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Production Induced Compaction of the Brent Field: An Experimental Approach

P.M.T.M. Schutjens, H. de Ruig, C.M. Sayers*, and J.G. van Munster, Shell Intl. E&P B.V, and J.L. Whitworth,** Shell U.K. E&P Summary The most attractive option to increase hydrocarbon recovery from the Brent and Statfjord reservoirs (Brent field, North Sea) is a gradual decrease of the reservoir fluid pressure. To provide laboratory data upon which estimates of the resulting reservoir compaction and surface subsidence could be made, we performed uniaxial compaction experiments at room temperature and in-situ stress conditions. Experimental observations suggest that the reloading of core samples to in-situ stress conditions closed coring-induced microcracks. Most Brent samples (porosity 6% to 30%) showed a compressibility that was constant with increasing effective stress (i.e., linear compaction) and increased with porosity. There was 30% to 75% strain recovery during unloading and an average permanent shortening of about 0.7%. Some high-porosity (25% to 30%) Brent samples showed a relatively high uniaxial compressibility that increased with stress (nonlinear compaction). Nearly all the Statfjord samples showed nonlinear compaction. The Statfjord samples from Core A, with a porosity of 8% and 20% to 22%, showed about 45% strain recovery upon unloading and an average permanent shortening of 0.6%. The Statfjord samples from Core B (porosity 22% to 28%) showed only 24% strain recovery and an average permanent shortening of 3.2%. Microscopy analysis of the Brent samples revealed no evidence for a compaction-induced change in microstructure. In contrast, the Statfjord samples from Core B (22% to 28% porosity) displayed numerous intergranular and transgranular cracks in quartz and feldspar grains, which probably triggered grain sliding and grain rotation. These inelastic brittle mechanisms, which occur together with elastic deformation of the load-bearing grain framework, seem dominant in high-porosity (Statfjord-type) sandstones and should be incorporated into predictive models of productioninduced compaction of quartz-rich reservoir rock. Introduction Up to now, the reservoir pressure in the Brent field (North Sea) has been maintained close to its initial value of 380 bar, primarily by water injectors positioned in the aquifer.1 To enhance the gas and oil recovery and extend the life of the Brent field, the water injection is planned to be stopped.2 The resulting depressurization of the reservoir fluid with ongoing production (depletion) is expected to oversaturate the oil inside and above the water-bearing zone with gas. The solution gas becomes mobile under these conditions and migrates vertically to the producing wells at the crest of the field, thereby remobilizing the bypassed and residual oil.2 Assuming homogeneous reservoir depressurization and assuming no compaction-induced horizontal tensile stresses in the overburden (stress arching), the planned decrease in pore fluid pressure in the Brent field from 380 bar to 70 bar will increase the average in-situ effective vertical stress (effective stress is defined here as the total--far-field--stress minus the pore fluid pressure) from about 190 bar to 500 bar. This leads to grain deformation and grain sliding/rotation, resulting in compaction (densification) and porosity reduction.3,4 Reservoir compaction in the Brent field could have an impact on the wave-height safety margin of the

*Now with Schlumberger Research, Cambridge, U.K. **Now with Petroleum Development Oman Copyright 1996 Society of Petroleum Engineers Original SPE manuscript received for review Nov. 21, 1994. Revised manuscript received April 19, 1996. Paper peer approved April 22, 1996. Paper (SPE 28096) first presented at the 1994 SPE/ISRM Rock Mechanics in Petroleum Engineering Conference held in The Netherlands, Aug. 29­31.

platforms and on the wellbore integrity.5­8 Therefore, it is important to predict how much reservoir compaction will occur with decreasing fluid pressure. This prediction requires knowledge of the rock's compressibility under the stress/strain conditions in the depleting reservoir. Given the large horizontal extension compared to vertical thickness and the depth of burial of the Brent and Statfjord reservoirs, we assume that reservoir compaction only occurs in the vertical direction and not in the horizontal direction (uniaxial compaction). Our study aimed to measure the uniaxial compressibility of core samples taken from the Brent reservoir and the underlying Statfjord reservoir in laboratory deformation experiments. We studied the variation in uniaxial compressibility between Brent and Statfjord samples, as well as the influence of porosity and effective axial (+vertical) stress on compressibility. These data can be used to set up empirical relationships describing compressibility as a function of lithology, porosity, and increasing effective axial stress (i.e., decreasing pore fluid pressure). However, extrapolation of these empirical relationships to predict reservoir compaction under field depletion conditions (i.e., at a different temperature, loading rate, and possibly also at a different horizontal stress state) requires that the compaction mechanism, or combination of compaction mechanisms, be the same in the laboratory as in the field. With this in mind, and to guide the development of mechanism-based models for production-induced reservoir compaction, we also attempted to identify the compaction mechanism(s) active in Brent and Statfjord core samples when these are compacted in the laboratory. The compressibility measurements were preceded by ultrasonic wave velocity measurements using samples from the Brent reservoir to investigate whether core damage had occurred. The results of these studies will be given first, followed by the results of the compaction experiments, some general considerations on the prediction of production-induced compaction, and a brief description of the application of the present data to the prediction of Brent compaction. Core Damage Investigation Introduction. It is important to determine whether coring-induced damage is present in cores before the experimental results are used to predict the compaction of the in-situ reservoir rock. Assuming core damage in the form of intergranular (and also possibly intragranular) microcracks, we investigated the dependence of the anisotropy in the ultrasonic compressional wave velocity, vp , on isostatic confining stress, s, following Teufel's approach.9,10 Sample Selection. We selected six cylindrical core pieces from a vertical core taken from the Brent reservoir. The diameter of the core pieces ranged from 7 to 7.5 cm. The length of each piece was about 10 cm. The core pieces were well-consolidated sandstones mainly composed of quartz (40% to 70%) with feldspar, clay, muscovite, biotite, siderite, and pyrite in different concentrations. The porosity was in the range of 10% to 28% (the percentages in this paper are always expressed with respect to the bulk sample). In all six samples, a sedimentary layering was present. In Cores R8, R9, and R10, it consisted of centimeter-thick yellow layers rich in quartz (u60%) with some feldspar (5% to 15%), alternating with dark streaks rich in clay, siderite, and mica. These streaks were either of irregular (wavy) shape and 0.5 to 1 cm thick, or laminated on a millimeter scale. Optical microscopy revealed that grains of mica, clay, and quartz were preferentially oriented parallel to the bedding plane. Cores R1, R5, and R7 appeared to be homogeneous sandstones when inspected with the naked eye, but computer tomography (CT) images revealed a layered-density variation. The angle between the

