tunnels were varied to study the cavity-evolution effect. The permeability around the perforation surface was reduced to 1/10 of the original rock permeability; the depth of the damaged zone was assumed to be 0.5 in. [1.3 cm] right after perforating, but was reduced as the damaged zone was removed during cavity enlargement caused by sand production. Non-Darcy flow was assumed to simulate the actual flow realistically because a high flow rate often induces a high pressure gradient around the cavity. After a proper in-situ stress was applied as the residual stress, the boundary pressures and flow rates were increased incrementally until the stress state or the plastic strain exceeded failure envelopes. Two sets of rock deformation and strength data were used to study the effect of rock strength on cavity stability. Figs. 2 through 4 show theoretical stress/strain and PV change curves simulating a set of data obtained for a weak formation in a North sea reservoir. A modified kinematic3 model with a cap4 was used because this model accurately simulates the behavior of weak sandstones, especially the complex behavior of volumetric shrinkage and expansion. The rock has approximately 150-psi [1034-kPa] unconfined compressive strength and is considered too weak to perforate. Another set of data used in this work is an intermediate-strength formation with approximately 1000-psi [6.9-MPa] unconfined compressive strength. The formation is strong enough to perforate but still may produce sand if flow-rate or well-pressure decline exceeds a certain critical value. Both sets have the following deformation and strength character typical of the North Sea Rannoch sandstones.The strength varies significantly depending on stress level. As shown in Fig. 2, the strengths with high confining pressures are 10 to 100 times higher than those with no confining pressure. Such core looks unconsolidated in a core box but may be strong deep in the reservoir.The sandstones deform nonlinearly and the nonlinear character varies depending on the stress state. Figs. 2 through 4 show two types of plastic behavior: compaction with high mean stress and volumetric expansion with a high deviatric stress state. A constitutive relation is constructed for each formation from a set of stress/strain data that covers the approximate range of the stress state around perforations. These constitutive relations are entered into the geostructural model to calculate the stability of perforation holes. For cyclic-loading problems, such as opening and closing valves to adjust flow, a linear stress/strain relation was used for the unloading path until microcracks appear in a rock or until the stress state encounters the yield surface again. Fig. 5 shows a calculated flow distribution around an enlarged cavity after some sand flow. The permeability within the region 0.2 in. [0.5 cm] from the cavity surface is assumed to be 1/10 of the formation permeability. Other conditions were specified in the calculation: 16.7-B/D-ft [8.7-m3/d·m] flow rate; -400-psi [-2758-kPa] well pressure (negative means below the reservoir pressure); 4-shots/ft [13-shots/m] perforations; enlarged ellipsoidal cavity 7.5 in. [19 cm] in length,3.6 in. [9.1 cm] in diameter, with a 0.85-in. [2.16-cm] outlet; kr/µ=(200 md)/(0.6 cp [0.6 mPa·s]); and steady-state flow. Fig.5 shows the pressure vs. distance along Paths 1 and 2. Although the pressure distribution is complex, the dominant flow pattern is a rapid pressure drop perpendicular to the cavity axis followed by the logarithmic radial flow around the borehole.
Summary An unconventional perforation-tunnel stability analysis is conducted in this work by separating the role of two independent factors on sand production: well pressure and local pressure gradient around a cavity Such a separation clarifies most of the phenomena observed during sand production in oil fields. Simple analytical solutions for poroelastoplastic materials allowed repeated calculations for a parameter sensitivity study. The results obtained should be used qualitatively because of some degree of simplification. Introduction Field observations have shown the following cases for sand production.Cavities, including boreholes, collapsed if the cavity or well pressures were too low. Collapse occurred while fluid was flowing but also, in some cases, without fluid flow.Sand tended to be produced with high flow rates.More sand tended to be produced after water cut.Sand production rate was normally high when the flow rate was being changed.For some cases, sand production could not be stopped even after the flow rate was lowered. In extreme cases, sand-up-a well filled with sand-occurred. No methods proposed by previous workers could consistently explain all the observed field phenomena because only one aspect of the problem was addressed. Note that some of the field observations are more affected by the local fluid force around a borehole while the others are more related to the well pressure and in-situ stress. Because of the obvious discrepancies between the field observations and the previously proposed methods, the present work used three fundamental steps:reexamination of the factors involved in cavity stability by parametric analysis,a parameter sensitivity study that uses a simple analytical method, anda quantitative study using a realistic numerical method. Steps 1 and 2 are covered in this paper; Step 3 is the topic of another paper. A dimensional analysis showed that factors affecting sand production from perforation cavities contain terms relating to boundary loads, such as well pressure and in-situ stress; fluid force, such as flow rate, permeability, fluid viscosity, relative permeabilities for two- or three-phase flow, and fluid