The Missing and Wrong Physics In The So-Called "Full Physics" Model

First this paragraph from George Box on "All models are wrong", "Since all models are wrong the scientist cannot obtain a "correct" one by excessive elaboration. On the contrary following William of Occam he should seek an economical description of natural phenomena. Just as the ability to devise simple but evocative models is the signature of the great scientist so overelaboration and overparameterization is often the mark of mediocrity".

That does not prevent some scientists try to include every thing they believe they understand, then promote their models as "full physics", not knowing many things in nature are not well-understood, or understood at all. Not knowing what is importantly wrong, they selectively worry about minor things that has no implication to the problem at hand. 

Are their models "full physics"? No, far from it. Basin modeling aims to model the physical/chemical/geological processes in hopes of better understanding these processes. However, we don't yet fully understand many of the processes, some important processes are obviously not accounted for in some basin models. Below I list some important physics that either are missing from current basin models, or are not correctly implemented. Hope this servers a reminder when you hear "full physics" marketing ploy again next time.

Migration modeling: Some Darcy flow migration models lack some well-known physics between saturation and capillary pressure, and as a result, oil accumulations occur in places without a trap (!!), or accumulations with unrealistic saturation distribution - Have you ever seen a 2km vertical HC water contact (??).  Also note the total column of the trap is 3 km!! Has anyone ever seen it exist in nature?

Figure 1. Darcy migration model without proper physics between fluids and rock. Saturation distribution is very unrealistic, and geologically impossible.  

Wrong rifting heat flow: Some so called full physics models still have the wrong idea about rifting and heat flow. Below is a heat flow model (red curve) of an area with a beta factor of 2. Notice the heat flow started at 32 mW/m2 (which is a unrealistically too low for any continent, especially where this basin is - Australia which has one of the hottest crust!), and at the end of rifting it doubled, and then over the next 100 million years it cooled off to 36 mW/m2. What's wrong you may ask? It is wrong because the model does not account for the fact that crust produces more than half of the heat - so attenuation of the crust by rifting will cause loss of heat production. Because of that, the heat flow at present day should be lower than before rifting!  But this model shows the opposite! 

Figure 2. Rift heat flow history from a certain "full physics" model that does not account for the loss of radiogenic heat production (RHP) by crust attenuation from rifting. 

Compaction: The compaction model is an essential part of modeling burial history and over-pressuring.  Current models assume a unique porosity-effective stress relationship that was first developed from soil mechanics. This is not appropriate as over geological time rocks are not elastic and continue to creep/lose porosity under the same load (effective stress), as evidenced by much lower porosity in older rocks, compaction curves correlate with formation age, etc. The immediate effect of not accounting for the effect of geological time is that it is very hard to maintain overpressure once loading stops, or with uplift and erosion. Almost all the unconventional plays have experienced uplift and still maintain significant overpressure.  

HC expulsion fractionation: Some researchers attempt to use the composition of fluid generated by lab pyrolysis for the initial composition of fluid expelled from the source rock in basin models. This ignores the observation that fluids found in source rock extracts are VERY different from fluids produced from accumulations - many things are happening between generation and accumulation that are not accounted for in basin models. It is pretty obvious that heavier HC molecules are preferentially retained by source rock (perhaps due to preferential adsorption), so the expelled fluids are much lighter, and higher GOR. A good reference on this is this study by Sonnenfeld and Canter, 2016   Many of us recognize the problem, but we don't have the physics worked out.  

Migration fractionation: At the typical depth petroleum fluid is generated, oil and/or gas are single phase. As migration of the fluid upward reaches bubble or dew point pressure, it separates into a vapor (gas) and liquid phase (oil). The two fluids now have very different composition - light liquid goes with the vapor phase, and the remaining liquid becomes lower GOR and lower gravity. In an oil dominated system - we find heavier, low GOR oil (than what was generated) in shallower reservoirs because of this. They are not what the source rock had generated. Same happens to gas systems. Migrating gas loses heaviest liquid first, so the remaining condensate gets lighter as the gas gets drier (higher GOR). See this post on observations. Loss of polar components along migration path due to adsorption on minerals has not been accounted for in models. 

Even during early single phase migration, the effects of composition grading ( observed compositional gradient in accumulations) especially in near critical conditions, in a fill-spill trap is that the spilled fluid is lower GOR and lower gravity, that the total fluid in the trap.   

