Catalog of Well-Test Responses in a Fluvial Reservoir System
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Well-test analysis in fluvial reservoirs remains a challenge because of the depositional environment conducive to significant internal heterogeneity. Analytical models used in conventional analysis are limited to simplified channel geometries and, therefore, fail to capture key parameters such as sand-body dimensions, orientations, and connectivity, which can affect control-fluid flow and pressure behavior. The complete paper aims at a better understanding of the effect of channel content in complex fluvial channel systems on well-test-derivative responses.
Geological Modeling. 3D geological models with a centrally located well were generated and populated with varying fluvial geologies. A 6950-m×6950‑m×300-ft geological model was set up that allowed the averaging effects of the heterogeneities and the reservoir boundaries to be visible on the derivative at late times.
Modeling the geology of a fluvial system is challenging because of changes in channel amplitude, amalgamation, and other processes through geological times, which yield highly variable distribution and shapes of fluvial deposits. Field X was modeled as isolated elliptical sand bodies and channel bodies, with sand-body dimensions of 105 m (width)×420 m (length)×5 ft (thickness) for the base case. The sand and channel bodies are schematically represented in Figs. 1 and 2.
Object-oriented modeling was used instead of stochastic, sequential indicator simulation and Gaussian simulation to retain control over the modeling parameters.
Numerical Simulation. The corresponding pressure and derivative dynamic responses were generated using a proprietary finite-element simulator with a uniform grid and a fine local grid refinement (LGR) around the wellbore. The fluid was black oil at a reservoir pressure greater than the saturation pressure, and the relative permeability to water was low enough to limit water movement within the model.
Results and Discussion of Base-Case Model
A drawdown of 115 years was simulated for a geological model 6950 m×6950 m×300 ft with a cell size of 50 m×50 m×5 ft in the x, y, and z directions, respectively (total cell count without LGR=1,159,260), with a fine Cartesian LGR around the wellbore to reduce numerical artifacts around the wellbore (total cell count with LGR=1,327,200). The model consists of two facies. All simulations were performed without including wellbore dynamics or mechanical skin.
Effect of Channel Content. The channel content was increased from 5 to 100% in 5% increments. Varying the sand content in the geological model affects the connectivity and flow communication within the reservoir. The models generated contained a column of sand around the wellbore to allow all layers to be connected.
The average permeability can be estimated from the value of the derivative of each plateau, with the late-time stabilization corresponding to the final effective permeability of the system. That permeability decreases with channel content, indicating a decrease in mobility away from the well.
An increase in channel content increases the lateral connectivity (and hence pressure communication). The initial radial-flow stabilization is followed by a shallow gradient transition of short duration, followed by a low final stabilization. This indicates a high-mobility reservoir.
A decrease in channel content corresponds to an increase in the duration of the transition zone with the gradient between the two stabilizations increasing to a near unit-slope as channel content approaches 5%. Effective permeability does not decrease to zero as channel content decreases but tends to the lowest permeability value of the system. The time for reaching the boundaries increases with decreasing channel content.
Effect of Horizontal Permeability. The contrast in horizontal permeability between channels and shale is varied. The permeability of the channel sands remains constant at 100 md, with the shale varying from 0 (an infinite permeability contrast) to 10 md. There is a well-established trend of increasing permeability contrast corresponding to an increase in the gradient of the transitional ramp and final stabilization (or decrease in the final effective permeability of the system). With decreasing permeability contrast, the length of transition zone decreases, resulting in the heterogeneities averaging within a shorter time period and the boundaries of the model being detected sooner because of the speed of the pressure-transient wave through the model.
The effect is more prominent where the contrast in permeability is infinite and in low-channel-content systems.
This is because of the connected volume resulting in the boundary of the reservoir being reduced for less than 25% channel content. At early and middle times, the responses are consistent, with only minimal changes reflected in the gradient of the slope. When the permeability contrast is high, the flow experienced is predominantly transitional for the majority of the duration of the test, with a short period of radial flow experienced at later late times. As the permeability contrast between the facies decreases, the period for transitional flow decreases, and a longer period of later-late-time radial flow is experienced.