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normal to the sedimentary layering and the core axis was more or less constant in the individual samples, and ranged from 11° (Sample R9) to 28° (Sample R7). Cubes with an edge length of 45 mm were sawn from the core pieces. The normals to the cube faces were termed X1, X2, and X3. Three cubes were prepared with X1 perpendicular to the dipping sedimentary layering (Samples R5, R8, and R9). The three other cubes were prepared with X1 parallel to the core axis (i.e., the vertical direction, Samples R1, R7, and R10). The cube faces were mechanically polished using sandpaper of decreasing grain size until the opposite faces were parallel to within 30 mm. Experimental Method. Equal loads were applied in all three directions perpendicular to the cube faces in a true triaxial-loading apparatus (see Ref. 11 for a detailed description). In this way, a near-isostatic stress was applied to the cubical samples. Pressurization occurred in a stepwise manner, with steps of 50 bar (about 10 kN) applied at a rate of about 5 bar per minute. About 5 minutes after a given confining stress was achieved, consecutive vp measurements were made along the three principal stress directions (i.e., perpendicular to the cube faces). The confining stress was incrementally increased until the samples started to fail at the corners, which occurred at confining stresses in the range 580 to 1310 bar. The samples were kept dry during the entire experiment. Results. Fig. 1 shows the vp data as a function of isostatic confining stress. In all six experiments, vp increased nonlinearly with increasing confining stress. In the range 25 to 300 bar, vp increased significantly faster with increasing confining stress than at confining stresses greater than 300 bar. Samples R5, R7, and R10 show a "cross-over" in vp measured in the X1, X2, or X3 direction at or below 300 bar. In Samples R5, R8, and R10 (porosity in the range 20% to 23%) the difference between the maximum and the minimum vp was too small to study the development of the vp -anisotropy on stress. In Sample R7 (with the highest porosity of 27.5%), the vp -anisotropy increased slightly with stress. The lowest-porosity samples, R1 and R9 (10.8% and 10.9% porosity), which contain most mica and clay, show the largest difference between the maximum and the minimum vp . In Sample R1, this difference decreases from 1.2 km/s at 50 bar to 0.6 km/s at 300 bar, and in Sample R9 from 2.0 km/s at 50 bar to 1.1 km/s at 300 bar (i.e., a decrease of about 50%). Fig. 2 shows the vp -anisotropy for these two samples, defined as the difference between the maximum and the minimum vp normalized to the average of the three vp measurements at that stress, as a function of the isostatic confining stress. We made two observations. First, the vp -anisotropy decreases with stress. Second, there is a clear change in the rate of decrease of the vp -anisotropy per unit increase in confining stress in both samples just below 300 bar (see arrow in Fig. 2). Interpretation. Anisotropic compressional wave velocities may result from fine-scale layering, a preferred orientation of nonspherical grains and anisotropic minerals, and the presence of oriented microcracks or fractures. At low-confining stress, any microcracks within the sample will be open and will contribute to the ultrasonic velocity anisotropy if the microcracks display a preferred orientation. However, at high­confining stress, microcracks or fractures will tend to close and the principal directions of the elastic stiffness tensor will be determined by the textural anisotropy of the rock, which results, in these samples, principally from the sedimentary layering. According to Teufel,9 the vp -anisotropy caused by an anisotropic distribution of the microcrack orientations will decrease or disappear when microcracks close with increasing isostatic confining stress. In contrast, a vp -anisotropy caused by a compositional or a textural inhomogeneity is expected to remain present. It is seen in Fig. 1 that the vp anisotropy for samples R5, R7, R8, and R10 is small and does not change dramatically with increasing confining stress. This may result either from the absence of any microcracks due to coring or from the microcracks being randomly oriented. Only the lowest porosity samples R1 and R9 (10.8% and 10.9% porosity) show a significant vp anisotropy, and this is reduced by 50% on increasing the isostatic compression from 50 to 300 bar.