This is not accounted for in basin models and it is not a good idea to think that basin models can predict fluid properties without accounting for this (thermodynamic) process. 

Using Heat flow as boundary condition: Many modelers use heat flow as the boundary condition at the base of sediment for modeling the temperature history.  This method ignores the effect of growing the sediment column has on heat flow itself. Adding sediment column moves the surface further away from the LAB (1300 °C). It lowers mantle heat flow by increasing dz in the equation Q = K*dT/dz. It also ignores the transient effect as the entire lithosphere now requires new equilibrium.

Figure 2. The effect of adding 1 km of sediment to the lithosphere column.  The red arrows show temperature increase required for new equilibrium. It is often mentioned that the new sediments need to warm up. But we cannot ignore that the rest of the lithosphere (~100 times the rock volume of the new sediments) also needs to warm up, on average 15°C, for every 1000 m of new sediment. And that is going to take a much longer time. And you can see that the new profile is a lower thermal gradient and thus lower heat flow.

Full lithosphere models show that rapid burial can reduce heat flow by 30% in some cases, depending on burial rate. This is physics that can be modeled correctly, but not if we assume some "basal heat flow" through time independent of the physics. To  account for this physics, a proper thermal model should use a boundary condition at the base of lithosphere. 

Relationships: Many of the functions, relationships used in basin models are empirical - which is not physics. A simple example is the permeability-porosity relationship below. There is no direct relationship between the two physically. Permeability varies by several orders of magnitude at the same porosity - even for the same rock type, same formation etc. Empirical models can be useful in many ways, but the uncertainty cannot be ignored - but basin models  often use these relationship to model fluid flow, pressure prediction and HC migration without addressing the huge uncertainty.

Relationship between porosity and permeability for porous rocks- modified from Ma and Morrow, 1996, 

Upscaling: Due to limited computation power, cellular basin models use grid cells on the order of 10s to 100s of meters in thickness. If we take a look at 100 m worth of well-log, or outcrop, how often it is entirely homogeneous ?  I think you can imagine petroleum migration thorough a homogeneous rock volume is entirely different from some sand-shale interbeds. I have not seen any published attempt at upscaling Sw-Pc curves of interbedded different rock types.  

We simply don't' have enough data for migration modeling. A parallel problem  is that seismic does not have the resolution for mapping the plumbing system to which the physics apply, for us to upscale from, not even close. We don't actually know the number of interbeds and their lateral distribution from the standard seismic interpretation - let alone all the properties of these rocks, such as the different Sw-Pc curves for each type.  Well that is even if you model actually implemented a Sw-Pc relationship in the first place.  If you are interested in this topic, you may want to look up the concepts of the Leverett-J function and FZI and HFU.       

Biogenic gas: The formation of biogenic gas is not well understood - especially when it comes to quantifying the volume. That does not stop vendors from making up a model for you (and charge you a lot of money for it). The current model assumes that the process of biogenic gas generation consumes part of kerogen - and asks you to input some equivalent TOC and a convertible fraction that is the source for biogenic gas. Well - that is not physics - the volume you are getting from these models are based on assumptions, so it is no different than you are assuming you know how much gas is generated per volume of rock - it is not based on any real science!    

Assumptions, assumptions:  Many assumptions are made in the traditional basin modeling, often an assumption is made just because we don't know it well not because it is insignificant. Yet we will forget that assumption when we discuss the result of the model. I will add some examples later. 

Conclusion: Don't be fooled by a fancy colorful 3D model, its usually not very useful. We actually don't need a full physics mode, we need something simple but when applied can answer important questions in exploration quickly. 

Are Faults Necessary Migration Conduits? A Simple Migration Model Says No.

We often observe petroleum accumulations in association with faults, especially in deltaic systems (Gulf coast, Niger delta, Mahakam delta, Nile delta ... and rift systems (Most basins in South East Asia, North Sea ...). Often in the literature the assumption is made that the faults act as path ways for migration up such systems. Here I make a simple argument that migration via faults is not necessary, or even possible in order to explain the distribution.  

This cross section is from the Hindel field, in Mahakam delta, Indonesia. Some obviously active faults cut through the large number of stacked oil and gas reservoirs.  This is very typical of deltaic systems. Question is, did the oil and gas migrate up the faults to charge these reservoirs?

