One of the most crucial decisions in any new oil field development project is to decide how many wells to drill. The optimal number of wells, of course, is a matter of economics. In this blog we are going to look at a quick method, based on analytical exponential theory, to answer that question by maximizing the net present value (NPV). Although the method is simple, it is surprisingly accurate, practical and useful. It has proven to provide excellent starting points in many actual studies and projects. Try it out yourself, retrospectively, on any existing oil field developments - you will likely find the answers remarkably precise. In the video at the bottom of this blog we will present the method in much more detail, and provide a graphical method to estimate the optimal number of wells. Use the chart near the bottom to estimate the optimal number of wells. All you have to do is to calculate two terms, A and B, and read the well count directly from a chart at the point specified by (A,B). Just make sure that if the NPV discount rate, r, is the yearly discount rate, then the flow rates should also be yearly flow rates (i.e. multiply daily flow rates by 365.25). Where: the ultimate volumetric recovery. The ultimate recovery is governed by the drive mechanisms, not by the number of wells. The reservoir is assumed to be connected, not compartmentalized, so a single well could in principle produce the UR. Many wells would not produce more than a single well, just faster.UR = NPV discount rate. It typically ranges from 0.05 to 0.15 and is normally set by management.r =the plateau rate.qp = the price of one volume unit (stb or Sm³) oil.Oilprice = the cost of drilling and completing one well.Costwell = The annual operating costs of one well.Opexwell = To find the optimal number of wells, calculate A and B from the formulas above (also shown in the axis titles on the chart itself). Mark the point (A, B) in the chart below and identify the number of wells by selecting the representative colored curve. Alternatively, you can find the exact number of wells by iteration, as explained in the text-box in the chart itself.The following video explains the method in greater detail. Enjoy! You can find this video and many more at our YouTube channel.
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To emulate a fractured well in ExcSim, follow these simple steps: - Make sure that the well block is square with X- and Y-dimensions equal to the length of the fracture from tip to tip. I.e dX=2xf and dY=2xf, where xf is the fracture half-length.
- If the fracture is oriented in the X-direction, enter a transmissibility multiplier of 1.5339025 in the well block cell in the X-transmissibility map on the "Grid" worksheet, just below the porosity map. Also add the same transmissibility multiplier in the grid block to the left of the well block.
- If the fracture is oriented in the X-direction, enter a transmissibility multiplier of 0.98666142 in the well block cell in the Y-transmissibility map on the "Grid" worksheet, just below the X-transmissibility map. Add the same transmissibility multiplier in the grid block above the well block.
- If the fracture is oriented in the Y-direction, just switch the two factors.
- Give the well a (negative) skin value of s = - ln(0.407646 xf/rw)
The skin value given in point 5. corresponds to an infinite conductivity fracture. Use a slightly higher skin (less negative) to account for any finite conductivity. Note, however, that very small increases in the skin factor may have significant impacts. A typical skin adjustment, to account for finite conductivity, would be in the +0.01 to +0.1 range. A 2012 study, evaluating several GOM reservoirs, comparing various methods for modeling fractured wells (including use of skin factor, local grid refinement (LGR), and ExcSim's method), concluded that: "Following [ExcSim's] method for infinite conductive fractures, we simulated the fractured vertical well for hydraulic fracture lengths of 75 ft and 200 ft and compared the results with the LGR method as shown in Figure 18 and Figure 19 respectively. They confirm that this up-scaling method provides an accurate estimate when the hydraulic fracture conductivity was 20000 md-ft. In Figure 20 it is shown how a realistic conductive fracture can be modeled by [ExcSim's] method by introducing a small skin factor." It should be noted that to use this method on other simulators (other than ExcSim), the transmissibility multipliers given above must be multiplied by 1.47467 and the pressure equivalent radius, ro, must be set to 0.346 DX (where DX is the sides of the square grid blocks). See our blog on Peaceman for further details. Reservoir simulators estimate fluid flow from grid block to grid block until the flow reaches a well somewhere in the simulation model. Inter grid block flow is approximated using Darcy's law, with one noticeable exception: Fluid flow from well blocks to wells within those grid blocks introduces some additional difficulties. Peaceman (1978) noted that "in numerical reservoir simulation, the pressure calculated for a well block is the same as the flowing pressure at an equivalent radius, ro. For a square grid, ro = 0.2 ∆x." The problem is that the equivalent radius should demonstrably be much greater than that. In fact:where ∆x is the length of the sides of the square grid block. The video above shows that Peaceman's