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The nonlinear increase of vp with increasing confining stress observed in all samples suggests that the average contact surface area between adjacent grains increases nonlinearly with stress. The relatively high dependence of vp on confining stress up to 300 bar observed in all samples (Fig. 1), and the strong reduction of vp -anisotropy observed in Samples R1 and R9 at confining stresses up to 300 bar (Fig. 2) suggest that the increase in average grain contact area at relatively low stress may be enhanced by a stress-induced closure of intergranular cracks.12,13 Some of these microcracks may well have formed during coring of the rock from the reservoir. In that case, the confining stress on the Brent samples should be above 300 bar to minimize the impact of coring-induced microcracks on rock compaction measured in the laboratory. With all six samples showing a sedimentary layering, the observation that only the lowest-porosity samples show a stress-induced decrease in acoustic anisotropy suggests that these samples may be more prone to core damage than the samples with a relatively high porosity. Compaction Experiments Experimental Method. Sample Preparation. Twenty-nine cylindrical samples with a diameter of about 25 mm were drilled parallel to the cylindrical axis of a vertical core drilled in the Brent reservoir. Eleven samples were also taken from two deviated cores from the Statfjord reservoir, termed Core A and Core B. Because the compressibility of Statfjord samples cored in three orthogonal directions was very similar (within 15%), we decided to take the samples parallel to the core axis and assume the compressibility in this Statfjord material to be independent of orientation. Most Brent samples were homogeneous yellow sandstone composed of quartz (u60%), feldspar (5% to 15%), and low concentrations (t5%) of mica (mainly muscovite), clay (illite and kaolinite), pyrite, and siderite. Some samples were shaly or laminated, and some were dark shaly sandstones. In nearly all Brent samples, a sedimentary layering was observed, with dips ranging from 5° to 35°. The Statfjord samples were all coarse-grained brown sandstones, mainly composed of quartz with some feldspar and lacking sedimentary layering. The cored samples were cut to a length of 30 mm using a diamond-impregnated circular saw, with the sample held in V-block fixtures to obtain parallel end-faces ("20 mm) at right angles to the cylindrical axis of the sample. We decided to compact the samples in the original (as-received, uncleaned) state to avoid possible disruption to the microstructure. The samples were saturated with artificial formation brine (composition shown in Table 1) at least 2 weeks before compaction to attain chemical equilibrium between grains and pore fluid. The sawn off end-pieces of the samples were cleaned of hydrocarbons and salts by extraction in an azeotropic mixture of chloroform, methanol, and water; then, we measured the porosity of the cleaned pieces. The porosity of the Brent samples was in the range 6% to 30%. The porosity of the Statfjord samples was in the range 20% to 28%, except for one sample with a porosity of 8%. Compaction Apparatus. Sample compaction was measured at the stress conditions, which are assumed to occur in the depleting Brent and Statfjord reservoirs, using a deformation apparatus equipped for simultaneous automated application of three independent stresses: (1) the total axial stress, stz , corresponding to the average total vertical (overburden) stress in the reservoir, (2) the total radial stress, str , corresponding to the average total horizontal stress, and (3) the pore fluid pressure, Pp , corresponding to the pressure of the fluid in the pores of the reservoir rock. The sample was enclosed in an impermeable elastomer sleeve (thickness 1.5 mm) and placed between a fixed bottom piston and a moveable top piston, both having a straight eccentric hole (diameter 3 mm) through which fluid could come into contact with the sample. The total axial stress was applied by hydraulically forcing the top piston downwards. The total radial stress was applied by increasing the pressure of the oil in the pressure vessel, which was transmitted to the sample by means of the elastomer sleeve. The pore fluid pressure was applied by pressurizing the fluid in the hole of the top piston. During an experiment, the pressure of the fluid in

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Fig. 1(a-f)--The compressional wave velocity (vp ) measured perpendicular to the faces of Brent cubical samples as a function of isostatic confining stress (s). In Samples R1, R7, and R10, the circles (v1) are the vp measurements in a direction parallel to the cylindrical axis of the core; the squares and triangles (v2 and v3) are the vp measurements parallel to the strike and parallel to the azimuth of the sedimentary layering (i.e., the bedding plane), respectively. In Samples R5, R8, and R9, the circles (v1) refer to the vp measurements made perpendicular to the sedimentary layering; the squares and triangles (v2 and v3) are the vp measurements perpendicular to each other within the layering. Note the change in the dependence of vp on s around 300 bar in most curves.

both top and bottom piston hole was measured to check whether there was pore pressure communication in the sample during compaction. Two permeable stainless steel endplates, each about 1.5 mm thick, were placed between sample and pistons to prevent clogging of the piston holes with sample material. Changes in the sample length were measured using the relative vertical displacement of two steel rods (diameter 3 mm) placed in straight concentric holes in the top and bottom piston and connected to the permeable plates covering the top and bottom of the sample. A rectangular steel frame, suspended in such a way as to be independent of the pistons, served to transmit the relative movement of the rods to a linear variable displacement transformer located beneath the pressure vessel. In this way, the shortening or lengthening of the sample was measured with an estimated precision of 1 mm. A change in the diameter of the sample was measured using a half-circular clip with strain gauges glued to both sides. This clip was clamped onto two pins with curved faces that pierced the elastomer sleeve on opposite sides of the sample to be in direct contact with it. During loading under uniaxial strain conditions, the strain gauge signal served to adjust the radial pressure pump in such a way that the total radial deformation was minimized. The raw radial displacement data were corrected for the effect of oil pressure on the strain gauge before the signal was used as a reference for the pump. Calibration tests on stainless steel and aluminium samples showed that the radial displacement under uniaxial strain conditions could be maintained within 1 mm. Compaction Method. The compaction experiment consisted of two phases. First, the sample was gradually loaded to the effective stress conditions inferred to be present in the reservoir before production (Phase 1). Starting from an effective axial stress of 190 bar and an effective radial stress of 95 bar, the effective axial stress was increased under uniaxial strain conditions (only axial compaction, no radial deformation) at a constant rate of about 70 bar/hr (Phase 2). In 22 experiments, the increase in the effective axial stress occurred by