 

Figure 1. Cross section through Handil Field, Mahakam delta, Indonesia, Antony Reynolds, 2016. There are some 500 stacked reservoirs vertically.

I have made a very simple model of the geology in Trinity (our popular 3D migration modeling software). There are only two (yes only 2) variables in this model. Capillary displacement pressure, Pd, and buoyancy. The faults are assumed to have a higher Pd than the shales, meaning NO migration along or across the faults. Oil is injected from below the field where the source is at. As the column of each accumulation grows and exceeds the capillary displacement pressure of the shale above, migration continues through the shale and into the next reservoir. It is amazing that such a simple model can explain the distribution of petroleum pools so well. So the first obvious conclusion is that the faults are NOT necessary to act as conduits for the filling of the reservoirs. In fact, if we allow migration along the faults, we could not form the accumulations.    

Figure 2. Simple capillary model to explain the accumulations in stacked reservoirs in a deltaic system. The faults are sealing.

With the high net to gross in this field, it is very conceivable that juxtaposition of sand on sand may allow migration across the faults. Below I made some of the sand-on-sand locations low capillary pressure so migration across faults is allowed. The patterns are a bit more complex and the main difference is that the shallow reservoirs between the faults are charged in such a case, compared to figure 1. 

Figure 3. Same as figure 2, except migration is allowed through some of the sand-on-sand juxtapositions. This is by lowering the capillary pressure of the faults at the juxtaposition locations. 

The second one is more reasonable compared to the actual field. Also keep in mind this is only a 2D model. Vertical migration may happen in different locations, and lateral migration along structure strike is also possible.  

An important observation I have made of similar fields in many basins that the sands in between large faults in these compressional flower structure are less frequently charged. I interpret this as indicating although cross fault migration is possible, but less frequent.  The faults are acting as barriers and thus creating migration shallows for vertical migration.  

I have paid attention to these observations to get a better understanding on migration. And I have always been able to explain them with a simple capillary model like this. This applies to stacked reservoirs in 3 ways against salt as well. 

A lot of papers mention faults are migration conduits, without further elaboration. In discussions I have had with colleagues and friends, I find that more than 50 of us would invoke faults as migration conduits. Some go as far as to believe no charge of shallow reservoirs is possible without faults. But when asked how can the oil come up the faults and fill a reservoir, but not leak up the fault the same way it came (both sealing and leaking). The answer is usually more strenuous and unconvincing, and usually involves some exotic episodic behavior. 

I think the main reasons geologists like to invoke faults for migration are 1) accumulations are often associated with faults, and 2) there have been a misconception that shales are "impermeable". The association argument works both ways, and the opposite is that faults act as seals so 3 way traps can be traps. The permeability is never zero for a shale, they are often quite permeable, and low-permeability is not the reason that oil is trapped below a shale, it is the entry pressure that is holding the column. Entry pressure is a finite pressure and can only hold a finite column. Additional oil will simply leak through.   

Since the simple assumption that faults are seals (vertically and laterally) can explain the distribution of accumulations beautifully, I suggest we stick to an Occam's Razor model.

I am not ignorant of anecdotal evidence for oil migrating though faults, most obviously the seeps along faults at surface, bitumen filled faults, among others. But for forming large accumulations that we observe we should assume faults, in most cases are sealing. If we look at accumulations in basins across the global, we can hardly find any fields that don't have faults across the structure - if faults are leaking, and not leaking, we would have no predictive power. Some of these have been there for many millions of years.

There, I said it. 

Migration and Trap Filling Models

This post compiles some of the images from my recent posts on LinkedIn, to show the important role capillary pressure plays in petroleum migration and trap filling. These models assume that migration rate is extremely slow, limited by supply rates from the source rock, and thus migration is always in equilibrium with the capillary pressure field of the geological system - the dynamic effects of viscosity (thus Darcy flow rates) can be safely ignored. In fact we have never observed any distribution patterns of petroleum pools that can not be explained by capillary pressure alone. All accumulations are constrained by a capillary system, except occasionally hydrodynamics and gravity (tar sands) play a role in part of the accumulation. The variation of pore throat sizes laterally due to facies change, and vertically due to different lithologies is the greatest force that controls the migration process and the distribution of petroleum pools - at all scales microscopic to 100 km+ scales, and tight reservoirs to the traditional traps.    