Effect of Vertical Permeability. Vertical flow communication is known to have a noticeable effect on the pressure-derivative response. The vertical permeability, as a function of the horizontal permeability, of the model is increased from a highly anisotropic case to an isotropic case. The gradient of the ramp increases inversely proportionally to vertical permeability, showing a lower effective permeability corresponding to a lower vertical-permeability contrast. With a low vertical permeability, the flow communication with the well decreases as vertical crossflow between layers decreases, resulting in layers away from the wellbore contributing less to production. The vertical permeability eventually restricts flow, preventing the boundaries of the system from being detected within the drawdown. The effect of vertical permeability is significant, affecting the vertical communication between layers and, therefore, connectivity with the wellbore.
Effect of Channel-Length Ratio. The channel length is a function of channel body width when modeled. Channel length is varied by use of the channel-length ratio, ranging from 4 to 32 times the width of the sand body. This relationship represents the first sensitivity where the geometry of the model is adjusted, with all other properties remaining constant. The size of channel body chosen for modeling is significant to predict because it will have a direct effect on the connectivity of the system.
In channel-content systems of less than 60%, a low channel-length ratio corresponds to the greatest gradient of transition zone at earlier late times between stabilizations, with the later-late-time stabilization developing within the shortest elapsed time. In high channel-length ratios, a shallow slope is witnessed at middle late times before a rapid decrease in mobility (or connectivity) at later late times resulting in a sharp increase in the slope of the transition zone. In low-channel-content systems with low channel-length ratios, the heterogeneities are encountered sooner, resulting in a greater decrease in effective permeability initially before averaging (or stabilizing). However, in high channel-length ratios, the pressure wave travels along the path of least resistance along the length of the channels (north to south) before spreading outward, encountering heterogeneities later, with a corresponding decrease in mobility at later late times. With increasing channel content, the behavior reverses, with an increase in channel-length ratio corresponding to the greatest slope before later-time stabilization.
Effect of Channel Width. In channel widths greater than 105 m, the pressure-derivative response shows two further stabilizations after the initial radial-flow stabilization. The intermediate radial-flow period corresponds to a large sand body being detected. A transition zone follows in which the heterogeneities of the system are detected with effective permeability decreasing until the final stabilization is reached at later late times. This behavior is consistent in low- and high-channel-content systems. The responses of widths less than 200 m do not reflect an intermediate stabilization, showing a significant decrease in effective permeability. Ultimately, a decrease in channel width corresponds to a greater slope of the transition zone and lower final effective permeability, with this behavior consistent through all channel contents. The effect of changing the channel width on final effective permeability decreases with an increase in channel content until the effect becomes negligible.
This paper systematically investigates the well-test-derivative responses of 870 unique geological realizations from a fluvial reservoir for different channel contents, body shapes, body dimensions, and permeability contrasts. All derivatives exhibit two radial-flow stabilizations separated by a monotonically increasing transition. Each radial-flow stabilization yields an average permeability, with the late-time stabilization corresponding to the final effective permeability of the system. Among the main conclusions of the sensitivity study are
- An increase in the horizontal-permeability contrast between channel and nonchannel decreases the final effective permeability, which tends toward the lowest value modeled in the system, in this case the nonchannel. This effect is more sensitive to an increase of channel content when channel content is less than 40%.
- In channel contents greater than 40%, the transition develops a one-half-unit slope when a sealing fault is encountered before the derivative stabilizes at a level that is twice that without a fault. In channel contents lower than 40%, the one-half-unit response is merged into the geological response of the system and, thus, the gradient of the transition is greater than one half. The ability to detect a fault decreases with decreasing channel content.
- In the case of a sealing fault of limited extent, the final radial-flow stabilization is between that for a fault of infinite extent and that for no fault.
Catalog of Well-Test Responses in a Fluvial Reservoir System
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