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decreasing the pore fluid pressure under a constant total axial (overburden) stress (i.e., DPp 00, Dstz +0). In the other 18 experiments, the axial permeability was too low (t1 mD) to attain pore fluid pressure equilibrium between top and bottom of the sample over the duration of the experiments (hours). In these tests, the effective axial stress was increased by increasing the total axial stress at a constant pore fluid pressure of one atmosphere (Dstz 00,DPp +0). All experiments were done at room temperature. Calculation of Uniaxial Compressibility. The raw data set contained axial and radial displacement, total axial stress, total radial stress, and the (pore) fluid pressure above and below the sample as

Fig. 2--The dependence of the anisotropy of the compressional wave velocity (vp ) on confining stress (s) in Sample R1 and R9. Note the strong decrease of the vp with increasing confining stress at stresses from 25 to 300 bar. Arrow indicates transition of dependence vp of s on around 300 bar. 101

TABLE 1--PORE FLUID COMPOSITION

Salt NaCl Na2SO4 KCl CaCl2.2H2O MgCl2.6H2O BaCl2.2H2O

Concentration (mg/l) 23230 49 324 954 544 69

bar­1, which is significantly higher than the compressibility obtained on the Statfjord sample from Core A (Fig. 4a) or on the highporosity Brent samples (Fig. 3c). All Statfjord Core-B samples show a strong nonlinear compaction, leading to progressive weakening of the samples with increasing stress/strain. The axial strain recovered during unloading ranged from 15% to 33% (average 24%) of the axial compaction strain recorded at maximum effective axial stress, yielding a ratio of elastic vs. inelastic strain of about 0.2 to 0.5 (average 0.3). The inelastic strain of the high-porosity

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a function of time. The raw axial displacement data were first corrected for axial deformation of the end plates. The uniaxial compressibility, c, was then calculated as follows. The effective axial stress, sez , applied during uniaxial compaction was subdivided into sequential intervals of Dsez of about 50 bar. From the corrected axial displacement (DL, i.e., the true change in sample length) over these stress intervals and from the sample length, L0, at the start of uniaxial compaction, c, was calculated according to c + 1 · DL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1) L 0 Ds ez Mechanical Data Brent Samples. Fig. 3 (a-c) shows the uniaxial compressibility of the 29 samples from the Brent reservoir as a function of effective axial stress in the range 200 to 480 bar, divided according to porosity before compaction (t10%, 10% to 20%, and u20%). The different compaction experiments are indicated with different symbols. The compressibility values obtained from the pore pressure depletion tests do not cluster themselves any differently than the compressibility values obtained from the tests in which the total axial stress was increased at constant pore pressure. Therefore, no distinction was made between the data obtained in these two types of tests. We made four observations. First, the uniaxial compressibilities are in the range 5 10­6 bar­1 to 4 10­5 bar­1, but the majority of them fall in the range 1 10­5 bar­1 to 3 10­5 bar­1. Second, the uniaxial compressibility appears to increase with increasing porosity (compare Fig. 3a with Fig. 3c; but note also the considerable spread in uniaxial compressibility obtained over a given effective axial stress interval: 1 10­5 bar­1 to 2 10­5 bar­1). Third, most experiments show a more or less linear stress-strain relationship, yielding approximately constant uniaxial compressibility values over the range of effective axial stress (200 to 480 bar). Some highporosity (25% to 30%) Brent samples show a relatively high uniaxial compressibility that increases with stress, i.e., the samples become weaker with increasing stress (nonlinear compaction, see arrow in Fig. 3c). Fourth, the axial strain recovered during unloading was 30% to 75% of the total axial compaction strain recorded at maximum effective axial stress, resulting in a ratio of elastic (recoverable) vs. inelastic (permanent) strain ranging from 0.4 to 3.0 (average 1.3). In 18 of the 29 Brent samples, the elastic compaction was larger than the inelastic compaction. The inelastic compaction of the Brent samples was in the range 0.3% to 1.5% (average 0.7%). No sample fracturing was observed. Statfjord Samples. The uniaxial compressibilities of the samples from Statfjord Core A (porosity 8% and 20% to 22%) and from Statfjord Core B (porosity 22% to 28%) are displayed in Figs. 4a and 4b, respectively, as a function of the effective axial stress. The compaction behavior of the Core-A samples is very similar to that of the Brent samples: uniaxial compressibility values in the range from 7 10­6 bar­1 to 3 10­5 bar­1, 30% to 60% strain recovery during unloading (average 45%), and an inelastic strain of 0.3% to 1.2% (average 0.6%). However, three of the four samples showed nonlinear compaction. No sample fracturing was observed. Fig. 4b shows the uniaxial compressibility obtained for the seven relatively high-porosity (22% to 28%) samples from Statfjord Core B as a function of effective axial stress. Note that the compressibility is plotted with a different ordinate scale than in Figs. 3 and 4a. The uniaxial compressibility is in the range 2 10­5 bar­1 to 12 10­5

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Fig. 3--The uniaxial compressibility obtained on 29 samples from the Brent reservoir as a function of effective axial stress in the range 200 to 480 bar, subdivided according to initial porosity. Fig. 3a:t10%; Fig. 3b: 10-20%, Fig. 3cu20%. Each experiment has its own symbol. Compressibility values were calculated over 50-bar intervals of effective axial stress.