These models use very simple geological models to demonstrate the useful physical principles, and real world geology is much more heterogenous and variable - we need to have in mind what we see in cores, on logs, and in outcrops when we make models. Models are useful because they help us understand the physics, and interpret observations, and make predictions, with the difference between nature and model in mind.  

Figure 1. Capillary displacement pressure, and Sw-Pc (Sw-Height) curves are fundamentally what control the trap filling process, and the resulting saturation profiles, and the variable oil water contacts. 

Figure 2. The saturation distribution in the model above. Saturation is a function of both height above FWL (ie. capillary pressure (Po-Pw), and the rock type. The low saturation occurs in tight rocks thus volume is reduced by both porosity and saturation.  

Figure 3. An idealized model to show OWC can be tilted if a systematic change in pore size exist across the entire field. Observation of a tilted, or variable OWC is not always due to hydrodynamics. When studying tilted OWCs, we should investigate not only the pressure gradient, but also capillary data, which can be inferred from porosity/permeability data. The Tin Fouye Tabankort (TFT) field in Algeria may be such an example.

Figure 4. A model demonstrating the mechanism of stratigraphic traps after Tim Schowalter 1979. Note that capillary seals are relative - a trap is formed when a tighter rock is above or up dip of a less tight rock. So reservoir rock of one accumulation can be the seal for another accumulation. In nature these changes are more subtle and hard to draw the boundaries. The main observation of these mechanisms are the correlation between saturation and rock quality.  

Figure 5. The purpose of this model is to demonstrate the effect of storage along migration pathway on the distance of migration for a given volume generated by the source rock. The poor reservoir (silty, or shalely) stores less along the carrier, and the result is that same volume of supply will travel further in the same time that volume is generated compared to a better quality carrier bed - everything else being equal. Effective carrier beds do not have to be very good quality.  

Now a couple of real examples:

Figure 6. The Parshall field on the eastern side of the Williston basin. The middle Bakken reservoir gradually thins to the east with lower porosity and permeability. The field does not reach the actual pinch out of the middle Bakken. This model shows that the gradual change of the middle Bakken facies is responsible for the trap, rather than the pinch out. This is probably true with many of the subtle accumulations elsewhere in the Middle Bakken, and in other unconventional plays. The traps are subtle!

Figure 7. The Kraka field in the Danish North Sea has a tilted FWL. This is a quick model to show how it works based on data from this paper.

Please feel free to use these images in your research or teaching. You may reference the petroleum system blog, by Zhiyong He, founder of  ZetaWare Inc. 

Key references:

T. T. Schowalter, 1979, Mechanics of Secondary Hydrocarbon Migration and Entrapment; AAPG Bulletin vol. 63 (5): 723–760.

T. T. Schowalter and P. Hess, 1982, Interpretation of Subsurface Hydrocarbon Shows;

AAPG Bulletin, V66, No.9, pp. 1302-1327

P. Frykman et al., The history of hydrocarbon filling of Danish chalk fields, Geological Society London Petroleum Geology Conference series · January 2004

What Is Migration Lag & Why Timing of Generation Is Not Important

 As a source rock begins to generate oil and gas, the generated HC fluid cannot just leave the source right away, it will first need to saturate the kerogen's adsorption capacity, which depends on the total organic carbon (TOC). The volume retained by adsorption can be a significant of the generative potential - 20% for a good source rock, and 50% or more for a poor one. This can be estimated by the extract of petroleum/bitumen in the source rock. After that, additional volume generated may be trapped within the pore systems (especially if the source is heterogeneous - with interbeds of  shales, limestone, marls, and silty interbeds) of the source rock as we see in shales that we produce from, and this can be very significant, also on the order of up to 50% of the generative potential of the source. There is no secondary migration up to the time until the saturation induced capillary pressure is high enough to allow primary migration out of the source rock. 

Secondary migration first occurs in "first carrier beds", which are layers of more porous beds directly above, or below, or interbedded with the source. In the carrier beds, it forms accumulations in structure (3, 4 ways) and stratigraphic traps, large and small (down to pore scales), that need to be filled before migration continues, either leaking up wards, or spilling out side of the mature kitchen. Since this happens near the source rock, the lateral extent is as large as the kitchen/fetch area. This consumes a large volume, up to 100% of the generated volumes, and the time it took to generate this additional volume. 

