Pore Pressure and Methods of Analysis Section 4 PPFG Modeling Process Part 4 The Normal Compaction Trend
Part 4.???The Normal Compaction Trend
Section 1. Applying the Definition of Normal Compaction Trend
???????????????“Normal pressure” is hydrostatic pressure.
???????????????The normal compaction trend is the trend of a property of clastic sediments (resistivity, sonic travel time, density, etc.) undergoing compaction due to increased burial through the hydrostatically pressured region of the depositional sequence. To properly create a normal compaction trend, it must be created to equal the measurements of a physical property through the normally pressured interval, then extended beyond the depth where the measured physical property begins to deviate from the normal compaction trend. Within a single depositional sequence, this deviation from the normal compaction trend is assumed to represent a change in the porosity decline rate, and is associated with a change of pore pressure gradient.
???????????????All compaction models are based on the principle that, if the pressure remains hydrostatic, there will be a corresponding porosity decline trend with increased depth of burial. Because the overburden stress is shared between the pore pressure of the fluid in the pore spaces of the rock and the grain-to-grain effective stress where the rock grains are in contact with each other, a change in pore pressure gradient will cause a corresponding change in the ability of the overburden stress to compact the sediments. Thus, the porosity decline rate with depth will deviate from the porosity decline rate that would exist if the pore pressure remained hydrostatic.
???????????????A common characteristic of the most commonly used equivalent depth method models is they are based on a logarithmic relationship with depth. Therefore, the normal compaction trend is not linear. On a lin-log graph, the normal compaction trend may appear as a straight line, as with the Eaton relationship. With the Bowers relationship, the normal compaction trend does not appear as a straight line on a lin-log graph. A mistake I have occasionally seen is graphically plotting a normal compaction trend as a straight line on a linear graph. This does not allow a valid graphical solution, and the linear graph does not allow an accurate perspective of the relationship between the porosity decline trend and the normal compaction trend. Often it is useful to visually examine a graph and mentally approximate the change of pore pressure gradient. Plotting a normal compaction trend on a linear graph does not allow this.
Figure 35.???????????Plotting the Normal Compaction Trend on a Linear Graph
???????????????On the linear graph, the graphical representation causes the appearance that the normal compaction trend was established in accordance with the definition of normal compaction trend, being plotted through the data in the normally pressured interval to a depth of approximately 17,500 feet, then extended beyond that depth. When the same normal compaction trend is viewed on a lin=log graph, it becomes obvious the normal compaction trend plotted on the linear graph violates the definition of normal compaction trend, and its values are not equal to the values of the data set in the normally pressured interval.
???????????????Logarithmic relationships should be displayed on a logarithmic graph (Lin-Log.)
???????????????The Normal Compaction Trend establishes the relationship between compaction due to increased burial and the pore pressure gradient. For active deposition, the shallowest clay sediments are suspended, and the effective stress is zero. As compaction progresses from the surface or mud line with depth, particles become closer and the porosity decreases. However, the pore pressure gradient will remain hydrostatic until the porosity is reduced sufficiently for the clay particles to become close enough to obstruct the generally upward movement of the water being squeezed out of the decreasing porosity below.
???????????????As the porosity decreases, the resistivity will steadily increase and the sonic travel time will steadily decrease. The trend of the resistivity and sonic values in this hydrostatic pressured zone defines the normal compaction trend. Resistivity and sonic values deviating from the normal compaction trend indicate a change in pore pressure gradient. When resistivity or sonic data are not available through the hydrostatic pressured zone, the normal compaction trend must be established to match existing information and data, assuming that trend extended to the surface or mud line is representative of normal pressure.
???????????????The most common models used to analyze pore pressure are the Eaton resistivity and sonic models and the Bowers sonic model. The Eaton and Bowers models are logarithmic mathematic relationships.
With the Eaton model, the normal compaction trend establishes the normal pressure trend, and the exponent determines the change in pore pressure associated with the difference between the normal compaction trend and the measured resistivity or sonic value.
The Bowers model is a mathematical curve fitting model. The parameters are adjusted for the best fit between measured sonic values and drilling information.
The parameters established for the Eaton and Bowers sonic models should be similar to the Eaton and Bowers interval velocity models at the same location.
???????????????After the normal compaction trend is established, the pore pressure can be calculated based on the data from either logs or seismic surveys.
Section 2.???????????????????????????The Eaton Models
???????????????The Eaton models were invented using data from the depositional basin of the northern Gulf of Mexico. The default exponents were derived from wells drilled in this basin. The analyst must assess the adequacy of the Eaton exponent for use in the basin within which they are working.
The default exponent for the sonic model is 3.0.
The default exponent for the resistivity model is 1.2.
Eaton pore pressure models associate a change in the trend of water-filled porosity as depth increases with a change in pore pressure gradient. For a given change in resistivity or sonic travel time, increasing the exponent will increase the change of calculated pore pressure gradient.