SPE Formation Evaluation, June 1996

Fig. 5--The uniaxial compressiblity data obtained on the Brent and Statfjord core samples as a function of porosity. Open squares+Brent data; large closed circles+Statfjord Core A; small closed circles+Statfjord Core B. Note that from each experiment four or five datapoints are plotted at the same initial porosity, representing the compressibility values calculated over 50-bar intervals of increasing effective axial stress. Note that above 20% porosity, the increase in average compressibility with increasing porosity is stronger for the Statfjord Core-B samples than for the Brent samples.

tion during diagenesis.14 Although considerable stress-magnification must have occurred at these intergranular contact surfaces during burial, no transgranular (cross-cutting) cracks and only very few intragranular (inside-grain) cracks were observed in the original material.

Fig. 4--The uniaxial compressibility as a function of effective axial stress obtained on 11 Statfjord samples, subdivided in 4 relatively low-porosity samples (Core A: 8% and 20-22%, Fig. 4a) and 7 relatively high-porosity samples (Core B: 22-28%, Fig. 4b, note different range of ordinate). Each experiment has its own symbol. Compressibility values were calculated over 50-bar intervals of effective axial stress.

Statfjord samples was about 2.5% to 5% (average 3.2%). Despite this high strain, no sample fracturing was observed. Brent and Statfjord (Cores A and B). Fig. 5 presents all uniaxial compressibility values obtained from the Brent and Statfjord samples as a function of the porosity measured on the sample end-pieces at atmospheric conditions. Note that for each experiment, four or five datapoints are plotted at the same porosity, representing the uniaxial compressibility values at the different intervals of increasing effective axial stress. The data suggest that, for porosity in the range 5% to 20%, the uniaxial compressibility is in the range 1.3 ("0.8) 10­5 bar­1 and independent of porosity. However, for samples with a porosity in the range 20% to 30%, the uniaxial compressibility increases with increasing porosity. For the Statfjord samples, this increase of uniaxial compressibility with increasing porosity is stronger (factor 2 to 4) than for the Brent samples (about a factor 1.5). During uniaxial compaction, the ratio of the change in effective radial stress to the change in effective axial stress was more or less constant in individual experiments, and in the range 0.05 to 0.3. Microstructural Analysis Original Samples. The original and compacted Brent and Statfjord samples were inspected with the optical microscope and with the scanning electron microscope (SEM) to identify the active compaction mechanisms. The original samples showed abundant tangential (i.e., long) contacts between adjacent quartz-quartz and quartz-feldspar grains, indicating the operation of intergranular pressure soluSPE Formation Evaluation, June 1996

Compacted Samples. For the Brent samples showing the constant uniaxial compressibility with increasing stress (see Fig. 3), the microstructure of the original samples could not be discerned from that after compaction. However, for those Statfjord samples showing the nonlinear compaction weakening, a clear difference was observed between the microstructure before and after experimental compaction. Fig. 6a shows the typical microstructure of a Statfjord sample from Core B in the as-received state (porosity 28%). Fig. 6b shows the microstructure of the twin sample after the experimental compaction, which was very nonlinear and resulted in a permanent axial shortening of 3.5%. About 30% of the quartz grains in the compacted Statfjord samples show cracks. As noted above, these were rare in the original material. Most microcracks are aligned with their long dimension in the direction of the effective axial stress (i.e., along the sample axis). Both intragranular and transgranular cracks were observed (Figs. 6c and 6d). The intragranular cracks either terminate at grain boundaries or at grain centers. Radiating "fans" of (often curved) microcracks, originating at grain-to-grain contacts, were also observed. About 50% of the feldspar grains showed multiple fractures, oriented preferentially along crystallographic planes. The transgranular cracks rarely continue in adjacent grains. Some evidence was found for transgranular crack formation in combination with intergranular sliding and the generation of small (<10 mm) rock fragments (fines). Interpretation. The mechanical data indicate that compaction of samples from the Brent reservoir occurs by elastic and inelastic deformation of the load-bearing grain framework. In 18 of the 29 Brent samples, elastic deformation is dominant. Under our experimental conditions (room temperature, high-loading rates), the most likely inelastic compaction mechanism is grain breakage with grain rotation/sliding;15­17 nonetheless, no evidence for this was found. The Statfjord Core-B samples show a much higher uniaxial compressibility than the Brent samples and the Statfjord Core-A samples. They also show a strong nonlinear compaction, a relatively