saturation; rock deformation characteristics; rock strength characteristics; perforation cavity geometries and shot density; and cyclic loading (stopping and restarting flow). A parametric sensitivity study was conducted with analytical solutions for poroelastic and strain-hardening plastic materials. The results clarify conditions for two type of sand production that depend on the listed factors: one is affected dominantly by fluid force and hence is controllable by adjusting flow rate; the other is affected dominantly by high in-situ stress and low well pressure and hence is controllable by avoiding low well pressure with pressure maintenance. These studies emphasize that unfavorable relative permeability and loss of capillary bending tend to result in sand-production problems after water cut. This paper resolves the discrepancy of two conventional cavity criteria: one emphasizing fluid flow force or completion pressure 10551 and another emphasizing boundary load. Theory and Assumption. Deformation and Strength Characteristics of Sandstones Prone to produce Sands. Figs. 1 through 4 show typical deformation and strength data of sandstones prone to produce sand in a North Sea reservoir. These sandstones are ductile and deform continuously without a clear, discontinuous, sliding surface; experience significant strength increases with stress level; show significant hysteresis during unloading; and have similar failure envelopes and yield curves for both extension and completion triaxial loading paths that can be approximately expressed by two invariants (J2, J1). Such rock deformations fit well to a Mohr Coulomb type plasticconstitutive relation. Hence, a constitutive relation with a Mohr-Coulomb yield surface is applied in this work, together with linear work-hardening stress strains, as shown in Fig. 5. The slope and the yield points were varied, depending on the weakness and ductibility of a formation. During a well shut-in, a linear stress/strain relation is assumed from unloading until the stress state again exceeds the yield surface. Although the present plastic model is simple, the comparison of the theoretical curves shown in Fig. 5 reflects reasonably well the complex character of the friable rocks shown in Figs. 1 and 2. More complex elastoplastic and nonlinear elastic models can be selected from a menu of constitutive relations for fitting various complex experimental data for the numerical data published elsewhere. Fig. 3 shows the peak rock strength in the J2-vs.-J1 coordinate. The black and white dots indicate strengths for extension and compression loading paths. Note that, as shown in Figs. 1 and 2, the yield points are slightly lower than the failure strength; hence, the yield envelope is also similar to the failure envelope for a rela-tively small J1. Fig. 3 shows that the application of f= Jg(J1) to such weak rocks can be justified for both yield and strength envelopes. The technical problem in using a failure envelope expressed by stresses, however, is that it is very difficult to judge a failure point because the stress state remains unchanged as a result of the significance ductile yielding. In this work, a failure envelope expressed by a plastic strain is used, although the plastic strains at the failure point vary significantly, as shown in Fig. 4. Note that failure envelopes expressed by a plastic strain are basically similar to those expressed by the stress because the plastic strain can often be expressed by a yield surface that coincides with a failure envelope. Previous work showed that the yield envelope-may be expressed by J2-vs. -(max + min) relation instead of J2-vs. J1 relation for friable rocks. To check the validity, more than 60 friable plugs were sent to three service companies. Two service companies initially reported that deviatric stresses at yield points for a triaxial extension loading path-were smaller and hence were better fitted by the J2-vs.-(max+ min) relation. It was found, however, that the small deviatric stress at the yield point for an extension loading path was caused by nonuniform loading, which in turn caused premature yielding by bending. Data taken after correction of the nonuniform loading resulting from a small misalignment of the triaxial loading machine showed that both the yield and failure envelopes were better represented by a J2-vs,-J1 relation, as shown in Fig. 3, than by the J2-vs.-(max + min) Holt also showed that yield envelopes of friable rocks for both extension compression loading paths fit the J2-vs.-J1 relation rather than J2-vs (max + min) relation. It was found, however of yield envelopes expressed by J2 and J1 in this paper. Further study is necessary, however, to investigate the property of friable rocks because their behavior is generally complex. Parametric Analysis. The results of a parametric analysis of a single cavity existing in an infinite space are shown in Appendix A. SPEPE February 1989 P. 25^