There can be additional carrier beds, and large and small traps that need to be filled before HC fluids finally reach our target trap. All of these cause the delay of charging the traps we want to drill. This delay/lag is a function of the volume of all of these traps (also called hotels, motels) between the source rock and the target trap. This lag explains in many basins where oil is found in traps that formed up to 10s of millions of years after oil generation occurred, such as the oil fields in the West of Shetlands basin:

Typical burial history of of the kitchen area for the Faroe-Shetlands basin. Despite oil generation from the Jurassic source rock (green start) occurring mainly in Cretaceous time, the lower Tertiary reservoirs (yellow start) are filled with low GOR black oils (eg. the Foinaven and Schiehallion fields). This was explained as migration delayed by first "moteling" in deeper traps, Scotchman et all 2006.  

HC migration does not stop when the source rock is exhausted as we might expect. This is because the volume of HC fluids trapped in these deeper traps (hotels) continue to mature - cracking from larger molecules to smaller ones, and gas oil ratios (GOR) continue to increase. This volume increase can be larger the the volume generated by the source rock. Continued compaction, diagenesis also reduce the size of these hoteling traps, and cause additional migration. This is why we are seeing very young traps being filled very recently, long after the source rock is spent. 

Schematic explanation of migration lag. Note that the present day condition of a basin/area could be at one of these stages. The target shallow trap has not been charged yet if the system is at stage 2 at present day, although the source rock is mature.  It should be obvious that the hoteling traps directly above the source should be the main targets in all stages.

Some times, or should I say very often,  the hoteling traps are so numerous, or large that generated volume is entirely consumed by them, and the traps above them we are targeting don't get charge at all. One very useful observation, globally, is that exploration targeting the hoteling traps (first carrier beds) are very successful - in fact - 80% of more of the world's petroleum reserves are found in these (Lower Cretaceous reservoirs of western Siberia, Jurassic/Cretaceous reservoirs in the Middle east, Middle Jurassic in the North Sea below the source rock, Wilcox play in deep water GoM ... ..., ). Success rate exponentially decreases for traps further up stratigraphy. 

Unconventional plays are essentially the hotels that we are now and producing from. East Texas field, Giddings Field are conventional reservoirs and the oil was generated and migrated from the Eagle Ford. The Eagle Ford retained about 15 mmbls/km2 of oil, which would have to be filled first before migration toward the conventional fields happened.  The Woodford, Meramec would have to be filled before oil could migrate northward to North Oklahoma and Kansas. 

Note that the original notion of hoteling/moteling may imply that some tectonic movement is necessary for the hotels to spill at a later time. This can happen of course, but more generically it is not necessary. Generation and cracking to lighter fluids is continuous, and volume expansion of HC trapped near the source is continuous, once a hoteling trap is filled, it will continue to leak/spill, porosity loss in the hoteling traps continues, all as long as the burial continues. In rift basins like the FSB, the thermal subsidence and the associated tilting toward the basin center, therefore spilling up-dip, is continuous too. 

More generally speaking, every trap is a hotel, while being filled, it causes a migration lag for the next trap in the chain of spilling or leaking. We can only drill and produce economically a limited number traps in a basin. The deeper, non-economical ones are then referred to as hotels, or migration losses. But they are all over the kitchen area and contain much more volumes. In some shallower basins we are drilling and producing from traps near the source and the source rock itself (unconventional). The Eagle Ford contains more oil and gas that ever been found in conventional traps sourced from it. Back in time, these conventional traps up dip had to wait until Eagle Ford itself was filled. The distribution of HC volumes in a basin is a pyramid stratigraphically speaking. The base is the source rock, and the bottom 1000 meters typically contains more than half the volume, and often > 90%.     

Further reading:

Scotchman, I; A. D. Carr and J. Parnell, 2006; Hydrocarbon generation modelling in a multiple rifted and volcanic basin: a case study in the Foinaven Sub-basin, Faroe–Shetland Basin, UK Atlantic margin 

Levell B., and M. Thompson: Atlantic margin: Faeroe-Shetland Introduction and review  

https://www.researchgate.net/publication/351516104_Migration_Loss_Lag_and_Fractionation_Implications_for_Fluid_Properties_and_Charge_Risk

https://www.searchanddiscovery.com/pdfz/documents/2017/42014he/ndx_he.pdf.html