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bination of elastic (recoverable) and inelastic (permanent) compaction of the load-bearing grain framework. Elastic deformation comprises (Hertzian) grain contact deformation, elastic crystal lattice deformation, and elastic crack opening/closure. Inelastic deformation mechanisms include grain fracturing and grain rotation/ sliding, intergranular pressure solution, stress-driven motion of atoms through the crystal lattice (intracrystalline diffusion), and stress-driven motion of crystal dislocations (intracrystalline plasticity). Two points should be noted regarding inelastic compaction. First, there is general agreement in the literature that at temperatures below 250°C, intracrystalline diffusion and intracrystalline plasticity are unimportant in quartz-rich sandstone.20,21 Second, inelastic compaction may show a time dependence. At temperatures below 250°C, one of the following mechanisms controls its rate in sandstones: (1) time-dependent microcracking, resulting from subcritical crack growth by stress-corrosion,22,23 or (2) intergranular pressure solution.14,24 Regarding the extrapolation of experimental compressibility data to predict depletion-induced compaction at in-situ reservoir conditions, the following main differences between the laboratory and the field should be reconciled. First, the loading rate in the laboratory experiment (50-500 bar/hour) is typically 4 to 6 orders of magnitude greater than the loading rate exerted on the reservoir rock by typical depletion rates of 5 to 50 bar/year. Second, the temperature in the laboratory experiment (here, 20°C) is often lower than in the reservoir (typically 100-200°C). Over the past three decades, both timedependent microcracking and intergranular pressure solution have been the subject of intensive experimental and theoretical research,24­26 but there is still no experimentally verified constitutive relationship to describe or predict compaction and deformation by these mechanisms as a function of time (loading rate) and temperature. Given the absence of a theoretical framework, extrapolation of experimental compressibility data to different conditions is hazardous, and hence the prediction of reservoir compaction is fraught with assumptions. If elastic and/or time-independent inelastic compaction dominates over time-dependent inelastic compaction mechanisms in the experiment (as it does in most Brent and Statfjord Core-A samples), a pseudo-elastic (i.e., macroscopically linear) reservoir compaction may be observed, which can be approximated using Eq. 2. However, time-dependent, thermally activated, inelastic mechanisms like stress corrosion cracking and intergranular pressure solution may also occur. Compared to the laboratory experiment, their contribution to the total strain will increase with decreasing loading rate and increasing temperature. In other words, from laboratory to field, there will probably be a loading rate/temperature-induced increase in the relative importance of time-dependent inelastic compaction at the expense of time-independent inelastic compaction. Consideration of such a shift may be particularly important when one is predicting reservoir compaction in relatively deep (u4 km) and hot (150-200°C) reservoirs or in overpressurized reservoirs with an under-compacted and thus friable microstructure prone to inelastic compaction. When one is using Eq. 2, it is therefore useful to make mention of the loading rate and temperature at which the uniaxial compressibility was measured and to emphasize that its magnitude will probably increase with decreasing loading rate and increasing temperature (i.e., towards more reservoir-realistic conditions). The high-porosity Statfjord samples from Core B showed clear evidence of pervasive inelastic brittle deformation by nucleation and propagation of intra- and intergranular microcracks, which triggered intergranular sliding and grain rotation. It is unknown to what extent the relative importance of this type of brittle compaction will change with decreasing loading rate. Nevertheless, in models for production-induced compaction of high-porosity (u20%) sandstone like Statfjord, the operation of such inelastic brittle mechanisms--both time-independent and time-dependent--should be incorporated. In addition to this, more experiments should be done with reservoir core to identify which time-independent and time-dependent inelastic compaction mechanisms occur as a function of variables like lithology, microstructure, temperature and depletioninduced change in reservoir stress change.

SPE Formation Evaluation, June 1996

Compaction in the Brent Field. The planned decrease in average fluid pressure in the Brent field from 380 bar to 70 bar will increase the average in-situ vertical effective stress from the present value of about 190 bar to 500 bar.2 With such a strong increase in vertical effective stress, compaction of the Brent and Statfjord reservoirs is highly likely and could result in significant subsidence at the seabed surface and severe damage to wells. Prediction of the magnitude of the seabed subsidence has therefore been an important part of assessing the risks and narrowing the uncertainties associated with reservoir depletion.2 The present laboratory results (obtained at a loading rate of 70 bar/hour and room temperature) were used in an approach to predict reservoir compaction and resulting surface subsidence. The dependence of vertical reservoir compressibility on effective stress was obtained from experimental data such as those shown in Figs. 3 and 4. The compressibility-porosity relationships were determined from experimental data, such as those shown in Fig. 5. Using wireline petrophysical data and core analyses from wells close to the platforms, the porosity distribution of sands and shales within the Brent and Statfjord reservoir was determined. On the basis of these data, the expected total reservoir compaction under each of the four platforms was calculated for a given incremental decrease of the reservoir fluid pressure. To predict how this reservoir compaction would translate to surface subsidence, a 2D finite-element cross-sectional model was used, developed by M.A. Hicks and colleagues at the U. of Manchester (U.K.). Monte Carlo simulations, in which probability distributions were sampled for all input parameters, were then used to estimate the sensitivities for the overall results and to assess the uncertainties quantitatively. Finally, the Brent reservoir simulator was used to model the decrease of the reservoir fluid pressure and a subsidence-vs.-time prediction was constructed. In parallel to the modeling work, a campaign of monitoring both compaction and subsidence has been initiated; the data from the monitoring program will be used to compare actual vs. predicted subsidence. The monitoring takes two approaches. 1. Radioactive marker bullets are to be shot into the entire thickness of each reservoir in at least one well per platform. The bullet locations are measured on a time-lapse basis using a new gammaray tool. Any changes observed in bullet separation will be compared with the predictions for reservoir compaction.5 2. Surface subsidence will be measured directly using modern global positioning system satellite technology. After a base survey conducted before depressurization starts, the elevation of a number of fixed points on each platform will be regularly measured. Platform height above sea level will also be monitored on a regular basis by using microwave methods. Although less accurate than the satellite positioning measurements because of variation in sea level and wave height, these direct air gap measurements are expected to provide useful information on trends in the subsidence rates. During depressurization, both subsidence and compaction will be compared with predictions and the rate of depressurization will be modified if necessary. In addition to the subsidence prediction, the same compressibility/porosity relationships were used in models to assess the effect of reservoir compaction on wellbore stability and casing integrity. The results indicate that problems are only likely to arise in one particular formation--and then only if there is no cement in place behind the casing. Conclusions 1. A decrease in the anisotropy of the compressional wave velocity with increasing isostatic confining stress, which was observed in two low-porosity samples from the Brent reservoir in the range 25 to 300 bar, was interpreted to be partly caused by the stress-induced closure of intergranular cracks that were opened during coring. 2. The uniaxial compressibility of the 29 Brent reservoir samples is in the range 1.3 ("0.8) 10­5 bar­1 (porosity 6% to 20%) to 2.3 ("1.0) 10­5 bar­1 (porosity 20% to 30%). The uniaxial compressibility of the 11 Statfjord reservoir samples ranges from 7 10­6 bar­1 to 3 10­5 bar­1 for samples with a porosity of 8%