Summary This paper provides a quick method to determine subsidence, compaction, and in-situ stress induced by pore-pressure change. The method is useful for a reservoir whose Young's modulus is less than 20% or greater than 150% of the Young's modulus of the surrounding formation (where the conventional uniaxial strain assumption may not hold). In this work, a parameter study was conducted to find groups of parameters controlling the in-situ stress, subsidence, and compaction. These parameter groups were used to analyze the numerical calculation results generated by a three-dimensional (3D), general, nonlinear, finite-element model (FEM). The procedure and a set of figures showing how to calculate the in-situ stress, subsidence, and compaction induced by pore-pressure changes are provided. Example problems are also included to prevent confusion on sign convention and units. This work showed that Geertsma's results, which are based on no modulus contrast between cap and reservoir rocks, should be extended to simulate more closely "real" reservoirs, which generally have distinct property differences between the cap and reservoir rocks. Highly porous and high-pressure North Sea reservoirs and tight sand formations surrounded by soft shale often fall into this category. The application is intended for sand-production control, casing buckling problems, design of hydraulic fracturing jobs, subsidence, and estimation of PV and formation damage resulting from permeability reduction during hydrocarbon production. Introduction The in-situ stress induced by pore-pressure change usually has been calculated on the assumption that a rock deforms uniaxially without inducing strain along the horizontal direction. The amount of subsidence was calculated by Geertsma, with the strain nuclei method. These calculations assume that a reservoir is thin, that its depth is reasonably great, and that its rigidity is close to that of the confining formation. However, statistics of field measurements has shown that many hydrocarbon reservoirs are thick or shallow or have elastic moduli that are significantly different from those of confining formations. For example, North Sea reservoirs often have static Young's moduli that are orders of magnitude smaller than those of the surrounding rocks before they are compacted because of hydrocarbon production, although the dynamic Young's modulus calculated from sonic logs may give only three to six times modulus contrast. Some tight formations in the U.S. also have rock several times more rigid than surrounding shale. When a hydraulic fracture, a sand-control process. a subsidence-control operation, or an evaluation of formation damage resulting from permeability reduction is conducted in such a reservoir, accurate information on the in-situ stress, reservoir compaction, or subsidence induced by pore-pressure changes helps in designing such operations. This work does not use or develop new mathematical techniques, but emphasizes two important issues. First, the common practice in the oil industry is to calculate PV compressibility, reservoir compaction, and in-situ stress change on the basis of reservoir-rock property data. However, this work emphasizes that some reservoirs also require the caprock property data to evaluate these quantities. Second, a quick method to evaluate PV compressibility, reservoir compaction, in-situ stress change, and subsidence has not been published previously. Although techniques to calculate these values are available, they require long times to run sophisticated simulation models. The purpose of this work is to provide a method for quick estimation of in-situ stress, compaction, and subsidence for a reservoir having simple geometry. A quick estimation of these values is often sufficient during the reservoir development stage because accurate reservoir descriptions are not available. Such a crude estimation is essential because the decisions on downhole and surface facility designs are made during the early stages of reservoir development. After more accurate reservoir descriptions are collected, however, we recommend that the 3D FEM be used for this work to get a better evaluation. The model can handle various complex problems, such as multilayer problems with heterogeneous rock properties, inclined reservoirs, irregular reservoirs, nonuniform pore pressure, nonlinear properties of rock, hysteresis effect of cyclic loading, and nonuniform reservoir pressure. Assumptions and Calculation Methods The in-situ stress is decomposed into two parts-original in-situ stress and-in-situ stress induced by pore-pressure change. ................................ (1a) and ............................ (1b) where K is the stress-ratio coefficient affected by rock grain shape, grain-size distribution, sedimentation process, present Poisson's ratio, tectonic force, temperature, and pore pressure. Delta sigma and delta sigma are in-situ stress components induced by pore-pressure change. If the pore-pressure change occurs over several years, we can reasonably assume that rock deforms elastically during the period. In addition, if the pore-pressure change is reasonably small and the state of stress is not far from hydrostatic-i.e., a small deviatoric stress-then a linear elastic deformation is a good approximation. Hence, a linear elastic deformation is assumed in this work for the calculation of delta sigma and delta sigma induced by the pore-pressure change. A disk-shaped reservoir is assumed for the present calculation as shown in Fig. 1. Although the moduli of the reservoir and the surrounding formation may vary within each formation, uniform moduli are assumed within both structures, respectively. The reservoir is located at depth D below the surface and its radius and height are r and h, respectively. More complex reservoir geometries require that data be entered directly into the 3D FEM used for the present calculations. Fig. 2 shows the finite-element meshes used for this work. The upper surface is free from a traction force, and the bottom surface is fixed to the rigid base rock. Infinite elements were used for the outer boundary. The hatched section is the reservoir and has elastic moduli different from those of surrounding formations. The pore pressure of the reservoir section is reduced to calculate the deformations and stress change of the reservoir and surrounding formations. Test runs were conducted for a well with and without a casing cemented to the borehole. JPT P. 9^
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