???????????????The Eaton resistivity and sonic equations are similar. However, the default exponents for each model is significantly different.
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Resistivity equation:
Sonic equation:
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The Eaton sonic function is used to explain why the default exponents for the sonic and resistivity models are different:
The Eaton sonic function:
where OBG, PPn, Δtmeasured , ΔtNCT are independent variables with respect to the Eaton exponent y, and y is an independent variable with respect to depth.
An increase in pore pressure with depth is:
The exponent controls the change in calculated pressure for a given change of the independent variables.
??? Conductivity unit of measurement is microsiemens/cm. (1,000 μs/cm=1mmho.) Water at 25,000 ppm will have a conductivity of approximately 40 mmho. Rock matrix conductivity is about 100μS/cm, which is 0.1 mmho. The ratio of conductivity of formation water to rock matrix is approximately 400. The sonic travel time for water is approximately 200 μs/ft. The sonic travel time for a rock matrix is 50 to 60 μs/ft. The ratio of Δtwater to Δtmatrix is 3.3 to 4. Therefore, because the ratio of conductivity of formation water to rock matrix is significantly greater than the ratio of sonic travel time of water to rock matrix, the default exponent for a resistivity model is significantly less than the default exponent for the sonic model.
Comparing the Eaton sonic equation to the Eaton resistivity equation, parameters (Rsh / Rnctl) and (?tnct /?tsh ) are similar, but not identically. The denominator for the resistivity equation is the normal compaction trend value in the resistivity equation, while the denominator for the sonic travel time equation is the log data set value. This is due to the relationship of resistivity being the reciprocal of conductivity, and sonic travel time being the reciprocal of acoustic velocity. If the resistivity formula used conductivity instead of resistivity, or the sonic travel time formula used acoustic velocity instead of sonic travel time, the relationship between the normal compaction trend and the data set values would not be reversed.
Figure 36.???????????Eaton Resistivity Model
Figure 37.???????????Eaton Sonic Model
Analyst / Prospect Generator at Geopressure Analysis Services
3 年?Part 1: ??Here is my humble opinion about the comments between Chris and Santhosh. They are completely explaining different subjects.? ?????Chris, is explaining the method of establish the so called NCT. Usually Pore Pressure Prediction is reasonably competent in young clastic sediments ( Recent to Cretaceous) using the Compaction Disequilibrium – Effective Stress theorem. This trend represents the petrophysical (v, R, density ..) drift with increasing the OB and expulsion of formation water/fluid. Therefore, Porosity/permeability, fluid and stress are needed for this process. Shale / Clay minerals transformation and ability of absorb and expel fluids play an essential part during compaction. Therefore, Compaction Trend should be correctly following the shale trend. (see part 2)
Analyst / Prospect Generator at Geopressure Analysis Services
3 年Part 2: On the other hand, Santhosh trying to apply this theorem on the > 300 million years Permian Hard rocks. The process of taking dry cores and applying stress tests for hydraulic fracture applications is not relevant to Pore Pressure.?The Diagnostic Fracture Injection Testing (DFIT) measures the impact of opening micro-factures on improving the flow of the residual HC/ fluid and not produced from the virgin porosity.?Pores are silicified and fluid has been drained through time and multiple tectonic events. I can go on and on .. Therefore, compaction trend to predict Non-Existing Pore Pressure due compaction is Not Viable in old unconventional resources. The Minor – Miniscule Pressure we detect sometimes in the Permian is related to Residual HC and is not related to stressed fluid in pores, that is why we Frack It !!! Hope this is helpful to distinguish the difference.???
Co-Founder and Principal Specialist at Pangea Geoscience
3 年Now, to my understanding, compaction velocity which is a nothing but a burial velocity, where the rock is fully compacted. Per that definition I took the dotted black line where the rock is fully compacted as "compaction velocity (Vp_NCT)" - before plastic and failure. So the ratio between dotted black line (Vp_NCT) to blue square (Vp) was different for different horizon and different facies. By compiling such data for different mineralogy I was able to build a correlation between Vp_NCT to Vp to use it in the Eaton or any other standard model. Tested this approach on several unconventional basins and validated using DFITs, DST and via history matching production. Any thoughts about this approach? Image is attached.
Co-Founder and Principal Specialist at Pangea Geoscience
3 年Hi Chris, This is an interesting conversation. I have always wondered what is this exponential/linear/power trend lines mean to the compaction behavior mean in the pressure estimation. I am happy to learn if there is there a real meaning or definition to it? Some of compaction models I have developed are using in-situ triaxial core velocity data. We measured compressional and shear velocities on each sample for every 500 to 1,000 psi overburden stress. Each rock compacted different depending on the mineralogy of the system by itself. Velocities from initial in-situ hydrostatic stress condition where S1'=S2'=S3' are used for sonic calibration (Vp)- blue square in the velocity plot (rather using linear portion of the testing).
Geology head / Senior Operations geologist / senior Wellsite Geologist
3 年Thank you Chris to share your knowlege with others ????