105

and 20% to 22%, and from 2 10­5 bar­1 to 12 10­5 bar­1 for samples with a porosity in the range 22% to 28%. 3. The uniaxial compressibility of the Brent and Statfjord samples depends on porosity. For the Brent samples, the uniaxial compressibility of high-porosity samples with porosity between 20% and 30% is roughly a factor 1.5 greater than for lower-porosity samples (6% to 20%). For the Statfjord samples, the uniaxial compressibility of high-porosity samples (22% to 28%) is roughly a factor of 2 to 4 times greater than for samples with a porosity of 20% to 22%. 4. Most Brent samples (porosity 6% to 30%) showed a compressibility that was constant with increasing effective stress (i.e., linear compaction) and increased with porosity, 30% to 75% strain recovery during unloading and a permanent shortening of about 0.7%. Some high-porosity (25% to 30%) Brent samples showed a relatively high uniaxial compressibility that increased with increasing stress (nonlinear compaction). 5. The two series of Statfjord samples (from Core A and Core B) showed very different compaction behavior. The compaction behavior of the Statfjord Core-A samples was very similar to that of the Brent samples: uniaxial compressibility values in the range from 7 10­6 bar­1 to 3 10­5 bar­1, 30% to 60% strain recovery during unloading, and an average inelastic strain of about 0.6%. Three of the four samples showed nonlinear compaction. 6. The Statfjord Core-B samples showed the highest uniaxial compressibility values: 2 10­5 bar­1 to 12 10­5 bar­1, a strong nonlinear compaction, only some 24% axial strain recovery, and an average inelastic strain of about 3.2%. Despite this high inelastic strain, no sample fracturing was observed. 7. The compaction of most of the Brent samples and of some of the Statfjord Core-A samples was dominated by elastic deformation of the load-bearing grain framework. In contrast, compaction of the high-porosity (22% to 28%) Statfjord Core-B samples was mainly inelastic and involved a widespread development of intragranular and transgranular microcracks, in combination with intergranular sliding and grain rotation. 8. The nonlinear compaction of the Statfjord samples may be explained by a progressive crack-induced reduction of the surface area of the load-bearing grain framework with increasing effective axial stress. 9. Models of production-induced compaction of high-porosity (u20%) sandstone like Statfjord should incorporate inelastic brittle mechanisms. 10. More experiments are required to evaluate the potential of time-independent and time-dependent inelastic compaction mechanism(s) during reservoir depletion with confidence. A first step in this direction may be the construction of empirical relationships expressing the dependence of compressibility on loading rate (time), temperature, stress state, and stress path under anticipated reservoir depletion conditions. Nomenclature c = uniaxial compressibility (zero radial strain, bar­1) L0 = sample length at start of experiment (m) H0 = reservoir thickness at start of depletion (m) Pp = pore fluid pressure (bar) s = isostatic confining stress (bar) sez = effective axial stress (bar) on the sample sev = effective vertical stress (bar) on the reservoir str = total radial stress (bar) stz = total axial stress (bar) vp = ultrasonic compressional wave velocity (m/s) Xi = direction normal to cube face i Acknowledgments The authors would like to thank Shell Intl. E&P B.V., Shell U.K. E&P, and Esso E&P U.K. Ltd. for their permission to publish this paper. We would also like to thank G. Tootill, M. Prins, C.I.M. Braithwaite, Y. Bernabé, G. Greenwell, and two anonymous reviewers for their valuable comments on the manuscript.