correction does not solve the problem noted by Peaceman, it only glosses over it. And in doing so, it introduces the distinct error stated above. Failing to solve the problem correctly may cause significant errors in the calculated fluid saturations and viscosities in the well block.Consequently, ExcSim does not use the Peaceman well correction at all. Instead, ExcSim attacks the cause of the problem and solves it by means of transmissibility corrections. See the video for details. For square grid blocks the equivalent well block radius is given by Fig2, and the transmissibility multiplier is: If the grid blocks are rectangular of size (A x B), then the transmissibility multiplier is a function of the ratio between the grid block sides, C=B/A. The formula below gives the transmissibility multiplier for the colored edges of the well block. The transmissibility multiplier for the other edges is found by inverting C, C’=1/C. The equivalent well block radius for rectangular well blocks is given by Fig. 6 below The following video shows how easy it is to make a cross sectional model in ExcSim. The flexibility and power of Excel opens an infinity of possibilities for creative and innovative users. One of the more powerfull features is the possibility of using macros, ideal for automating repetitive tasks. This video demonstrates and shows a simple macro for running uncertainty analyses. The macro works with both the and StandardPersonal of ExcSim and can be downloaded for free from here. Use it as an inspiration for your own taylor-made macros and uncertainty studies.Editions There is practically no limit to what you can do within the Excel framework. ExcSim is living proof of that! Kick back and enjoy the movie! We will demonstrate how to generate a structure map for your ExcSim simulations. Linear RegressionYou trace the depth contours on an imported image of your reservoir and ExcSim does the rest. ExcSim will create a polynomial best fit surface that closely matches the contours of your map. Check out this video: The Contouring worksheet lets you generate numerical maps for input to the simulation model. The numerical maps will be 2-dimensional 35x35 matrices matched to contours traced by the mouse cursor.
The procedure for generating a map is as follows: - Open the “Contouring” worksheet.
- Delete all pictures, drawings and shapes from previous sessions, if any.
- Paste a picture or drawing with contours of the map to be traced anywhere in the worksheet.
- Select Excel’s Rectangle Tool from the Shapes palette and draw a rectangle on top of the contoured picture, representing the extent of the desired ExcSim map.
- Remove the Rectangle’s color filling so the whole image becomes visible.
- Select the rectangle by clicking on it. Its default name appears in the box to the left of the formula bar.
- Change the name to ‘Model’.
- Do
*not*rotate the rectangle. If you want the simulation model to be rotated relative to the map image, you must rotate the map image instead.
- Specify the model dimensions in the green cells under the ‘Model size’ heading.
- Select Excel’s ‘Free form’ drawing tool from the Shapes palette and trace one contour at a time on the picture.
- Only the points of the free form shape matter. The lines connecting the points are irrelevant.
- Make sure that the contours do not cross the upper or left edges of the 'Model' rectangle. Failing to do so will result in an error.
- Remove the internal filling color so you can see behind it. Name the first contour “Cont1”. Subsequent contours should be named “Cont2”, “Cont3”, etc.
- Write their contour levels in the Contour Levels list , in column "B" next to their names. Extend the list with more names and contour levels as required.
- Depending on the number of crests and troughs (ups and downs) in the picture, select suitable numbers of degrees for the polynomial best-fit, in the Best Fit table.
- Check that all ‘Free form’ contours have been given correct names and numeric contour levels, and that the outlining ‘Rectangle’ (named ‘Model’) has correct dimensions.
- Press the ‘Generate Map’ ribbon button.
- When the map has been generated, copy it and paste it in its correct location in the ‘Grid’ worksheet.
Have you ever wondered which recovery method to apply in any given case? The obvious approach is first to understand how effective the various drive mechanisms are. ExcSim does that for you. ExcSim automatically gives you both the daily and cumulative effectiveness of the drive mechanisms, as shown below.Furthermore, ExcSim gives you detailed and summarized drive mechanism contributions in tabulated numeric format, as shown below:Next, you need to identify exactly where any remaining oil is located. ExcSim does that for you, too. One quick glance at the before and after images below and you'll know the answer to that question!ExcSim even lets you play the recovery process forwards and backwards like a movie. Thirdly, ask yourself whether you can improve the sweep by optimizing your well locations? ExcSim comes with an Excel macro (as a bonus example) that does just that, too!!!A growing list of very useful macros can be downloaded for free. You can download and edit the macros (or write your own macro from scratch) to achieve whatever you heart desires.
ExcSim is the for professional reservoir engineers - every time!first choice |
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