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References

1. Livera, S. and Gdula, J.E.: "The Brent Oil field," Beamont, E.A. & Foster, N.H. (compilers). "Structural Traps II. Traps associated with tectonic faulting," A.A.P.G. Treatise for Petr. Geology. Atlas of Oil and Gas Fields (1990) Vol. A017, 21­63. 2. Braithwaite, C.I.M. and Schulte, W.M.: "Transforming the future of the Brent field: Depressurisation--The Next Development Phase," paper SPE 25026 presented at the EUROPEC, Cannes, November 16-18, 1992, 95­106. 3. Martin, J.C. and Serdengecti, S.: "Subsidence over oil and gas fields," Geol. Soc. Am. Reviews in Engng Geol. (1984) 6, 23­34. 4. Schutjens, P.M.T.M., Fens, T.W. & Smits, R.M.M.: "Experimental observations of the uniaxial compaction of quartz-rich reservoir rock at stresses of up to 80 MPa," In Barends, F.B.J., Brouwer, F.J.J. & Schröder, F.H. (eds): Land Subsidence Proceedings of the Fifth International Symposium on Land Subsidence, The Hague, the Netherlands (16­20 October 1995). Published by the International Association of Hydrological Sciences, No. 234. 5. Doornhof, D.: "Surface subsidence in the Netherlands: the Groningen gasfield," Geologie & Mijnbouw (1992) 71, 119­130. 6. Sulak, R.M. and Danielsen, J.: "Reservoir aspects of Ekofisk subsidence," JPT (1989) 709­716. 7. Yudovich, A., Chin, L.Y. and Morgan, D.R.: "Casing deformation in Ekofisk," Proc. Offshore Technology Conf. Houston, Texas, OTC (1988) 5623, 63­72. 8. Bruno, M.S.: "Subsidence-Induced Well Failure," DC (June 1992) 148. 9. Teufel, L.W.: "Determination of in-situ stress from anelastic strain recovery measurements of oriented core," (1983) paper SPE 11649 presented at 1983 SPE/DOE Symp. on Low Permeability Reservoirs, Denver, 14­16. 10. Sayers, C.M.: "Orientation of microcracks formed in rocks during strain relaxation," Techn. Note Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. (1990a) 27, 437­39. 11. Sayers, C.M., Van Munster, J.G., and King. M.S.: "Stress-induced ultrasonic anisotropy in Berea sandstone," Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. (1990b) 27, 429­36. 12. King, M.S.: "Wave velocities in rocks as a function of changes in overburden pressure and pore fluid saturants," Geophysics (1966) 31, 50­73. 13. Schutjens, P.M.T.M., Hausenblas, M., Dijkshoorn, M. and Van Munster, J.G.: "The influence of intergranular microcracks on the petrophysical properties of sandstone--Experiments to quantify effects of core damage," Paper presented at the 1995 Symposium of the Society of Core Analysts, San Francisco, USA, September 12­14 1995. 14. Houseknecht, D.W.: "Intergranular pressure solution in four quartzose sandstones," Journal of Sedimentary Petrology (1988) 58, No 2, 228­246. 15. Dunn, D.E., LaFountain, L.J. and Jackson, R.E.: "Porosity dependence and mechanism for brittle fracture in sandstones," J. Geophys. Res. (1973) 78, 2403­2417. 16. Scott, T.E. and Nielsen, K.C.: "The effect of porosity on the brittle-ductile transition in sandstones," J. Geophys. Res. (1991) 96, 405­414 17. Bernabé, Y, Fryer, D.T. and Shively, R.M.: "On the elastic and cataclastic behaviour of porous sandstones," Geophys. Jnl. Int. (1994) 117, 403­418. 18. King, M.S.: "Static and dynamic elastic moduli of rocks under pressure," In Somerton (ed.) Rock Mechanics--Theory and Practice. Proceedings of the Eleventh U.S. Symposium on Rock Mechanics, Society of Mining Engineers, New York (1969), Chapter 19, 329­351. 19. Teufel, L.W., Rhett, D.W. and Farrell, H.E.: "Effect of reservoir depletion and pore pressure drawdown on in situ stress and deformation in the Ekofisk Field, North Sea," in: Roegiers (ed.) Rock Mechanics as a Multidisciplinary Science (1991) Balkema, Rotterdam, 63­72. 20. Stocker, R.L. and Ashby, M.F.: "On the rheology of the upper mantle," Rev. of Geophys. and Space Physics (1973) 11, No 2, 391­426. 21. Heard, H.C. and Carter, N.L.: "Experimentally induced `natural' intragranular flow in quartz and quartzite," American Journal of Science (1968) 266, 1­42. 22. Costin, L.S.: "Time-dependent deformation and failure," In Fracture Mechanics of Rock, B.K. Atkinson (ed.) Academic Press (1987) 167­216. 23. Swanson, P.L.: "Subcritical crack growth and other time- and environment-dependent behaviour in crustal rocks," J. Geophys. Res. (1984) 89, 4137­4152. 24. Knipe, R.J.: "Deformation mechanisms--recognition from natural tectonites," J. Struct. Geol. (1989) 11, 127­146. 25. Lehner, F.K.: "A model for intergranular pressure solution in open systems," Tectonophysics (1995) 245, 153­170. SPE Formation Evaluation, June 1996

26. Atkinson, B.K. (ed.) Fracture mechanics of rock. (1987) Academic Press, London.

SI Metric Conversion factors ft 3.048 E*01 +m °F (°F*32)/1.8 +°C in. 2.54 E)00 +cm psi 6.894 E)00 +kPa bar E)01 +MPa

*Conversion factor is exact.

SPEFE

Peter Schutjens joined Shell Research Rijswijk to experimentally investigate causes and magnitudes of production induced res ervoir compaction. His research interests include compaction mechanisms in depleting deep sandstone reservoirs, fluid rock interaction, core damage, and the influence of microstructure on static and dynamic compressibility. Previously, he worked in the high pressure/high temperature laboratory of the Inst. of Earth Sciences at Utrecht U. on intergranular pressure solution as a compaction mechanism in halite aggregates and quartz sands. He received his PhD degree in 1991. Hessel de Ruig worked as a technical assistant in Shell Research for 34 years in the area of mud chemistry, PVT, and core analysis. His interests include compressibility of sandstones and the influence of com paction on permeability. Colin Sayers is a senior research scien tist in the Seismics Dept. of Schlumberger Cambridge Research. His research interests include wave propagation in heterogene ous and anisotropic media, velocity analysis, damage me chanics, and fluid flow in fractured media. Previously, he worked for Shell Research in the Netherlands and the Materials

Physics and Metallurgy Div. of the Atomic Energy Research Es tablishment, Harwell. He holds a PhD degree in physics from Im perial C., U. of London. Hans van Munster is an associate re search physicist at Shell. He began work at Shell in 1975 in the Instrumentation and Automation Dept., followed by research in rheology and soil mechanics. He is currently working in geome chanics and well technology, and he is involved in the applica tion and development of ultrasound and acoustic emission measurement techniques. John Whitworth is a senior explora tion petrophysicist with Petroleum Development Oman in Mus cat. He joined Royal Dutch Shell in 1990 and has worked for them as a petrophysicist/geologist in Columbia, the U.K., Aus tralia, and Oman. Before working for Shell, he worked for Tenne co Oil from 1981 to 1990 as a geological engineer. He holds a BS degree in geology from Cast Inst. of Technology.

Schutjens

de Ruig

Sayers

van Munster

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SPE Formation Evaluation, June 1996

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Production-Induced Compaction of the Brent Field: An Experimental Approach